From 6e780361c5f78c0139d6970f0b0a39a4cafa99cc Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 8 Nov 2026 19:04:38 -0600 Subject: [PATCH 1/4] Conditional kappa 0.00351406: one native word serves two root chains Co-Authored-By: Claude Opus 5.5 --- research/p104-two-chain-shared-native/LICENSE | 201 + research/p104-two-chain-shared-native/NOTICE | 3 + .../PROOF-OWNED-ASCENT.md | 33 + .../p104-two-chain-shared-native/README.md | 66 + .../p104-two-chain-shared-native/SOURCES.json | 48 + .../p104-two-chain-shared-native/TASK.json | 148 + .../p104-two-chain-shared-native/VERIFY.json | 60 + .../caller_physical.py | 63 + .../p104-two-chain-shared-native/check.py | 381 + .../cover_check.py | 96 + .../data/base_invoice.json | 61 + .../data/caller.json | 1 + .../data/invoice_check.json | 1 + .../data/prior_root_6889.json | 1 + .../data/prior_word_6889.json.gz | Bin 0 -> 747483 bytes .../data/root.json | 1 + .../data/word.json.gz | Bin 0 -> 188389 bytes .../p104-two-chain-shared-native/ordinary.py | 48 + .../p104-two-chain-shared-native/physical.py | 118 + .../retained/bit/FRAGMENT-BIT-ADMISSION.json | 19115 ++++++++++++++++ .../retained/native/clifford_exact.py | 149 + .../retained/physical-review/NOTICE | 12 + .../retained/physical-review/verify.py | 568 + .../retained/runtime/DATA-PHASES.json | 1 + .../retained/runtime/endpoint.py | 240 + .../retained/runtime/intervals.py | 421 + .../retained/runtime/second_intervals.py | 291 + .../root_check.py | 130 + .../verify_relaxed.py | 34 + .../verify_strict.py | 34 + 30 files changed, 22325 insertions(+) create mode 100644 research/p104-two-chain-shared-native/LICENSE create mode 100644 research/p104-two-chain-shared-native/NOTICE create mode 100644 research/p104-two-chain-shared-native/PROOF-OWNED-ASCENT.md create mode 100644 research/p104-two-chain-shared-native/README.md create mode 100644 research/p104-two-chain-shared-native/SOURCES.json create mode 100644 research/p104-two-chain-shared-native/TASK.json create mode 100644 research/p104-two-chain-shared-native/VERIFY.json create mode 100644 research/p104-two-chain-shared-native/caller_physical.py create mode 100644 research/p104-two-chain-shared-native/check.py create mode 100644 research/p104-two-chain-shared-native/cover_check.py create mode 100644 research/p104-two-chain-shared-native/data/base_invoice.json create mode 100644 research/p104-two-chain-shared-native/data/caller.json create mode 100644 research/p104-two-chain-shared-native/data/invoice_check.json create mode 100644 research/p104-two-chain-shared-native/data/prior_root_6889.json create mode 100644 research/p104-two-chain-shared-native/data/prior_word_6889.json.gz create mode 100644 research/p104-two-chain-shared-native/data/root.json create mode 100644 research/p104-two-chain-shared-native/data/word.json.gz create mode 100644 research/p104-two-chain-shared-native/ordinary.py create mode 100644 research/p104-two-chain-shared-native/physical.py create mode 100644 research/p104-two-chain-shared-native/retained/bit/FRAGMENT-BIT-ADMISSION.json create mode 100644 research/p104-two-chain-shared-native/retained/native/clifford_exact.py create mode 100644 research/p104-two-chain-shared-native/retained/physical-review/NOTICE create mode 100644 research/p104-two-chain-shared-native/retained/physical-review/verify.py create mode 100644 research/p104-two-chain-shared-native/retained/runtime/DATA-PHASES.json create mode 100644 research/p104-two-chain-shared-native/retained/runtime/endpoint.py create mode 100644 research/p104-two-chain-shared-native/retained/runtime/intervals.py create mode 100644 research/p104-two-chain-shared-native/retained/runtime/second_intervals.py create mode 100644 research/p104-two-chain-shared-native/root_check.py create mode 100644 research/p104-two-chain-shared-native/verify_relaxed.py create mode 100644 research/p104-two-chain-shared-native/verify_strict.py diff --git a/research/p104-two-chain-shared-native/LICENSE b/research/p104-two-chain-shared-native/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/p104-two-chain-shared-native/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Apache-2.0. + +Retained, unchanged: retained/runtime (interval engines and outer ledger) and retained/native/clifford_exact.py keep their original headers and lineage from the #6833 package. The native word run verbatim is the #6824 word (#6702 native source by DreamingOfClouds, helper-basis mechanism by Ali Romman, retiming and helper retirement by Jerry Chen / @CubeJerry with OpenAI Codex assistance). The caller line follows #6726 (zxv) and #6716 (thu-nmrc). diff --git a/research/p104-two-chain-shared-native/PROOF-OWNED-ASCENT.md b/research/p104-two-chain-shared-native/PROOF-OWNED-ASCENT.md new file mode 100644 index 0000000000..7929b21a81 --- /dev/null +++ b/research/p104-two-chain-shared-native/PROOF-OWNED-ASCENT.md @@ -0,0 +1,33 @@ +# Owned ascent (assumption A6): declaration, cost proof, precedent + +## The change (one line) +`local.py:126` / `native.py:55`, rule "Nested chronological transport": for an owned MOVE the requirement `frames[b] < frames[a]` (descend) becomes +`frames[b] < frames[a] or frames[a] < frames[b]` (nested either way). Public MOVEs still ascend strictly. Nothing else changes: `verify_strict.py` is the +predecessor rule, `verify_relaxed.py` the changed rule; `check.py` runs both and shows that the strict verifier rejects this word at exactly the 23 owned-ascent events (rank mass 56). + +## A6, stated as an assumption +An owned nested rise costs one paid H_r plus rank-0 adapters, with no credit, on arbitrary contents, factorwise at every tensor width, and CLEAR at any frame stays under the +owned_erasure assumption. It is load-bearing: no ascent, no word. The reported kappa is conditional on A6. + +## Direction-free cost +Each MOVE a to b between nested frames applies C_b C_a^{-1}, of rank |dim b - dim a|; the inverse of a rank-r chart change is a rank-r chart change +((C_b C_a^{-1})^{-1} = C_a C_b^{-1}), so a rise and a fall between the same frames are paid the same r. The word's histogram charges every MOVE |delta dim|, owned rises included +(the owned rises are 10, 4, 1, 6, 1, 1 events of ranks 1..6, mass 56), and `check.py` takes helpers (credit) only from public endpoints: dim(final) - dim(initial) with an exact identity row. An owned register is never an input, +earns no target, and is cleared (owned_erasure) before return, so a rise creates no credit and cannot fake an independent field. The stream replay in `physical.py` executes all 23 rises through the compiled chart changes. +The compiled rank equals |delta dim| for every distinct chart pair of this word under the predecessor native compiler (2964 pairs, run separately, not part of the replay budget here). + +## Precedent (read at the base commit) +* `research/kappa-rebuild/complex/native_extensions.py:126`: `N.need(spaces[old] < spaces[new] or spaces[new] < spaces[old], 'Nested center transport')`, while public climbs on line 123 must ascend (`'Ascending borrowed climb'`). +* `research/pooled-native-hosting-admission/NATIVE-ADMISSION.md:249`: "An owned centre copy, its complete descending/ascending child path and its clear therefore realize exactly the emitted common-label centre macro." +* The vendored main native (`research/direct-mixed-flow/vendor/THREE-base-FULL-IDENTITY-NATIVE.json.gz`) has 16 owned centre transports per call in each orientation (8 of rank 3, 8 of rank 5); forward they descend 8 to 3 to 0, and the backward orientation traverses them the other way. +* `notes/copied-centers-lemma.tex:58-62` and `:71`: in the reverse complementary orientation the copy is transformed up by rank r; "These are the same charged ranks, implemented by the retained forward/inverse residual interface." That text is about a copy. +* The P112 backward word (`research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz`) is accumulate-first: clear, ADD x22 into the owned centre at frame 0, MOVE rank 3 up, MOVE rank 5 up, one read, clear (8 per call); `pr4416/PROOF-REVIEW.md:58-62` prices both directions. +* #2479 (merged 2026-10-15): "Equal native rank mass does not admit these changed lifetimes to the original pure-copy storage/owner bill." Changed owned lifetimes were merged as exact finite work with the owner contract flagged; this package states the same. +The compiler text is on main: `research/lever-mixed-targets-2979/PROOF.md:14-16,25` (Theorem 1G pays "rounds j, in word order, of ranks r_j >= 1"; hypothesis (S) is about ranks only); +`research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md:258-268` ("An owned center can be the physical field of a paid round. ... These are field-identity and chronological requirements; statistical independence of current values is not required."); `pr4416/PROOF-REVIEW.md:115-117` (owners "may be correlated and may include owned centers; arbitrary-input correctness permits that, but does not permit aliasing two physical slots"); +`upstream/build/sections/05-layers.tex:83` ("including on decreasing edges"). No sentence there mentions direction. What this word does beyond P112 and no sentence decides: 3 lifetimes read before the rise, 3 with contacts between rises, rises from nonzero frames, both directions in one word and one gauge. + +## Direction-based lower bounds are scoped, not global +These results assume that owned registers only descend and are not valid against a word that uses A6: the owned-paid-56 floor of #6315 (Lemma S: "public ascents shrink C^perp for free, owned descents grow it at their price"), +the eight-unit relay floor of #6229, the reader-497 cache floor of #6257 (descending owned caches; ascending carriers outside its scope), and the surplus accounting of #6831 ("public registers only climb and private registers only descend", surplus -(16p + O)). +#6881 states that ascend-only public paths are verifier behaviour; its bound S <= sum(L_p - 1) - sum c_j takes c >= 56 (H6), which is the owned-descent floor and is scoped the same way. diff --git a/research/p104-two-chain-shared-native/README.md b/research/p104-two-chain-shared-native/README.md new file mode 100644 index 0000000000..4e24287fbd --- /dev/null +++ b/research/p104-two-chain-shared-native/README.md @@ -0,0 +1,66 @@ +# Conditional κ = 0.00351406 (+1.652% over #6889): one native word serves two root chains + +**Result.** The exact-kernel crossing of the complete signed invoice is **0.00351406186742169**, which is **+1.6523% over #6889** (0.00345694177515779; exactly 1.65233%). +The claim for the outer statement is **κ = 0.00351406** with tested price 0.00351406007 (grid 10⁻¹¹), both strictly below the raw crossing, which lies in (0.003514061867421, 0.003514061867422). +The package builds on #6889: it keeps the #6889 native word's structure (the hosted native of #6883 with its shared cover, the deletions, the joint merges and the direct reads), its owned-ascent declaration and its BIT line, and changes what the native serves: one native word now delivers **two** copies of the #6833 chain root at once, on separate main registers. + +**Conditional statement.** The result holds under the five framework assumptions of #6833; under assumption A6 (owned ascent) as declared in #6883; under the BIT saving of the open #6726 (below, necessary for this claim); and under the new forms declared below (a reducible root, one native contact serving two chains, same-label second mains). + +## What the construction is +* **Root.** Two #6833 chain roots on orthogonal coordinates (n = 2×20 = 40, N = 42 units, 18 stages, 6 thin units), one stage variable per stage, units interleaved (chain A, chain B). `root_check.py` regenerates the chain root from its closed form and requires **all 21 units of each chain to equal the file**, the cross Gram between the chains to vanish, each chain's Gram to be sgn(i−j), and then re-proves the SPEC-level identities for the whole root in exact Fractions: isotropy, product −I, stage order, units inside masks, masks commuting with the prefix before and after each stage, the symbolic whole-job identity M(D) = −diag(∏D^ε) with each of the 18 stage variables once and affine, full mask credit, dyadic entries. +* **A wrong root fails, directly.** The composition replay reads the root only through its masks, so a wrong X or Y entry does not fail it. The block identities do, and `check.py` asserts it: a wrong X entry, a wrong Y entry in chain B, and two swapped unit rows each fail `root_check.py`; a wrong mask bit fails the caller replay and the mask comparison. +* **Caller.** The #6833 caller twice, on roles 0–19 and 20–39, with one HOST2 event per stage: the shared native delivers `Y += Q⁻¹X` on the first plane and `X2 += α₂ Q Y2` (α₂ = −1) on the second, times the stage variable D on all four registers. The second chain's LAMBDA pair is flipped. 124 LAMBDA events (62 per chain), 32 IDLE_ONE, 6 thin queries. +* **Native word.** Endpoint X = x, Y = x + y, X2 = x2 − y2, Y2 = y2, helpers identity: 38,334 events, 1375 public registers (416 mains, 4 per port, and 959 helpers), 6440 MOVEs; the first-plane mains and the second-plane mains pay 917 MOVEs each, no move is shared or fused. +* **Invoice.** The root part is exactly twice the #6833 chain root part (`check.py` asserts it): there is no root discount, and nothing is fused. The native part is 18 calls of the helper and paid histograms of this word. S = 104·34 − 36·56 = 1520, net of 56 per call. + +## Why this is not row 19 (stated plainly) +Row 19 reads "many registers, same frame transition, same time: one job per register": it forbids fusing the jobs of two registers. No two registers' jobs are fused here: every register pays its own moves (first and second mains 917 each), and the root has no discount. What is shared is a helper, and a shared helper is **one field, one job, one credit**: FP section 1 (`research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md:32-35`) requires "At every integer column count c, the unit computes exactly its independent rank k*c output jobs ... All borrowed data return to the declared endpoint, and owned storage is explicitly initialized and erased"; FP section 3 matches job copies by the Pascal bijection and its edges "carry complete array jobs"; FP section 6 (lines 258-268) asks for "field-identity and chronological requirements; statistical independence of current values is not required"; the review of #4416 allows owners that "may be correlated and may include owned centers; arbitrary-input correctness permits that, but does not permit aliasing two physical slots". Whole-job matching constrains the fields, not who reads them. This is the accounting the line already uses for ports: in the #6889 word 844 of the 1153 helpers already read or write mains of 9 or more ports (`cover_check.py` recounts it). +The planes meet inside the core only through helpers and owned registers; the 174 events that couple a first-plane main with a second-plane main directly are all in the two gate blocks (at frames Z and V). Doubling with no sharing is an exact tie; the gain is entirely from the helpers read by both chains. + +## The family lines this root does not meet, and why they do not apply +The predecessor family checks have three lines that this root fails: `hosted t not 0, not -1` (here t = α·β = 0 at every stage: two separate planes per stage, no coupled plane), `hosted alpha,beta dyadic units` (α = β = 0), and `Gram digraph strongly connected` (added by the #6883 `root_check.py` itself, "Added here", not a SPEC line; the Gram digraph has two components). T4′ needs only 1 + t ≠ 0, and t = 0 satisfies it; the condition t ≠ 0 came from the definition of the two-way plane host. What the outer theorem requires is on the unit identity and the whole-job credit: Theorem 1G pays "rounds j, in word order, of ranks r_j >= 1" with hypothesis (S) about ranks only (`research/lever-mixed-targets-2979/PROOF.md:14-16,25`), and FP requires the all-column word above. `root_check.py` re-proves the SPEC-level identities for this root; none of the three lines is used by Theorem 1G or FP. + +## BIT: the open #6726 is necessary +The ledger needs the BIT saving to exceed κ + 4·gap = 0.00351406004. `check.py` runs it at eight values: 0.0034 (main's admitted saving), 0.00343, 0.0034363538396 (main's ordinary stock), #5421's 0.00344412, #4760's 0.0034597, #4814's 0.003475458 and #5512's 0.003483969976 all **fail**; #6726's 0.00376669 passes all 54 + 4 inequalities, with margin 2.526e-4 over the tested price. #6834's figure 0.00385248 also clears it but is the title figure of an open pull request, not in this package and not run. Unlike the earlier words of this line, the archive-only savings no longer suffice. **This claim therefore depends on #6726 (or #6834), both open.** The #6726 admission is read from the pinned file `retained/bit/FRAGMENT-BIT-ADMISSION.json` (git blob 482f9525…, sha256 86955dcd…, #6726 head 435bbe91) and is not re-derived; its raw BIT tested saving 0.0037667 exceeds the pin by 1.0e-8, and its raw BIT crossing lower bound exceeds the raw BIT tested saving by 2.3e-8. + +## Raw bound and growth +* Raw bound, all three definitions below 10⁹ (main boundary terms doubled for the second planes): literal 18×10⁷ + terms **963,421,184**; actual per-call work **965,490,968**; reviewed scalar upper **971,071,328** (margins 36.6M, 34.5M, 28.9M). The reviewed-upper line is under 10⁹ here for the first time in this line of work. Per call: 10,114,988 (allowance) or 10,425,008 (reviewed upper), both just above the displayed 10⁷ of pricing.py:93. +* Substitution (FP:278-283): events 38,334; scalar allowance 292,988 or reviewed upper 603,008; routes 9,822,000; caller envelope 331,735,040; paid rank mass R = 316,128; growth bound 2^(971,071,328 + 316,128·f) on the conservative count. No term of the outer ledger reads it (`check.py` verifies that the ledger source has none). +* Growth of the scalar updates: events 38,334 (above the 26,000 of the productive-controller text, as in every word of this line); sum of log2(1+|q|) over the ADD coefficients 27,718 (#6889: 282,880) against 416,000; largest |q| 45, peak |row entry| on any prefix 2^7.5, peak row denominator 2^8, coefficient bits at most 7 and 8; no ADD has |q| ≥ 2¹². +* Precision, as a reading: the quantizer method of CubeJerry (#6900) transfers to this word with its literal hypotheses replaced (free Laurent prefixes, numerators ≤ 16 and its constants), giving W = p + h + 153f + 25, F = p + ⌈153f/2⌉ + 7, temporaries W + 9; the ledger ignores W. This is a reading from the review of the method, not re-derived here; the precision-tape assumption is inherited. + +## LAMBDA is a review question +LAMBDA at width f is the single elementary gate C on (q,…,q), not a lift of the width-one LAMBDA (they agree only at f = 1). The caller identity holds under both readings, so the algebra does not decide it; the price does. If each LAMBDA had to be paid as a rank-1 job per port, S = 1520 − 124·104 = **−11,376 < 0** and no crossing exists (the #6889 caller: 1520 − 82·104 = −7,008). The κ rests on pricing LAMBDA as ordinary work, as in every caller of this line from #6726 on, including #6833 (62 events per chain here). Declared as a convention, not admitted on main. + +## Logarithm power +The smallest admissible value at this price is **2133**; **2134 is written** and used. 2100 fails here: the complement-capacity line (η > (63/64)^logp at maximum target rank 145) binds at 2100 for a tested price of about 0.0034607, below this claim. The power is a free parameter of the compiler theorem (`research/higher-moment-strictification/vendor/LOG-MAJORANT.md:110-122`; stated with an integer q and 1/q in the bound, its literal conditions fail for the real exponent used, and the code uses the same argument with a real p, which a reviewer of #6884 re-walked and I did not). The interval engines are the retained rational ones (no Decimal) at the tested price: α = 0.9999999975, γ = 0.9480, δ = 0.8116 (< 31/32), the composite bound 1/(1+power·reserve) + 4·decay^power < 1 holds, the 54 strict and 4 functional outer inequalities are positive (their smallest value is the chosen parameter r0 = gap/10, not a measured margin). The input-lift saving lemma of #6833 has its cap moved to the pin and passes. + +## Declared, and inherited +| class | declaration (counts recomputed by `check.py`) | +|---|---| +| new family | reducible root: two #6833 chain roots, t = 0, three family lines not met (above) | +| new event | HOST2: one native contact per stage serving both chains (18 events), second chain's LAMBDA pair flipped | +| new form | same-label second mains: X2, Y2 carry the same initial and final frame labels as X, Y; 4 mains per port | +| convention (A6, load-bearing) | owned ascent: 23 owned rises, rank mass 56, peak owned 30 (#6889: 25); **8 owned reads of Y2**, events 14676, 14744, 14746, 14768, 14770, 14774, 14776, 18579 (#6889 had one read of Y; this word none). No ascent, no word. The strict verifier rejects the word at exactly the 23 rises; the evidence for A6 and its direction-free cost argument are in `PROOF-OWNED-ASCENT.md`. Direction-based lower bounds (#6315 Lemma S, #6229, #6257, #6831, and the c ≥ 56 input of #6881) are scoped to words whose owned registers only descend | +| verifier | endpoint literal native.py:75-77 / local.py:168: the target is X = x, Y = x + y, X2 = x2 − y2, Y2 = y2 on 104 ports | +| verifier | events 38,334, public 1375, owned roles 51, 54 lifetimes (local.py:52,54,103; pricing.py:84-87); per-call scalar work 10,114,988 against the displayed 10⁷ | +| convention | LAMBDA (124 events) and IDLE_ONE (32 events), inherited from the open callers #6726 and #6716/#6763, not on main; the one-site idles are priced as whole H8 jobs (FP:23-26); the LAMBDA price is the review question above | +| assumption | dirty owned erasure (53 erasures), the existing owned_erasure assumption | + +## Check +`check.py` (about 25 s): exact event replay with the two-plane endpoint; strict and relaxed verifiers with the rejection control; the root and its failing controls; the HOST2 caller at the four central characters with controls (wrong α₂, a deleted idle, a deleted thin query, a flipped LAMBDA at one contact, a wrong mask bit); the invoice rebuilt from word, root and caller, with the #6889 word (through its own root) and #6833 rebuilt by the same code as controls; the three raw figures; growth, the owned reads of Y2; the BIT pins; interval engines, logarithm power, strictification, compiler and outer ledger; departures. +`ordinary.py` (seconds): the raw figures. `cover_check.py` (about 6 s): the counts above and controls on 12 sampled events that read or write a second main (a wrong weight, a missing event, an event taken twice, all rejected). `physical.py` (about 30 s): all 38,334 events as 512-component streams over F_p[i] (p = 10⁹+9), chart predictions for helpers and for all four main types, the raw main-pair identities by tableau and phase on all 104 ports, with controls. `caller_physical.py` (about 10 s): the caller's physical replay through the retained independent physical audit (one declared line changed for A6): 7,488 contact phases, the reverse cross term of the second plane, main targets on 40 roles, whole idles on every owner and port, an injective field map with four mains per port and the aliasing control, the invoice, the adapters. + +## Not claimed, and not independently examined +No frontier change; no claim without A6 and the admission of #6726; the precision-tape and compiler assumptions are not discharged. The all-columns statement for this word is algebraic and holds under ideal owned resets, after the method of CubeJerry's #6890: an independent run found 0 failures over 2,954 chart pairs, 1,664 port identities, 7,488 contacts and paths, and 0 of 1,600 entries wrong in the exact backward controller. **No streams at tensor width 2 or more were run**, and the root identity M(D) is not re-proved beyond the checks above. Not examined: the adjoint (transpose) physical replay of this word; Theorem 1G itself and the compiler (read as the conditional claims they are); the BIT verifiers (the savings are read, not re-run); the compiler texts beyond the parts quoted here and in `PROOF-OWNED-ASCENT.md`. Reviewers may still object to the new forms: no text read forbids them and none names them. The physical replay uses one prime and one random input per run. `data/word.json.gz` is the only word input; a word with the same invoice can replace it, and the constants asserted in `check.py` and `cover_check.py` are the ones to update. + +## Open next questions +1. Is owned ascent (A6), with the eight owned reads of Y2, accepted for the native verifier, as it is in the P112 native? +2. Is the BIT admission 0.00376669 of the open #6726 (or #6834's figure) accepted for the outer statement? Nothing on main clears κ + 4·gap. +3. Are a reducible root, one native contact serving two chains and same-label second mains admitted forms for the compiler's job list, and may LAMBDA and IDLE_ONE be priced as ordinary work? +4. Can the first-plane and second-plane chains use a native that is not the mirror, which would drop A6 and may free more helpers? + +## Credit +Builds on #6889 (the hosted native word and its package: the base of this one), #6833 (the chain-nested root, invoice and outer ledger, used twice), the line #6883, #6884, #6886, #6887 behind #6889, #6726 (zxv; the BIT admission used for the pin), #6716 (thu-nmrc, common idle fusion), the #6702 native source by DreamingOfClouds with the helper-basis mechanism of Ali Romman and the retiming and helper-retirement extension of Jerry Chen / @CubeJerry (#6805, #6824), whose #6890 method (Gauss-trace acceptance), #6900 (quantizer composition) and #6901 (fixed-root context count) underlie the all-columns and precision statements, and the retained interval engines and Clifford compiler of their authors. + +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. diff --git a/research/p104-two-chain-shared-native/SOURCES.json b/research/p104-two-chain-shared-native/SOURCES.json new file mode 100644 index 0000000000..fa230d7216 --- /dev/null +++ b/research/p104-two-chain-shared-native/SOURCES.json @@ -0,0 +1,48 @@ +{ + "schema_version": 1, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + }, + { + "path": "docs/research/pr-intake-evidence/pr6030-audit/PROOF-REVIEW.md", + "usage": "provenance", + "git_blob": "26f2f6324bce57e69e861d2aae5a27c9de325a8e", + "sha256": "8bd158b8ef68202000f167b9b78db0b31531b5b067b5cbd91b5bf35f3ddd1ab6" + }, + { + "path": "research/p104-helper-subspace-splits/search.py", + "usage": "provenance", + "git_blob": "1bf5329658683919a97430138b57860751da7ba9", + "sha256": "668022953f53929fd4d95ed1b5c01ac2ba3b4bdf6be7babae511757eb21b7e6a" + } + ], + "source_availability": "Every executable input is committed inside this package; the retained interval engines and the Clifford compiler are unchanged copies from the predecessor package.", + "pending_heads": { + "native_pr6702": "edd6a37a9ff87b254fb7466184348d1432d0c8c0", + "native_pr6805": "0ecd4fd79f4f7fc21b2ef7a9cdc73912fa4a804b", + "native_pr6824": "2a7ca44fbda3abaa4df355b183ed7d7478eef7c1", + "hosted_pr6883_fork_commit": "3652e9191530fb02e2e5efe92b2b53386890874d", + "bit_pin_pr6726": "435bbe91fb28cb1d7a569ca70c6c4e9eb302d486", + "hosted_pr6884_fork_commit": "f33c5bd58d10d6c7244975cd34401ef13237c8a1", + "hosted_pr6886_fork_commit": "187aa656e9cc9f5f7b6f202c137a9aba8d3c1144", + "hosted_pr6887_fork_commit": "a3d665bf170a0a3ebc5ea60354ae9e19a199388d", + "hosted_pr6889_fork_commit": "50f860cc64dbc18a5d64927a4e544418c41421c6" + }, + "retained_bit": { + "path": "retained/bit/FRAGMENT-BIT-ADMISSION.json", + "origin": "#6726 head 435bbe91fb28cb1d7a569ca70c6c4e9eb302d486, research/p104-paid-idle-fragmentation/frozen/bit/FRAGMENT-BIT-ADMISSION.json", + "git_blob": "482f9525d4b75b704018c8d8eba5a00af423dac5", + "sha256": "86955dcd74bc3fa1a940419474d45054fa7b0366b71b242568680366923d9311" + } +} diff --git a/research/p104-two-chain-shared-native/TASK.json b/research/p104-two-chain-shared-native/TASK.json new file mode 100644 index 0000000000..badb699a50 --- /dev/null +++ b/research/p104-two-chain-shared-native/TASK.json @@ -0,0 +1,148 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "original_card": { + "id": "p104-side-correction", + "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "research/p104-helper-subspace-splits/README.md", + "research/dyadic-helper-channel-capacity/README.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "P104", + "helper basis", + "helper split", + "5718", + "dyadic capacity" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Can one hosted native word serve two copies of the chain-nested root at once, on separate main registers, so that the helpers are shared between the chains and the complete signed invoice improves?", + "scope_change_reason": "Same hosted native, A6 declaration and BIT line as #6889. Changed: the root becomes two #6833 chain roots on orthogonal coordinates (t = 0, a reducible root), the caller gets one HOST2 contact per stage serving both chains, and the word carries four main registers per port (same-label second mains, 959 helpers, 38,334 events). Correctness rests on the exact replay of the final word and the root block identities. The BIT saving of the open #6726 (.00376669) is necessary: nothing else on main clears kappa + 4 gap. The logarithm power is written as 2134 (minimum 2133). Raw counts 963,421,184 / 965,490,968 / 971,071,328, all below 10^9. LAMBDA priced as ordinary work is a review question (paid rank 1 per port gives S < 0). Inherited: owned ascent (A6, 23 rises of mass 56, peak 30, 8 owned reads of Y2), LAMBDA and IDLE_ONE.", + "bottleneck_link": "docs/research/research-family-status.md; complete signed native/caller invoice and all supplier-admission gates", + "stop_rule": "The claim is conditional on the five retained framework assumptions, the declared owned ascent (A6), the BIT saving of the open #6726, and the declared new forms (reducible root, HOST2, same-label second mains); no claim above the pin; LAMBDA must be priced as ordinary work for any crossing to exist.", + "evidence": "README.md, PROOF-OWNED-ASCENT.md, check.py, root_check.py, cover_check.py, physical.py, caller_physical.py, ordinary.py, verify_strict.py, verify_relaxed.py, data/ (word, caller, root, #6889 word and root, base invoice, physical invoice), retained/bit (the pinned #6726 admission file); claimed kappa 0.00351406 (crossing 0.00351406186742169).", + "author": "DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code", + "ai_assistance": "Written with Claude Code; the native word is the #6824 word, whose lineage is recorded in the #6833 package.", + "outcome": "completed", + "open_questions": [ + { + "question": "Is the declared owned ascent (assumption A6, with eight owned reads of Y2: 23 rises of mass 56, peak 30, load-bearing) accepted for the native verifier?", + "why_it_matters": "Without it there is no word.", + "first_step": "Adopt the declared one-line change of the owned-move rule (PROOF-OWNED-ASCENT.md), with the P112 native as precedent.", + "blocked_by": "A verifier convention, not a theorem." + }, + { + "question": "Is the BIT saving .00376669 of the open #6726 (or #6834's figure) accepted for the outer statement?", + "why_it_matters": "The ledger needs more than kappa + 4 gap = .00351406004 and nothing merged or admitted on main reaches it.", + "first_step": "Merge or re-verify the #6726 BIT admission (retained/bit/FRAGMENT-BIT-ADMISSION.json) and replace the pin accordingly.", + "blocked_by": "#6726 and #6834 are open pull requests; the admission is read here and not re-derived." + }, + { + "question": "Are a reducible root, one native contact serving two chains and same-label second mains admitted forms for the compiler's job list, and may LAMBDA and IDLE_ONE be priced as ordinary work?", + "why_it_matters": "If LAMBDA were a paid rank-1 job per port, S = 1520 - 124*104 < 0 and no crossing exists.", + "first_step": "Locate the forms in the compiler's job list, or have them added with the substitution of constants written.", + "blocked_by": "None of them is named on main." + }, + { + "question": "Can the second chain use a native that is not the mirror of the first, so that A6 is no longer needed?", + "why_it_matters": "The blocks of the target only need the cross terms to vanish.", + "first_step": "Build a second chain on a non-mirror network and replay it exactly.", + "blocked_by": "Not tried." + } + ], + "research_context": { + "base": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "builds_on": [ + "#6889 hosted native word and package (the base)", + "#6833 chain-nested root (used twice)", + "#6887, #6886, #6884, #6883 behind #6889", + "#6824 native word", + "#6805 helper recount", + "#6702 native source", + "#6726 BIT admission (pin)", + "#6890, #6900, #6901 method of CubeJerry" + ], + "credit": "The prior work above; #6889 is the baseline." + }, + "selected_frontier_changed": false +} diff --git a/research/p104-two-chain-shared-native/VERIFY.json b/research/p104-two-chain-shared-native/VERIFY.json new file mode 100644 index 0000000000..3a6cf32612 --- /dev/null +++ b/research/p104-two-chain-shared-native/VERIFY.json @@ -0,0 +1,60 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/check.py" + ], + "timeout_seconds": 300, + "checks": "Exact replay of the 38,334-event word with two main planes per port; the two-chain root regenerated from the closed form with failing controls; the HOST2 caller at four central characters with controls; the invoice rebuilt with the #6889 word and #6833 as controls; the three raw figures; growth figures; BIT pins; rational interval engines, logarithm power 2134, strictification, compiler and outer ledger; declared departures." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/physical.py", + "{package}/data/word.json.gz", + "{package}/retained/native/clifford_exact.py" + ], + "timeout_seconds": 200, + "checks": "Physical replay of every register as a 512-component stream over F_p[i] with random inputs through every chart change (owned ascent included), chart predictions for helpers and both main outputs, and the raw main-pair identities by tableau and phase on all 104 ports with controls." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/ordinary.py", + "{package}/data/word.json.gz", + "{package}/data/caller.json" + ], + "timeout_seconds": 100, + "checks": "Recount of the ordinary (non-recursive) raw total under all three per-call counts, including the reviewed upper count, which exceeds 10^9 as stated in the README." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/caller_physical.py", + "{package}/data/word.json.gz", + "{package}/data/caller.json" + ], + "timeout_seconds": 100, + "checks": "Physical replay of the literal caller through the retained independent physical audit with HOST read as the native contact: 7488 absolute-phase contacts, reverse cross term, main targets, whole-idle rank and axes on every owner and port, field map with alias control, complete invoice, adapter inventory, controls." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/cover_check.py" + ], + "timeout_seconds": 200, + "checks": "What changed against the #6883 word: 342 core ADD events removed and nothing else but MOVEs, no silent helper left, silent-helper removal leaves the invoice unchanged, and controls (one more ADD removed, an ADD duplicated, sampled ADDs removed) all break the endpoint." + } + ] +} diff --git a/research/p104-two-chain-shared-native/caller_physical.py b/research/p104-two-chain-shared-native/caller_physical.py new file mode 100644 index 0000000000..c252d83efa --- /dev/null +++ b/research/p104-two-chain-shared-native/caller_physical.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Physical replay of the literal two-chain caller (standard library): every HOST2 event is a native contact at its stage and port, read through the +retained independent physical audit (retained/physical-review/verify.py) with the one adaptation that HOST2 is read as the LOCAL contact (stage, source, destination) of the first plane; +the second plane (x2, y2) sits on the same frames and ports. +python3 -B caller_physical.py data/word.json.gz data/caller.json +Checks: absolute contact phases of the four native boundary maps at every stage and port (7488 contacts), fresh D_stage diagonal and Q^-1 cross term, the reverse cross coefficient D_stage Q^+1 of the second plane, +main-target exponents and translations on all 40 roles, whole-idle rank and axis disjointness on every owner and port, an injective field map with FOUR distinct main registers per port and fresh helpers (with the aliased-helper control), +the complete invoice from the physical audit against data/invoice_check.json, and the canonical adapter inventory.""" +import copy, gzip, importlib.util, json, sys +from collections import Counter +HERE = __import__('os').path.dirname(__import__('os').path.abspath(__file__)) +spec = importlib.util.spec_from_file_location('review', HERE + '/retained/physical-review/verify.py'); P = importlib.util.module_from_spec(spec); spec.loader.exec_module(P) +W = json.load(gzip.open(sys.argv[1], 'rt')); C = json.load(open(sys.argv[2])) +recipes = json.load(open(HERE + '/retained/runtime/DATA-PHASES.json')) +def need(ok, msg): + if not ok: raise SystemExit('FAIL ' + msg) + print('PASS', msg, flush=True) +shim = copy.deepcopy(C); shim['events'] = [['LOCAL', e[1], e[2], e[3]] if e[0] == 'HOST2' else e for e in shim['events']] +need(sum(e[0] == 'LOCAL' for e in shim['events']) == 18, 'the caller has 18 native contacts (HOST2 read as LOCAL)') +ph = P.physical(shim, W, recipes) +need(ph['contacts'] == 4 * 18 * 104, 'absolute phase of all %d native boundary contacts (4 per stage and port), fresh D_stage diagonal and D_stage Q^-1 cross term' % ph['contacts']) +need(sum(ph['main'].values()) == C['roles'] * 104 and sum(ph['idle'].values()) == sum(e[0] == 'IDLE_ONE' for e in C['events']) * 104, 'main targets on all %d roles and ports; every IDLE_ONE owner has a whole idle (%s) with disjoint fresh axes' % (C['roles'], dict(sorted(ph['idle'].items())))) +dim = C['ambient_rank']; axes = [1 << i for i in range(dim)]; bad = ctl = cnt = 0 +for e in C['events']: + if e[0] != 'HOST2': continue + st = e[1] + for q in W['ports']: + x0 = P.terms((a, 1) for a in axes[:9 + 8 * (st - 1)]); y0 = P.terms(list(x0.items()) + [(q, -1)]) + x1 = P.terms((a, 1) for a in axes[:9 + 8 * st]); body = P.terms((a, 1) for a in axes[9 + 8 * (st - 1):9 + 8 * st]) + rev = P.difference(x1, y0) + bad += P.translation_for(P.difference(rev, P.terms(list(body.items()) + [(q, 1)]))) != 0 + ctl += P.translation_for(P.difference(rev, P.terms(list(body.items()) + [(q, -1)]))) == 0 + cnt += 1 +need(bad == 0 and ctl == 0, 'reverse cross coefficient D_stage Q^+1 of the second plane at %d stage-port pairs (control Q^-1 matches %d)' % (cnt, ctl)) +led = P.native_ledger(W, check_rows=False) +H2 = set(W['hosted']['X2']) | set(W['hosted']['Y2']) +labels = [(f, r) for f, r in led['helper_labels'] if f not in H2] +need(len(led['helper_labels']) - len(labels) == 208 and len(labels) == led['public'] - 416, 'second mains are public, not helpers: %d helpers, %d public' % (len(labels), led['public'])) +Tb = Counter(ph['main']); Pb = Counter(ph['idle']) +for f, r in labels: Tb[r] += 18 +for k, v in led['paid'].items(): Pb[k] += 18 * v +Pb[1] += 104 * sum(e[0] == 'QUERY' for e in C['events']) +for ev_i, e in enumerate(c for c in C['events'] if c[0] == 'HOST2'): + st, src, dst, x2, y2 = e[1:]; pm = {} + for i, q, a, b in zip(W['live'], W['ports'], W['hosted']['X2'], W['hosted']['Y2']): + pm[i] = ('main', src, q); pm[112 + i] = ('main', dst, q); pm[a] = ('main', x2, q); pm[b] = ('main', y2, q) + for f, r in labels: pm[f] = ('helper', ev_i, f) + if len(set(pm.values())) != led['public'] or len(pm) != led['public']: raise SystemExit('FAIL field map at stage %d' % st) +need(True, 'injective public allocation with four distinct main registers per port and fresh helpers at every one of the 18 contacts') +inv = json.load(open(HERE + '/data/invoice_check.json')) +need(dict(+Tb) == {int(k): v for k, v in inv['T'].items()} and dict(+Pb) == {int(k): v for k, v in inv['P'].items()}, 'complete invoice from the physical audit equals data/invoice_check.json (targets and paid)') +def rejected(f): + try: f(); return False + except (ValueError, SystemExit): return True +sh2 = copy.deepcopy(shim); idx = [i for i, e in enumerate(sh2['events']) if e[0] == 'LOCAL']; sh2['events'][idx[0]][1], sh2['events'][idx[1]][1] = 2, 1 +need(rejected(lambda: P.physical(sh2, W, recipes)), 'control: native stages out of chronological order are rejected') +de = copy.deepcopy(shim); del de['events'][next(i for i, e in enumerate(de['events']) if e[0] == 'IDLE_ONE')] +phd = P.physical(de, W, recipes) +need(Counter(phd['idle']) != Counter(ph['idle']), 'control: deleting one idle job changes the physical idle bill (the idle layout is bound to the invoice)') +rec = P.adapter_inventory(shim, W, recipes); ad = P.check_adapter_inventory(rec, shim, ph) +print(' adapter inventory', {k: v for k, v in ad.items() if k != 'payload_sha256'}) +need(ad['main_jobs'] == C['roles'] * 104 and ad['idle_jobs'] == sum(ph['idle'].values()), 'adapters for every main job and every whole idle job, distinct') +print('PASS_CALLER_PHYSICAL') diff --git a/research/p104-two-chain-shared-native/check.py b/research/p104-two-chain-shared-native/check.py new file mode 100644 index 0000000000..b62c5b4409 --- /dev/null +++ b/research/p104-two-chain-shared-native/check.py @@ -0,0 +1,381 @@ +#!/usr/bin/env python3 +"""One native word serving two root chains: exact replay of the word, the two-chain root, the HOST2 caller, the complete invoice and the outer constants. +Standard library only (plus the retained interval engines). python3 -I -B check.py (writes nothing) +Steps: (1) event-by-event exact replay of data/word.json.gz, endpoint with two main planes per port; (2) the root, literally two #6833 chain roots, with a direct check that a wrong root X/Y FAILS; +(3) the HOST2 caller at the four central characters, its targets read from the root masks, with controls; (4) the invoice rebuilt from word, root and caller, with the #6889 word (through its own root) and #6833 as controls; +(5) raw bound by three definitions, growth figures; (6) BIT pins, interval engines, strictification, compiler and outer ledger; departures. +Prints PASS_P104_TWO_CHAIN_SHARED_NATIVE. (physical.py, caller_physical.py, cover_check.py are the other commands.)""" +import gzip, json, os, sys, subprocess, importlib.util, random, hashlib, math, copy +from collections import Counter +from decimal import Decimal as D, getcontext +from fractions import Fraction as Q +getcontext().prec = 60 +HERE = os.path.dirname(os.path.abspath(__file__)) +def need(ok, msg): + if not ok: raise SystemExit('FAIL ' + msg) + print('PASS', msg, flush=True) +data = lambda n: os.path.join(HERE, 'data', n) +PIN = Q(376669, 100000000) # ordinary BIT saving of the open #6726 two-fragment admission (retained/bit/FRAGMENT-BIT-ADMISSION.json) +def ldmod(path, name): + s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); sys.modules[name] = m; s.loader.exec_module(m); return m + +# ---- (1) replay of the word ------------------------------------------------------------------- +W = json.load(gzip.open(data('word.json.gz'), 'rt')) +def span(b): + s = {0} + for v in b: + if not (isinstance(v, int) and 0 < v < 512 and v not in s): raise SystemExit('FAIL dependent basis') + s |= {x ^ v for x in s} + return frozenset(s) +fr = W['frames']; sp = [span(b) for b in fr]; dim = [len(b) for b in fr] +n = len(W['initial']); NO = W['owned_fields']; NR = n + NO +cur = list(W['initial']) + [None] * NO; row = [({r: Q(1)} if r < n else {}) for r in range(NR)] +owned = set(); viol = Counter(); owned_up = Counter(); up_idx = []; paid = Counter(); peak = life = dirty = 0; maxq = Q(0); logq = 0.0; pmax = Q(0); dmaxb = 0; nbits = dbits = 0 +dy = lambda q: q.denominator & (q.denominator - 1) == 0 +for i, e in enumerate(W['program']): + op, r = e[0], e[1] + if op == 'MOVE': + _, r, a, b, pv = e + if cur[r] != a or (r in owned) != bool(pv): viol['transport source or ownership'] += 1 + if pv: + if sp[a] < sp[b]: owned_up[dim[b] - dim[a]] += 1; up_idx.append(i) + elif not sp[b] < sp[a]: viol['owned move not nested'] += 1 + elif not sp[a] < sp[b]: viol['public move not strictly ascending'] += 1 + paid[abs(dim[b] - dim[a])] += 1; cur[r] = b + elif op == 'INIT': + if not (r >= n and r not in owned): viol['INIT'] += 1 + owned.add(r); life += 1; peak = max(peak, len(owned)); cur[r] = e[2]; row[r] = {} + elif op == 'CLEAR': + if not (r in owned and cur[r] == e[2]): viol['CLEAR'] += 1 + dirty += bool(row[r]); owned.discard(r); cur[r] = None; row[r] = {} + else: + q = Q(e[2] if op == 'SCALE' else e[3]); f = e[-1] + if q == 0 or not dy(q) or not abs(q) + 1 < 2 ** 16: viol['coefficient alphabet'] += 1 + maxq = max(maxq, abs(q)); nbits = max(nbits, abs(q.numerator).bit_length()); dbits = max(dbits, q.denominator.bit_length()) + if op != 'SCALE': logq += math.log2(1 + float(abs(q))) + if op == 'SCALE': + if cur[r] != f or abs(q.numerator) & (abs(q.numerator) - 1): viol['SCALE'] += 1 + row[r] = {k: v * q for k, v in row[r].items()} + for v in row[r].values(): + if abs(v) > pmax: pmax = abs(v) + if v.denominator.bit_length() > dmaxb: dmaxb = v.denominator.bit_length() + else: + s = e[2] + if not (cur[r] == f == cur[s] and s != r): viol['common chart'] += 1 + if op == 'COPY': + if not (r in owned and not row[r]): viol['COPY'] += 1 + row[r] = {} + for k, v in row[s].items(): + t = row[r].get(k, 0) + q * v + if t: + row[r][k] = t + if abs(t) > pmax: pmax = abs(t) + if t.denominator.bit_length() > dmaxb: dmaxb = t.denominator.bit_length() + else: row[r].pop(k, None) +need(not owned and cur[:n] == W['final'], 'owned all cleared; final frames as declared') +need(dict(viol) == {}, 'frame law, common chart, dyadic alphabet, public ascent: no violation beyond the declared one') +up_mass = sum(k * v for k, v in owned_up.items()) +need(up_mass == 56 and sum(owned_up.values()) == 23, 'declared OWNED UP: %d events, rank mass %d (convention: owned ascent)' % (sum(owned_up.values()), up_mass)) +def verifier(name): + return subprocess.run([sys.executable, '-I', '-B', os.path.join(HERE, name), data('word.json.gz')], capture_output=True, text=True).stdout +os_, or_ = verifier('verify_strict.py'), verifier('verify_relaxed.py') +rej = [int(x) for x in os_.split('indices')[1].split('\n')[0].split()] +need(os_.strip().endswith('REJECTED_STRICT') and rej == up_idx and "['move nesting']" in os_, 'rejection control: the strict (predecessor) verifier rejects this word at exactly the %d owned-ascent events and nothing else' % len(rej)) +need(or_.strip().endswith('ACCEPTED_RELAXED'), 'relaxed verifier (only the owned-move direction rule changed, paid |delta dim| either way) accepts every event') +H = W['hosted']; al, be = Q(H['alpha']), Q(H['beta']); a2, b2 = Q(H['alpha2']), Q(H['beta2']) +live = W['live']; X = set(live); Y = {r + 112 for r in live}; X2 = H['X2']; Y2 = H['Y2']; X2s = set(X2); Y2s = set(Y2) +need(H['mode'] == 'decoupled-t0' and (al, be, a2, b2) == (0, 1, -1, 0) and len(live) == len(W['ports']) == len(X2) == len(Y2) == 104 and not ((X2s | Y2s) & (X | Y)) and len(X2s | Y2s) == 208, + 'two main planes per port: plane 1 (alpha,beta)=(%s,%s), plane 2 (alpha2,beta2)=(%s,%s), t = 0 in both; 104 ports, 4 distinct main registers per port' % (al, be, a2, b2)) +x2of = dict(zip(X2, Y2)); bad = 0 +for r in range(NR): + if r >= n: ex = {} + elif r in X: ex = {r: Q(1), r + 112: al} if al else {r: Q(1)} + elif r in Y: ex = {r - 112: be, r: 1 + al * be} + elif r in X2s: ex = {r: Q(1), x2of[r]: a2} + elif r in Y2s: ex = {r: Q(1)} if b2 == 0 else None + else: ex = {r: Q(1)} + bad += row[r] != ex +need(bad == 0, 'endpoint exact on all %d public and owned rows: X=x, Y=x+y, X2=x2-y2, Y2=y2, helpers identity, owned empty' % NR) +for r, q, x2, y2 in zip(live, W['ports'], X2, Y2): + if fr[W['initial'][r]] != [q] or dim[W['final'][r]] != 9 or dim[W['initial'][r + 112]] != 0 or sp[W['final'][r + 112]] != frozenset(x for x in range(512) if not (x & q).bit_count() % 2): raise SystemExit('FAIL main frames') + if W['initial'][x2] != W['initial'][r] or W['final'][x2] != W['final'][r] or W['initial'][y2] != W['initial'][r + 112] or W['final'][y2] != W['final'][r + 112]: raise SystemExit('FAIL second main frames') +need(True, '104 literal central ports; the second mains carry the same initial and final frame labels as the first mains (declared: same-label second mains)') +main = X | Y | X2s | Y2s +hel = Counter(dim[W['final'][r]] - dim[W['initial'][r]] for r in range(n) if r not in main) +need(min(hel) > 0 and all(sp[W['initial'][r]] < sp[W['final'][r]] for r in range(n) if r not in main), 'every helper strictly ascends (rank > 0); %d helpers, %d mains, %d public' % (sum(hel.values()), len(main), n)) +print(' events', len(W['program']), 'public', n, 'owned roles', NO, 'peak owned', peak, 'owned lifetimes', life, 'dirty owned erasures', dirty, 'max |coefficient|', maxq) +need(peak == 30, 'peak owned fields 30 (#6889: 25)') + +# ---- (2) the root ----------------------------------------------------------------------------- +RC = ldmod(os.path.join(HERE, 'root_check.py'), 'rootcheck') +R = json.load(open(data('root.json'))) +need(RC.run(R) == [], 'root checker: two #6833 chain roots regenerated (21/21 units of each), cross Gram 0, SPEC-level identities, each stage variable once and affine') +Rm = copy.deepcopy(R); Rm['X'][5][3] = str(Q(Rm['X'][5][3]) + 1) +need(RC.blocks(Rm) != [] and RC.run(Rm) != [], 'control: a wrong X entry in the root FAILS the block identities (%s)' % RC.blocks(Rm)[:1]) +Rm = copy.deepcopy(R); Rm['Y'][30][23] = str(Q(Rm['Y'][30][23]) - 1) +need(RC.blocks(Rm) != [], 'control: a wrong Y entry in chain B FAILS the block identities (%s)' % RC.blocks(Rm)[:1]) +Rm = copy.deepcopy(R); Rm['X'][7], Rm['X'][9] = Rm['X'][9], Rm['X'][7] +need(RC.run(Rm) != [], 'control: two unit rows swapped in chain A FAIL') +ST = R['stages'] +mask_inc = lambda c, RR: [int(c in set(s['mask'])) for s in RR['stages']] + +# ---- (3) the caller ----------------------------------------------------------------------------- +C = json.load(open(data('caller.json'))) +pM = 2147483629 +IM = next(pow(g, (pM - 1) // 4, pM) for g in range(2, 99) if pow(g, (pM - 1) // 2, pM) == pM - 1); HALF = (pM + 1) // 2 +fm = lambda x: (lambda f: f.numerator % pM * pow(f.denominator, pM - 2, pM) % pM)(Q(x)) +def replay(Wc, qv, Dv, a2_): + n_ = Wc['roles']; Rm_ = [[int(i == j) for j in range(n_)] for i in range(n_)]; qi = pow(qv, pM - 2, pM); seen = [] + for e in Wc['events']: + o = e[0] + if o == 'ADD': Rm_[e[1]] = [(a_ + fm(e[3]) * b_) % pM for a_, b_ in zip(Rm_[e[1]], Rm_[e[2]])] + elif o == 'SCALE': c = fm(e[2]); Rm_[e[1]] = [a_ * c % pM for a_ in Rm_[e[1]]] + elif o == 'SWAP': Rm_[e[1]], Rm_[e[2]] = Rm_[e[2]], Rm_[e[1]] + elif o == 'QUERY': c = pow(qv, e[3] % 4, pM); Rm_[e[1]] = [(a_ + c * b_) % pM for a_, b_ in zip(Rm_[e[1]], Rm_[e[2]])] + elif o == 'LAMBDA': + s_ = e[2]; c = ((1 + s_ * IM) * HALF + (1 - s_ * IM) * HALF * qv * qv) % pM; Rm_[e[1]] = [a_ * c % pM for a_ in Rm_[e[1]]] + elif o == 'IDLE_ONE': + c = 1 + for k in e[2]: c = c * Dv[k] % pM + Rm_[e[1]] = [a_ * c % pM for a_ in Rm_[e[1]]] + elif o == 'HOST2': + st, src, dst, x2, y2 = e[1:]; d = Dv[st]; seen.append(st) + Rm_[dst] = [(a_ + qi * b_) % pM for a_, b_ in zip(Rm_[dst], Rm_[src])] + Rm_[x2] = [(a_ + fm(a2_) * qv % pM * b_) % pM for a_, b_ in zip(Rm_[x2], Rm_[y2])] + for r_ in (src, dst, x2, y2): Rm_[r_] = [a_ * d % pM for a_ in Rm_[r_]] + else: raise SystemExit('FAIL unknown caller event ' + o) + if sorted(seen) != list(range(1, Wc['stages'] + 1)): return 10 ** 6 + bad_ = 0 + for i in range(n_): + c = pow(qv, Wc['diagonal'][i][0] % 4, pM) + for k, bit in enumerate(Wc['diagonal'][i][2:]): + if bit: c = c * Dv[k + 1] % pM + bad_ += sum(Rm_[i][j] != (c if i == j else 0) for j in range(n_)) + return bad_ +need(C['roles'] == 40 and C['stages'] == 18 and Q(C['alpha2']) == a2 and Q(C['beta2']) == b2 and sum(e[0] == 'HOST2' for e in C['events']) == 18, 'caller: 40 roles, 18 HOST2 events (one native contact per stage serving both chains), plane parameters equal the word\'s') +need(all(C['diagonal'][c][2:] == mask_inc(c, R) for c in range(40)), 'caller target exponents equal the root mask incidence (field by field, stage by stage; roles 0-19 chain A, 20-39 chain B)') +rnd = random.Random(5); tot = cnt = 0 +for qv in (1, IM, pM - 1, pM - IM): + for _ in range(2): + Dv = {s_: rnd.randrange(2, pM) for s_ in range(1, 19)}; tot += replay(C, qv, Dv, a2); cnt += 1 +need(tot == 0, 'composition: the caller with the shared native replays to the diagonal root target at all four central characters, random stage values (%d evaluations, 0 bad of 1600 coefficients each)' % cnt) +Dv = {s_: rnd.randrange(2, pM) for s_ in range(1, 19)} +muts = [] +Cm = copy.deepcopy(C); muts.append(replay(Cm, IM, Dv, Q(1))) # wrong alpha2 +Cm = copy.deepcopy(C); del Cm['events'][next(i for i, e in enumerate(Cm['events']) if e[0] == 'IDLE_ONE')]; muts.append(replay(Cm, IM, Dv, a2)) +Cm = copy.deepcopy(C); del Cm['events'][next(i for i, e in enumerate(Cm['events']) if e[0] == 'QUERY')]; muts.append(replay(Cm, IM, Dv, a2)) +Cm = copy.deepcopy(C); i = next(i for i, e in enumerate(Cm['events']) if e[0] == 'HOST2'); Cm['events'][i - 1][2] *= -1; muts.append(replay(Cm, IM, Dv, a2)) # one contact LAMBDA flipped +need(all(muts), 'controls: wrong alpha2, a deleted idle, a deleted thin query, a flipped LAMBDA at one contact are all rejected by the replay (bad %s)' % muts) +Cm = copy.deepcopy(C); Cm['diagonal'][3][2 + 4] ^= 1 +need(replay(Cm, IM, Dv, a2) > 0 and Cm['diagonal'][3][2:] != mask_inc(3, R), 'control: a wrong mask bit in the caller target fails the replay and the mask comparison') +need(all(C['diagonal'][c][2:] == mask_inc(c, Rm) for c in range(40)), 'note (asserted): the composition reads the root only through the masks, so a wrong X or Y entry does not fail it; the block identities above do') + +# ---- (4) invoice --------------------------------------------------------------------------------- +def kappa(T, P): + rs = sorted(set(T) | set(P)); ln = {r: D(r).ln() for r in rs} + e = lambda k: sum((D(T.get(r, 0)) - D(P.get(r, 0))) * (ln[r] * (1 - k)).exp() for r in rs) + lo, hi = D('1e-6'), D('0.05') + for _ in range(220): + m = (lo + hi) / 2 + if e(m) > 0: lo = m + else: hi = m + return lo +def root_fields(RR): + S_ = RR['stages']; Xr = RR['X']; Yr = RR['Y']; F = [] + for c in range(RR['n']): + ms = [k for k, s_ in enumerate(S_) if c in set(s_['mask'])] + F.append((ms, [k for k in ms if any(Q(Yr[u][c]) != 0 for u in S_[k]['units'])])) + dot = lambda a_, b_: sum(Q(u) * Q(v) for u, v in zip(a_, b_) if Q(u) and Q(v)) + planes = [] + for s_ in S_: + u, v = s_['units']; planes.append(2 if dot(Yr[u], Xr[v]) == 0 and dot(Yr[v], Xr[u]) == 0 else 1) + return F, planes, RR['N'] - sum(len(s_['units']) for s_ in S_) +def outer(F, planes, thin, nst=18): + T = Counter(); P = Counter(); hc = Counter() + for ms, host in F: + T[8 * len(ms) + 1] += 104 + for k in host: hc[k] += 1 + run = 0; prev = None + for k in ms: + if k in host: + if run: P[8 * run] += 104 + run = 0; prev = None; continue + if prev is not None and k == prev + 1: run += 1 + else: + if run: P[8 * run] += 104 + run = 1 + prev = k + if run: P[8 * run] += 104 + for k in range(nst): + if hc[k] > 2 * planes[k]: P[8] += 104 * (hc[k] - 2 * planes[k]) + P[1] += 104 * thin + return T, P +def invoice(hel_, paid_, RR): + F, planes, thin = root_fields(RR); T, P = outer(F, planes, thin) + for r, k in hel_.items(): T[r] += 18 * k + for r, k in paid_.items(): P[r] += 18 * k + return T, P +def census(Wx): + nx = len(Wx['initial']); lx = set(Wx['live']); mx = lx | {r_ + 112 for r_ in lx} + if Wx.get('hosted', {}).get('X2'): mx |= set(Wx['hosted']['X2']) | set(Wx['hosted']['Y2']) + dx = [len(b_) for b_ in Wx['frames']] + return (Counter(dx[Wx['final'][r_]] - dx[Wx['initial'][r_]] for r_ in range(nx) if r_ not in mx), Counter(abs(dx[e_[3]] - dx[e_[2]]) for e_ in Wx['program'] if e_[0] == 'MOVE')) +bi = json.load(open(data('base_invoice.json'))) +T0 = Counter({int(k): v for k, v in bi['targets'].items()}); P0 = Counter({int(k): v for k, v in bi['paid'].items()}) +chain = [(list(range(18)), list(range(18)))] + [(list(range(i, 9)), [i]) for i in range(9)] + [(list(range(9, 10 + m)), [9 + m]) for m in range(9)] + [([], [])] +Tc_, Pc_ = outer(chain, [1] * 18, 3) +Tb, Pb = Counter(Tc_), Counter(Pc_) +for r_, k_ in bi['helpers'].items(): Tb[int(r_)] += 18 * k_ +for r_, k_ in bi['local_paid'].items(): Pb[int(r_)] += 18 * k_ +need(+Tb == T0 and +Pb == P0, 'control: the same code rebuilds the #6833 invoice term for term') +kb = kappa(T0, P0) +need(abs(kb - D(bi['kappa_literal'])) < D('1e-17'), 'control: #6833 kappa %s' % str(kb)[:20]) +Fn, plan_n, thin_n = root_fields(R) +need(all(p_ == 2 for p_ in plan_n) and thin_n == 6, 'root: every stage holds two separate planes (units of the two chains have zero cross terms); 6 thin units') +To, Po = outer(Fn, plan_n, thin_n) +need(To == Counter({r_: 2 * v_ for r_, v_ in Tc_.items()}) and Po == Counter({r_: 2 * v_ for r_, v_ in Pc_.items()}), 'the root part of the invoice is exactly twice the #6833 chain root part (no root discount: nothing is fused, each chain pays its own idles)') +Tn, Pn = invoice(hel, paid, R) +kn = kappa(Tn, Pn) +need(abs(kn - D('0.00351406186742169')) < D('1e-16'), 'new kappa %s' % str(kn)[:22]) +Wp = json.load(gzip.open(data('prior_word_6889.json.gz'), 'rt')); Rp = json.load(open(data('prior_root_6889.json'))) +hp, pp = census(Wp); Tp, Pp = invoice(hp, pp, Rp); kp = kappa(Tp, Pp) +need(abs(kp - D('0.00345694177515779')) < D('1e-17'), 'control: the #6889 word through its own hosted root and the same code gives %s (its crossing)' % str(kp)[:22]) +print(' gain over #6889: %.4f%% (exactly kappa_new / kappa_6889 - 1 = %s)' % (100 * float(kn / kp - 1), str(100 * (kn / kp - 1))[:9])) +S = sum(r * (Tn.get(r, 0) - Pn.get(r, 0)) for r in set(Tn) | set(Pn)) +need(S == 1520, 'rank-mass surplus S = %d (104*34 - 36*56, net of the 56 owned-ascent mass per call)' % S) +Tc = Counter(); Pc = Counter(); nh = 0 +for e in C['events']: + if e[0] == 'HOST2': Tc.update(hel); Pc.update(paid); nh += 1 + elif e[0] == 'QUERY': Pc[1] += 104 + elif e[0] == 'IDLE_ONE': Pc[8 * len(e[2])] += 104 + elif e[0] == 'IDLE': raise SystemExit('FAIL unexpected IDLE') +for tt in C['diagonal']: Tc[int(tt[0] % 2) + 8 * sum(tt[2:])] += 104 +need(nh == 18 and +Tc == +Tn and +Pc == +Pn, 'emitted caller events recount the same invoice (18 native calls, 6 thin queries, one-site idles)') +need(sum(e[0] == 'LAMBDA' for e in C['events']) == 124, 'LAMBDA events in the caller: 124 (62 per chain)') +lam_neg = S - 124 * 104 +need(lam_neg < 0, 'review question, stated plainly: if each LAMBDA had to be paid as a rank-1 job per port, S = %d - 124*104 = %d < 0 and no crossing exists (#6889: 1520 - 82*104 = %d); kappa rests on pricing LAMBDA as ordinary work, as in every caller of this line' % (S, lam_neg, 1520 - 82 * 104)) + +# ---- (5) raw bound, growth, alphabet -------------------------------------------------------------- +def swaps(sel): + wanted = set(range(len(sel))); return len(list(zip(sorted(set(sel) - wanted), sorted(wanted - set(sel))))) +amb = C['ambient_rank']; roles = C['roles']; evs = C['events']; main_maps = 0 +for role, (qp, zero, *sel) in enumerate(C['diagonal']): + axes = ([0] if qp else []) + [x_ for st, y_ in enumerate(sel, 1) if y_ for x_ in range(9 + 8 * (st - 1), 9 + 8 * st)] + main_maps += 104 * (2 * swaps(axes) + 2 * bool(qp) + int(qp == -1)) +idle_ex = qmaps = 0 +for e in evs: + if e[0] == 'IDLE_ONE': idle_ex += 104 * 2 * swaps([x_ for st in e[2] for x_ in range(9 + 8 * (st - 1), 9 + 8 * st)]) + elif e[0] == 'QUERY': qmaps += 104 * (2 + int(e[3] == -1)) +rest = 32 * roles * 104 * len(evs) + sum(e[0] == 'QUERY' for e in evs) * 16 * 104 + roles * 104 * 26 + 1000 * main_maps + 1000 * idle_ex + 1000 * qmaps +allow = upper = 0 +for e in W['program']: + if e[0] in ('INIT', 'CLEAR'): allow += 2 + elif e[0] == 'SCALE': + q = Q(e[2]); a_, d_ = abs(q.numerator), q.denominator + allow += 2 * (abs(a_.bit_length() - d_.bit_length()) + int(q < 0)); upper += 4 * (a_.bit_length() + d_.bit_length() + 1) + elif e[0] in ('ADD', 'COPY'): + q = Q(e[3]); a_, d_ = abs(q.numerator), q.denominator + allow += 2 * (3 + a_.bit_length() - 1 + bin(a_).count('1') + d_.bit_length() - 1); upper += 4 * (a_.bit_length() + bin(a_).count('1') + d_.bit_length() + 1) +routes = (sum(paid.values()) + 2 * sum(hel.values()) + 416 + 8 * 104 + 4 * life) * 1000 # main boundary terms doubled for the second planes +per_call = allow + routes; per_up = upper + routes +raw_lit, raw_act, raw_rev = 18 * 10 ** 7 + rest, 18 * per_call + rest, 18 * per_up + rest +print(' raw pieces: caller+thin+outputs+idle adapters+query adapters = %d; per call (word scalar + routes) = %d (allowance) or %d (reviewed upper) against the displayed 10^7' % (rest, per_call, per_up)) +need((raw_lit, raw_act, raw_rev) == (963421184, 965490968, 971071328) and max(raw_lit, raw_act, raw_rev) < 10 ** 9, 'raw bound, all three definitions below 10^9: literal %d, actual per-call work %d, reviewed scalar upper %d (margins %d, %d, %d); the reviewed-upper line is under 10^9 for the first time in this line of work' % (raw_lit, raw_act, raw_rev, 10 ** 9 - raw_lit, 10 ** 9 - raw_act, 10 ** 9 - raw_rev)) +Rm_paid = sum(r_ * v_ for r_, v_ in Pn.items()) +print(' CONSTANT SUBSTITUTION (FINITE-PRECOMPILATION.md:278-283): events %d; scalar allowance %d; reviewed scalar upper %d; routes %d; per call %d or %d; caller envelope %d; raw upper %d (allowance) or %d (reviewed upper); paid rank mass R = %d; growth bound 2^(raw + R f) = 2^(%d + %d f) on the conservative count' % (len(W['program']), allow, upper, routes, per_call, per_up, 32 * roles * 104 * len(evs), raw_act, raw_rev, Rm_paid, raw_rev, Rm_paid)) +src_ep = open(os.path.join(HERE, 'retained', 'runtime', 'endpoint.py')).read() +need(not any(t_ in src_ep for t_ in ('10**9', '10 ** 9', '10**7', '10 ** 7', '1e9')), 'the outer ledger source contains no scalar-work or 10^9 term') +def logsum(Wx): return sum(math.log2(1 + float(abs(Q(e_[3])))) for e_ in Wx['program'] if e_[0] in ('ADD', 'COPY')) +l89 = logsum(Wp) +print(' GROWTH (productive-controller PROOF.md section 5: fewer than 26000 events, |q|+1 < 2^16, local bound 2^(16*26000) = 2^416000):') +print(' events %d (#6889 word 164533), both above the 26000 of that text; sum of log2(1+|q|) over the ADD coefficients %d (#6889 %d) against 416000; peak |row entry| on any prefix 2^%.1f; peak row denominator 2^%d; coefficient bits numerator <= %d, denominator <= %d; largest |q| %s' % (len(W['program']), round(logq), round(l89), math.log2(float(pmax)), dmaxb, nbits, dbits, maxq)) +need(round(logq) == 27718 and round(l89) == 282880 and maxq == 45, 'sum of log2(1+|q|): %d here and %d in the #6889 word, both below 416000; largest |q| %s, far below 2^16' % (round(logq), round(l89), maxq)) +oy = [i_ for i_, e_ in enumerate(W['program']) if e_[0] == 'ADD' and e_[1] >= n and e_[2] in set(Y2)] +oyY = [i_ for i_, e_ in enumerate(W['program']) if e_[0] == 'ADD' and e_[1] >= n and e_[2] in Y] +need(oy == [14676, 14744, 14746, 14768, 14770, 14774, 14776, 18579] and oyY == [], 'owned registers reading a main Y2 register: 8 events %s (declared with A6; #6889 had one read of Y, this word none of Y); peak owned fields %d' % (oy, peak)) +big_ = sum(1 for e_ in W['program'] if e_[0] in ('ADD', 'COPY') and abs(Q(e_[3])) >= 2 ** 12) +need(big_ == 0 and maxq + 1 < 2 ** 16, 'alphabet: no ADD has |q| >= 2^12 (largest %s)' % maxq) + +# ---- (6) outer conditions ---------------------------------------------------------------------- +E, SE, OUT = ldmod(os.path.join(HERE, 'retained', 'runtime', 'intervals.py'), 'intervals'), ldmod(os.path.join(HERE, 'retained', 'runtime', 'second_intervals.py'), 'second_intervals'), ldmod(os.path.join(HERE, 'retained', 'runtime', 'endpoint.py'), 'endpoint') +BITF = json.load(open(os.path.join(HERE, 'retained', 'bit', 'FRAGMENT-BIT-ADMISSION.json'))) +need(hashlib.sha256(open(os.path.join(HERE, 'retained', 'bit', 'FRAGMENT-BIT-ADMISSION.json'), 'rb').read()).hexdigest() == '86955dcd74bc3fa1a940419474d45054fa7b0366b71b242568680366923d9311' and BITF['status'] == 'PASS_TWO_FRAGMENTS_BIT_ORDINARY_00376669' and Q(BITF['ordinary_admitted']) == PIN, 'BIT pin %s = ordinary_admitted of the pinned #6726 admission file (status %s); not re-derived here' % (float(PIN), BITF['status'])) +KAPPA, TESTED = Q('.00351406'), Q('.00351406007') +LOW, UP = Q('.003514061867421'), Q('.003514061867422') +Tq = Counter({r: v for r, v in Tn.items() if v}); Pq = Counter({r: v for r, v in Pn.items() if v}) +need(KAPPA < TESTED < LOW < UP and TESTED < PIN and Q(BITF['raw_crossing'][0]) > Q(BITF['raw_tested']) > PIN, 'claim %s, tested %s, both strictly below the raw crossing %s; BIT side: raw crossing > raw tested saving > pin > tested price' % (float(KAPPA), float(TESTED), str(kn)[:19])) +print(' BIT margins: pin - tested complex price = %.3e; raw BIT tested saving - pin = %.1e; raw BIT crossing lower bound - raw BIT tested saving = %.3e' % (float(PIN - TESTED), float(Q(BITF['raw_tested']) - PIN), float(Q(BITF['raw_crossing'][0]) - Q(BITF['raw_tested'])))) +for name, k, pos in (('lower', LOW, 1), ('upper', UP, -1), ('tested', TESTED, 1)): + a, b = E.moment(Tq, 1 - k), E.moment(Pq, 1 - k); first = (a[0] - b[1], a[1] - b[0]) + tl, th = SE.moment(Tq, k); pl, ph = SE.moment(Pq, k); second = (tl - ph, th - pl) + need((first[0] > 0 and second[0] > 0) if pos > 0 else (first[1] < 0 and second[1] < 0), 'both interval engines (rational interval arithmetic, no Decimal): sign of the margin at the %s price endpoint' % name) +signed = Counter(Tq); signed.subtract(Pq); d = Q(0) +for r, c in signed.items(): + lg = E.log_bounds(r); d -= c * (E.mul(E.power(r, 1 - PIN), lg)[0] if c >= 0 else r * lg[1]) +need(d < 0, 'unique raw crossing through the BIT pin (derivative upper bound negative at the pin)') +cutoff, floor, power, offset = 11, 12, 1920, Q(1, 7); LP = 2134 +tt_ = 1 - TESTED; target, paidm = E.moment(Tq, tt_), E.moment(Pq, tt_) +alpha = E.divide(paidm, target); gamma = E.divide(E.moment(Pq, tt_ + offset), E.mul(E.power(cutoff, offset), target)) +delta = E.divide((Q(sum(Tq.values()) * floor),) * 2, E.mul(E.power(cutoff, TESTED), target)) +reserve, decay = Q(1, 10 ** 27), Q(31, 32) +need(alpha[1] < 1 - reserve and gamma[1] < decay and delta[1] < decay, 'tail ratios (interval engine): alpha %.12f gamma %.4f delta %.4f (cutoff 11, floor 12, offset 1/7, power 1920)' % (float(alpha[1]), float(gamma[1]), float(delta[1]))) +normalized = 1 / (1 + power * reserve) + 4 * decay ** power +need(normalized < 1, 'composite bound (predecessor pricing.py:211): 1/(1+power*reserve) + 4*decay^power < 1 at power 1920 (excess over the first term %.2e)' % float(4 * decay ** power)) +maxT = max(Tq); quarter = E.power(maxT, Q(power, 4) * TESTED); factor = E.mul(E.mul(quarter, quarter), E.mul(quarter, quarter)) +eta = E.scale(E.divide((Q(1), Q(1)), factor), tt_) +need(eta[0] > Q(63, 64) ** LP and factor[1] < 2 ** LP and cutoff ** 64 < floor ** 63 and 2 * (cutoff ** power) ** 64 <= (maxT ** power) ** 63, 'compiler complement capacity and shifted exits at logarithm power %d (max target rank %d)' % (LP, maxT)) +lp_ = LP +while eta[0] > Q(63, 64) ** (lp_ - 1): lp_ -= 1 +need(lp_ == 2133 and Q(63, 64) ** 2100 > eta[0], 'logarithm power: the smallest admissible value at this price is %d, written as %d (2100 FAILS here: it is a free parameter, LOG-MAJORANT.md:110-122, and the wall of 2100 is at a tested price near .0034607, below this claim)' % (lp_, LP)) +gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'compiler grid: (tested-kappa)/7 = %s' % gap) +step = gap.denominator +wins = lambda j: (step * j + 1) ** LP < 2 ** j +lo_, hi_ = 1, 2 +while not wins(hi_): lo_, hi_ = hi_, 2 * hi_ +while hi_ - lo_ > 1: + m = (lo_ + hi_) // 2 + if wins(m): hi_ = m + else: lo_ = m +need(step * hi_ > 8 * power and wins(hi_) and not wins(hi_ - 1), 'explicit uniform threshold H=%d (logarithm power %d)' % (step * hi_, LP)) +params = {'kappa': KAPPA, 'tested_saving': TESTED, 'complex_uniform_saving': KAPPA + 6 * gap, 'b': KAPPA + 5 * gap, 'a': KAPPA + 4 * gap, 'q': KAPPA + 3 * gap, 'bit_saving': PIN, + 'epsilon': 1 - gap, 'beta': 1 - 3 * gap, 'r0': gap / 10, 'stop': gap, 'layout': gap, 'd': gap} +led = OUT.ledger(params); led['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - Q(1, 250)) +need(len(led['strict_checks']) == 54 and len(led['functional_checks']) == 4 and all(v > 0 for k in ('strict_checks', 'functional_checks') for v in led[k].values()), 'outer inventory: 54 strict and 4 functional inequalities all positive at the pin') +PINS = [('main admitted', Q('.0034'), False), ('.00343', Q('.00343'), False), ('main ordinary stock', Q('.0034363538396'), False), ('#5421', Q('.00344412'), False), + ('#4760', Q('.0034597'), False), ('#4814', Q('.003475458'), False), ('#5512', Q('.003483969976'), False), ('#6726 (the pin used)', PIN, True)] +for lab_, pin_, want_ in PINS: # the ledger needs bit_saving > kappa + 4 gap = .00351406004 + L_ = OUT.ledger(dict(params, bit_saving=pin_)); L_['functional_checks']['actual_new_BIT_stock_sublinear'] = params['beta'] * (1 - Q(1, 250)) + ok_ = TESTED < pin_ and all(v > 0 for kk in ('strict_checks', 'functional_checks') for v in L_[kk].values()) + need(ok_ == want_, 'ledger at the BIT saving %s (%s): %s%s' % (float(pin_), lab_, 'all 54 + 4 positive' if ok_ else 'fails', ', margin over the tested price %.3e' % float(pin_ - TESTED) if ok_ else '')) +need(any(v <= 0 for kk in ('strict_checks', 'functional_checks') for v in OUT.ledger(dict(params, bit_saving=params['a'] - Q(1, 10 ** 12)))[kk].values()), 'control: a BIT saving just below kappa + 4 gap (%s) is rejected' % float(params['a'])) +plus = [(7, 1), (3, 1), (5, 1)]; minus = [(9, 1), (4, 1), (1, 2)] +def dlog(terms): + lo = hi = Q(0) + for x, c in terms: + a_ = E.mul((Q(x), Q(x)), E.log_bounds(x)); lo += c * a_[0]; hi += c * a_[1] + return lo, hi +def d2log(terms): + hi = Q(0) + for x, c in terms: + a_ = E.mul(E.mul((Q(x), Q(x)), E.log_bounds(x)), E.log_bounds(x)); hi += c * a_[1] + return hi +dpl, dmi = dlog(plus), dlog(minus); d1 = (dpl[0] - dmi[1], dpl[1] - dmi[0]); Mq = d2log(plus) + d2log(minus) +need(d1[1] + PIN * Mq < 0, 'input-lift saving lemma of #6833 (pricing.py:128-156), cap moved to the pin: g prime negative on 1-pin..1 (its crude bound holds to about .0037765)') +for nm, k_ in (('claim', KAPPA), ('tested', TESTED)): + tl_ = 1 - k_; gl = sum(c * E.power(x, tl_)[0] for x, c in plus) - sum(c * E.power(x, tl_)[1] for x, c in minus) + need(gl > 0 and k_ * (-d1[1]) - k_ * k_ * Mq / 2 > 0, 'input-lift saving positive at the %s price' % nm) + +# ---- declared departures ----------------------------------------------------------------------- +print('DEPARTURES (class; exact count here):') +for cls, what in ( + ('new family: reducible root', 'the root is literally two #6833 chain roots on orthogonal coordinates, t = 0 at every stage, Gram digraph with two components; the family lines t != 0 (ROOTAUDIT-style rootcheck line "hosted t not 0, not -1"), alpha and beta dyadic units, and "Gram digraph strongly connected" (added by the #6883 root_check.py, not a SPEC line) do not hold. What the outer theorem requires is the unit identity and whole-job credit, which root_check.py re-proves (SPEC-level lines all pass).'), + ('new event', 'HOST2: one native contact per stage that serves both chains (18 events, forward contact q^-1 on the first plane, q on the second, 124 LAMBDA events with the second chain flipped).'), + ('new form', 'same-label second mains: X2 and Y2 carry the same initial and final frame labels as X and Y (asserted above); 4 main registers per port, 416 mains; per-port boundary terms are doubled in the raw count.'), + ('convention (A6, load-bearing)', 'owned ascent: 23 owned rises (rank mass 56) against native.py:55 / local.py:126; peak owned 30; 8 owned reads of Y2 (events %s). No ascent, no word.' % oy), + ('verifier', 'endpoint literal native.py:75-77 / local.py:168: the target is X=x, Y=x+y, X2=x2-y2, Y2=y2 on 104 ports.'), + ('verifier', 'events %d, public %d, owned roles %d, lifetimes %d, peak owned %d against local.py:52,54,103 and pricing.py:84-87 literals; per-call scalar work %d against the displayed 10^7 (pricing.py:93).' % (len(W['program']), n, NO, life, peak, per_call)), + ('convention', 'LAMBDA (124 events) and IDLE_ONE (32 events) inherited from the open callers #6726 and #6716/#6763; not on main; the price of LAMBDA is a review question (above).'), + ('assumption', 'dirty owned erasure (%d erasures): the owned_erasure assumption, unchanged.' % dirty)): + print(' [%s] %s' % (cls, what)) +need(True, 'departures listed') +print('PASS_P104_TWO_CHAIN_SHARED_NATIVE') diff --git a/research/p104-two-chain-shared-native/cover_check.py b/research/p104-two-chain-shared-native/cover_check.py new file mode 100644 index 0000000000..eabfa670e8 --- /dev/null +++ b/research/p104-two-chain-shared-native/cover_check.py @@ -0,0 +1,96 @@ +#!/usr/bin/env python3 +"""What the word is made of, counted on the word and compared with the #6889 word (standard library). python3 -I -B cover_check.py +Counts the second main planes and the helpers they share with the first planes, the events that touch second mains, and runs controls on a random-evaluation replay (mod 2^61-1): +a wrong weight (x2), a missing event and an event taken twice, on every sampled event that reads or writes a second main, are all rejected.""" +import gzip, json, os, random +from collections import Counter +from fractions import Fraction as Q +HERE = os.path.dirname(os.path.abspath(__file__)) +def need(ok, msg): + if not ok: raise SystemExit('FAIL ' + msg) + print('PASS', msg, flush=True) +def load(n): return json.load(gzip.open(os.path.join(HERE, 'data', n), 'rt')) +new, old = load('word.json.gz'), load('prior_word_6889.json.gz') +H = new['hosted']; X2 = H['X2']; Y2 = H['Y2']; live = new['live'] +X = set(live); Y = {r + 112 for r in live}; M1 = X | Y; M2 = set(X2) | set(Y2); n = len(new['initial']) +P = new['program']; lo = next(i for i, e in enumerate(P) if e[0] == 'MOVE'); hi = max(i for i, e in enumerate(P) if e[0] == 'MOVE') +Po = old['program'] +dim = [len(b) for b in new['frames']] +hel_n = [r for r in range(n) if r not in M1 and r not in M2] +no = len(old['initial']); mo = set(old['live']) | {r + 112 for r in old['live']}; hel_o = [r for r in range(no) if r not in mo] +print(' #6889 word: events %d, public %d (%d mains, %d helpers), MOVEs %d' % (len(Po), no, len(mo), len(hel_o), sum(e[0] == 'MOVE' for e in Po))) +print(' this word : events %d, public %d (%d mains, %d helpers), MOVEs %d' % (len(P), n, len(M1) + len(M2), len(hel_n), sum(e[0] == 'MOVE' for e in P))) +need(len(M1) == 208 and len(M2) == 208 and len(M1 | M2) == 416 and n == 1375 and len(hel_n) == 959 and len(hel_o) == 1153, 'four main registers per port (416 mains, 959 helpers, 1375 public); the #6889 word has 208 mains and 1153 helpers') +mv_by = Counter() +for e in P: + if e[0] == 'MOVE': + mv_by['second main' if e[1] in M2 else 'first main' if e[1] in M1 else 'owned' if e[1] >= n else 'helper'] += 1 +need(mv_by['first main'] == mv_by['second main'] and mv_by['first main'] > 0, 'each plane pays its own moves: first-plane mains %d MOVEs, second-plane mains %d MOVEs (no move is shared or fused)' % (mv_by['first main'], mv_by['second main'])) +need(all(new['initial'][x2] == new['initial'][x] and new['final'][x2] == new['final'][x] and new['initial'][y2] == new['initial'][x + 112] and new['final'][y2] == new['final'][x + 112] for x, x2, y2 in zip(live, X2, Y2)), 'second mains carry the same initial and final frame labels as the first mains (declared)') +touch = [i for i, e in enumerate(P) if e[0] == 'ADD' and (e[1] in M2 or e[2] in M2)] +share = Counter() +for i in touch: + e = P[i]; other = e[2] if e[1] in M2 else e[1] + if other in M1: share['plane 2 with plane 1 directly'] += 1 + elif other < n: share['plane 2 with a helper'] += 1 + else: share['plane 2 with an owned register'] += 1 +print(' events that read or write a second main: %d (%s)' % (len(touch), dict(share))) +direct = [i for i in touch if (P[i][1] in M2 and P[i][2] in M1) or (P[i][2] in M2 and P[i][1] in M1)] +need(direct and all(i < lo or i > hi for i in direct) and len(direct) == share['plane 2 with plane 1 directly'], 'the %d events that couple a first-plane main with a second-plane main directly all lie in the two gate blocks (before the first MOVE or after the last, at frames Z and V); inside the core the planes meet only through helpers (%d events) and owned registers (%d events)' % (len(direct), share['plane 2 with a helper'], share['plane 2 with an owned register'])) +H1 = set(); H2 = set() +for e in P[lo:hi + 1]: + if e[0] != 'ADD': continue + for a, b in ((e[1], e[2]), (e[2], e[1])): + if b in M1 and a < n and a in set(hel_n): H1.add(a) + if b in M2 and a < n and a in set(hel_n): H2.add(a) +both = H1 & H2 +need(len(both) > 0 and len(H1 | H2) <= len(hel_n), 'helpers with ADD events directly against mains of both planes: %d of %d (one field, one job, one credit each; this counts direct adjacency only, not the helper rows the replay shows to hold inputs of both chains)' % (len(both), len(hel_n))) +# helpers touching 9+ ports in the #6889 word (the statement of the baseline) +def ports_of(W): + liv = W['live']; pr = {} + for r, q in zip(liv, W['ports']): pr[r] = q; pr[r + 112] = q + return pr +po = ports_of(old); hs = {} +for e in Po: + if e[0] == 'ADD': + for a, b in ((e[1], e[2]), (e[2], e[1])): + if b in po and a < no and a not in mo: hs.setdefault(a, set()).add(po[b]) +need(sum(1 for r in hel_o if len(hs.get(r, ())) >= 9) == 844, 'in the #6889 word 844 of the %d helpers already read or write mains of 9 or more ports' % len(hel_o)) +# random-evaluation replay +M = (1 << 61) - 1 +al, be, a2, b2 = Q(H['alpha']), Q(H['beta']), Q(H['alpha2']), Q(H['beta2']) +fm = lambda q: (lambda f: f.numerator % M * pow(f.denominator, M - 2, M) % M)(Q(q)); x2of = dict(zip(X2, Y2)); X2s = set(X2); Y2s = set(Y2) +def endpoint_ok(prog, K=2, seed=3): + NR = n + new['owned_fields']; rnd = random.Random(seed) + v0 = [[rnd.randrange(M) for _ in range(K)] for _ in range(n)]; v = [x[:] for x in v0] + [[0] * K for _ in range(new['owned_fields'])] + for e in prog: + op = e[0] + if op in ('INIT', 'CLEAR'): v[e[1]] = [0] * K + elif op == 'SCALE': + c = fm(e[2]); v[e[1]] = [a * c % M for a in v[e[1]]] + elif op in ('ADD', 'COPY'): + c = fm(e[3]); s = v[e[2]] + if op == 'COPY': v[e[1]] = [c * b % M for b in s] + else: v[e[1]] = [(a + c * b) % M for a, b in zip(v[e[1]], s)] + for r in range(NR): + if r >= n: ex = [0] * K + elif r in X: ex = list(v0[r]) + elif r in Y: ex = [(v0[r - 112][k] + v0[r][k]) % M for k in range(K)] + elif r in X2s: ex = [(v0[r][k] + fm(a2) * v0[x2of[r]][k]) % M for k in range(K)] + elif r in Y2s: ex = list(v0[r]) + else: ex = v0[r] + if v[r] != ex: return False + return True +need(endpoint_ok(P), 'random-evaluation replay accepts the word (endpoint exact on every public and owned row, both planes)') +rnd = random.Random(9); smp = rnd.sample(touch, 12); bw = bm = bd = 0 +for i in smp: + e = list(P[i]); e[3] = str(Q(e[3]) * 2) + bw += not endpoint_ok(P[:i] + [e] + P[i + 1:]) + bm += not endpoint_ok(P[:i] + P[i + 1:]) + bd += not endpoint_ok(P[:i + 1] + [P[i]] + P[i + 1:]) +need(bw == bm == bd == len(smp), 'controls on %d sampled events that read or write a second main: a wrong weight (x2), a missing event and an event taken twice are all rejected' % len(smp)) +adds = [i for i in range(lo, hi + 1) if P[i][0] == 'ADD'] +need(not endpoint_ok(P[:adds[0]] + P[adds[0] + 1:]), 'control: removing the first core ADD is rejected') +sample = rnd.sample(adds, 12); broke = sum(not endpoint_ok(P[:i] + P[i + 1:]) for i in sample) +need(broke >= 9, 'control: removing any one of 12 sampled core ADDs breaks the endpoint in %d cases' % broke) +print('PASS_COVER_CHANGES') diff --git a/research/p104-two-chain-shared-native/data/base_invoice.json b/research/p104-two-chain-shared-native/data/base_invoice.json new file mode 100644 index 0000000000..f2a6958ee2 --- /dev/null +++ b/research/p104-two-chain-shared-native/data/base_invoice.json @@ -0,0 +1,61 @@ +{ + "helpers": { + "1": 14, + "2": 8, + "3": 4, + "4": 109, + "5": 17, + "6": 3, + "7": 10, + "8": 40, + "9": 359 + }, + "kappa_literal": "0.00337180047549672", + "local_paid": { + "1": 2234, + "2": 454, + "3": 489, + "4": 110, + "5": 152, + "6": 7, + "7": 9, + "8": 1 + }, + "paid": { + "1": 40524, + "16": 208, + "2": 8172, + "24": 208, + "3": 8802, + "32": 208, + "4": 1980, + "40": 208, + "48": 208, + "5": 2736, + "56": 208, + "6": 126, + "64": 208, + "7": 162, + "8": 226 + }, + "targets": { + "1": 356, + "145": 104, + "17": 208, + "2": 144, + "25": 208, + "3": 72, + "33": 208, + "4": 1962, + "41": 208, + "49": 208, + "5": 306, + "57": 208, + "6": 54, + "65": 208, + "7": 180, + "73": 208, + "8": 720, + "9": 6670 + } +} \ No newline at end of file diff --git a/research/p104-two-chain-shared-native/data/caller.json b/research/p104-two-chain-shared-native/data/caller.json new file mode 100644 index 0000000000..e1e162bbf1 --- /dev/null +++ b/research/p104-two-chain-shared-native/data/caller.json @@ -0,0 +1 @@ +{"schema": "decoupled-root-caller/1", "roles": 40, "stages": 18, "ambient_rank": 153, "events": [["ADD", 0, 1, "-1"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 1, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["ADD", 1, 0, "1"], ["ADD", 1, 2, "-2"], ["ADD", 0, 2, "-1"], ["SWAP", 1, 2], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["ADD", 20, 21, "1"], ["SCALE", 21, "-1"], ["ADD", 21, 20, "1"], ["ADD", 21, 22, "-2"], ["ADD", 20, 22, "-1"], ["SWAP", 21, 22], ["ADD", 22, 20, "-2"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 2, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["IDLE_ONE", 2, [2, 3, 4, 5, 6, 7, 8, 9]], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 1, 2], ["ADD", 2, 0, "1"], ["ADD", 1, 0, "2"], ["ADD", 2, 3, "-2"], ["ADD", 1, 3, "-2"], ["ADD", 0, 3, "-1"], ["SWAP", 2, 3], ["SWAP", 1, 2], ["ADD", 3, 0, "-2"], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["IDLE_ONE", 22, [2, 3, 4, 5, 6, 7, 8, 9]], ["ADD", 20, 21, "1"], ["SCALE", 21, "-1"], ["SWAP", 21, 22], ["ADD", 22, 20, "1"], ["ADD", 21, 20, "2"], ["ADD", 22, 23, "-2"], ["ADD", 21, 23, "-2"], ["ADD", 20, 23, "-1"], ["SWAP", 22, 23], ["SWAP", 21, 22], ["ADD", 23, 20, "-2"], ["ADD", 22, 20, "-2"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 3, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["IDLE_ONE", 3, [3, 4, 5, 6, 7, 8, 9]], ["SWAP", 2, 3], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 1, 3], ["ADD", 3, 0, "1"], ["ADD", 2, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 3, 4, "-2"], ["ADD", 2, 4, "-2"], ["ADD", 1, 4, "-2"], ["ADD", 0, 4, "-1"], ["SWAP", 3, 4], ["SWAP", 2, 3], ["SWAP", 1, 2], ["ADD", 4, 0, "-2"], ["ADD", 3, 0, "-2"], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["IDLE_ONE", 23, [3, 4, 5, 6, 7, 8, 9]], ["SWAP", 22, 23], ["ADD", 20, 21, "1"], ["SCALE", 21, "-1"], ["SWAP", 21, 23], ["ADD", 23, 20, "1"], ["ADD", 22, 20, "2"], ["ADD", 21, 20, "2"], ["ADD", 23, 24, "-2"], ["ADD", 22, 24, "-2"], ["ADD", 21, 24, "-2"], ["ADD", 20, 24, "-1"], ["SWAP", 23, 24], ["SWAP", 22, 23], ["SWAP", 21, 22], ["ADD", 24, 20, "-2"], ["ADD", 23, 20, "-2"], ["ADD", 22, 20, "-2"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 4, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["IDLE_ONE", 4, [4, 5, 6, 7, 8, 9]], ["SWAP", 3, 4], ["SWAP", 2, 4], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 1, 4], ["ADD", 4, 0, "1"], ["ADD", 3, 0, "2"], ["ADD", 2, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 4, 5, "-2"], ["ADD", 3, 5, "-2"], ["ADD", 2, 5, "-2"], ["ADD", 1, 5, "-2"], ["ADD", 0, 5, "-1"], ["SWAP", 4, 5], ["SWAP", 3, 4], ["SWAP", 2, 3], ["SWAP", 1, 2], ["ADD", 5, 0, "-2"], ["ADD", 4, 0, "-2"], ["ADD", 3, 0, "-2"], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["IDLE_ONE", 24, [4, 5, 6, 7, 8, 9]], ["SWAP", 23, 24], ["SWAP", 22, 24], ["ADD", 20, 21, "1"], ["SCALE", 21, "-1"], ["SWAP", 21, 24], ["ADD", 24, 20, "1"], ["ADD", 23, 20, "2"], ["ADD", 22, 20, "2"], ["ADD", 21, 20, "2"], ["ADD", 24, 25, "-2"], ["ADD", 23, 25, "-2"], ["ADD", 22, 25, "-2"], ["ADD", 21, 25, "-2"], ["ADD", 20, 25, "-1"], ["SWAP", 24, 25], ["SWAP", 23, 24], ["SWAP", 22, 23], ["SWAP", 21, 22], ["ADD", 25, 20, "-2"], ["ADD", 24, 20, "-2"], ["ADD", 23, 20, "-2"], ["ADD", 22, 20, "-2"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 5, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["IDLE_ONE", 5, [5, 6, 7, 8, 9]], ["SWAP", 4, 5], ["SWAP", 3, 5], ["SWAP", 2, 5], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 1, 5], ["ADD", 5, 0, "1"], ["ADD", 4, 0, "2"], ["ADD", 3, 0, "2"], ["ADD", 2, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 5, 6, "-2"], ["ADD", 4, 6, "-2"], ["ADD", 3, 6, "-2"], ["ADD", 2, 6, "-2"], ["ADD", 1, 6, "-2"], ["ADD", 0, 6, "-1"], ["SWAP", 5, 6], ["SWAP", 4, 5], ["SWAP", 3, 4], ["SWAP", 2, 3], ["SWAP", 1, 2], ["ADD", 6, 0, "-2"], ["ADD", 5, 0, "-2"], ["ADD", 4, 0, "-2"], ["ADD", 3, 0, "-2"], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["IDLE_ONE", 25, [5, 6, 7, 8, 9]], ["SWAP", 24, 25], ["SWAP", 23, 25], ["SWAP", 22, 25], ["ADD", 20, 21, "1"], ["SCALE", 21, "-1"], ["SWAP", 21, 25], ["ADD", 25, 20, "1"], ["ADD", 24, 20, "2"], ["ADD", 23, 20, "2"], ["ADD", 22, 20, "2"], ["ADD", 21, 20, "2"], ["ADD", 25, 26, "-2"], ["ADD", 24, 26, "-2"], ["ADD", 23, 26, "-2"], ["ADD", 22, 26, "-2"], ["ADD", 21, 26, "-2"], ["ADD", 20, 26, "-1"], ["SWAP", 25, 26], ["SWAP", 24, 25], ["SWAP", 23, 24], ["SWAP", 22, 23], ["SWAP", 21, 22], ["ADD", 26, 20, "-2"], ["ADD", 25, 20, "-2"], ["ADD", 24, 20, "-2"], ["ADD", 23, 20, "-2"], ["ADD", 22, 20, "-2"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 6, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["IDLE_ONE", 6, [6, 7, 8, 9]], ["SWAP", 5, 6], ["SWAP", 4, 6], ["SWAP", 3, 6], ["SWAP", 2, 6], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 1, 6], ["ADD", 6, 0, "1"], ["ADD", 5, 0, "2"], ["ADD", 4, 0, "2"], ["ADD", 3, 0, "2"], ["ADD", 2, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 6, 7, "-2"], ["ADD", 5, 7, "-2"], ["ADD", 4, 7, "-2"], ["ADD", 3, 7, "-2"], ["ADD", 2, 7, "-2"], ["ADD", 1, 7, "-2"], ["ADD", 0, 7, "-1"], ["SWAP", 6, 7], ["SWAP", 5, 6], ["SWAP", 4, 5], ["SWAP", 3, 4], ["SWAP", 2, 3], ["SWAP", 1, 2], ["ADD", 7, 0, "-2"], ["ADD", 6, 0, "-2"], ["ADD", 5, 0, "-2"], ["ADD", 4, 0, "-2"], ["ADD", 3, 0, "-2"], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["IDLE_ONE", 26, [6, 7, 8, 9]], ["SWAP", 25, 26], ["SWAP", 24, 26], ["SWAP", 23, 26], ["SWAP", 22, 26], ["ADD", 20, 21, "1"], ["SCALE", 21, "-1"], ["SWAP", 21, 26], ["ADD", 26, 20, "1"], ["ADD", 25, 20, "2"], ["ADD", 24, 20, "2"], ["ADD", 23, 20, "2"], ["ADD", 22, 20, "2"], ["ADD", 21, 20, "2"], ["ADD", 26, 27, "-2"], ["ADD", 25, 27, "-2"], ["ADD", 24, 27, "-2"], ["ADD", 23, 27, "-2"], ["ADD", 22, 27, "-2"], ["ADD", 21, 27, "-2"], ["ADD", 20, 27, "-1"], ["SWAP", 26, 27], ["SWAP", 25, 26], ["SWAP", 24, 25], ["SWAP", 23, 24], ["SWAP", 22, 23], ["SWAP", 21, 22], ["ADD", 27, 20, "-2"], ["ADD", 26, 20, "-2"], ["ADD", 25, 20, "-2"], ["ADD", 24, 20, "-2"], ["ADD", 23, 20, "-2"], ["ADD", 22, 20, "-2"], ["SWAP", 20, 21], ["SCALE", 21, "-1"], ["LAMBDA", 20, 1], ["HOST2", 7, 1, 0, 20, 21], ["LAMBDA", 20, -1], ["SCALE", 21, "-1"], ["LAMBDA", 0, 1], ["ADD", 0, 1, "-1"], ["IDLE_ONE", 7, [7, 8, 9]], ["SWAP", 6, 7], ["SWAP", 5, 7], ["SWAP", 4, 7], ["SWAP", 3, 7], ["SWAP", 2, 7], ["ADD", 0, 1, "1"], ["SCALE", 1, "-1"], ["SWAP", 1, 7], ["ADD", 7, 0, "1"], ["ADD", 6, 0, "2"], ["ADD", 5, 0, "2"], ["ADD", 4, 0, "2"], ["ADD", 3, 0, "2"], ["ADD", 2, 0, "2"], ["ADD", 1, 0, "2"], ["ADD", 7, 8, "-2"], ["ADD", 6, 8, "-2"], ["ADD", 5, 8, "-2"], ["ADD", 4, 8, "-2"], ["ADD", 3, 8, "-2"], ["ADD", 2, 8, "-2"], ["ADD", 1, 8, "-2"], ["ADD", 0, 8, "-1"], ["SWAP", 7, 8], ["SWAP", 6, 7], ["SWAP", 5, 6], ["SWAP", 4, 5], ["SWAP", 3, 4], ["SWAP", 2, 3], ["SWAP", 1, 2], ["ADD", 8, 0, "-2"], ["ADD", 7, 0, "-2"], ["ADD", 6, 0, "-2"], ["ADD", 5, 0, "-2"], ["ADD", 4, 0, "-2"], ["ADD", 3, 0, "-2"], ["ADD", 2, 0, "-2"], ["SWAP", 0, 1], ["LAMBDA", 0, -1], ["ADD", 20, 21, "-1"], ["IDLE_ONE", 27, [7, 8, 9]], ["SWAP", 26, 27], ["SWAP", 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zmOEbU=Lv2qCU!_`wq0C8lV6h>s3t|zvI_e(=p%t-J1_=As&Yl8t}(oG%tm%*{D&LP`N<~w z?@iB7L*@f%Tdo!XP_@>+IaB1Tx$Y;%ijK0c`i_4TcPy(rK57kLq@Qoc_pS@gb@;eV zKW_);9-EUwbi;&xc#s@`a3nH3?CYj;9XxHCQg=HZ4B6*){$~l%4OFc)wGc;S!i35^ z;&(y+0cp_xk@WwCGwp+({Ka>FOZ-Q*e?u_6&v?18Hge`{lC%w zP4izH{}+d#5|8*zkcAk+0CrIdR24SE5l4K62^Dyd?126a4H1Dq*sUfA%~~9_l)L)T Xh>&|TEG#Sx1_!GN%#P~kr@;Czs~Jls literal 0 HcmV?d00001 diff --git a/research/p104-two-chain-shared-native/ordinary.py b/research/p104-two-chain-shared-native/ordinary.py new file mode 100644 index 0000000000..6185d49e5e --- /dev/null +++ b/research/p104-two-chain-shared-native/ordinary.py @@ -0,0 +1,48 @@ +#!/usr/bin/env python3 +"""Ordinary (non-recursive) raw bound, own recount. python3 -I -B ordinary.py WORD.json.gz CALLER.json +Definitions read from the predecessor review (ordinary()), its adapter inventory and pricing.py:93,102-113.""" +import gzip, json, sys +from fractions import Fraction as Q +from collections import Counter +W = json.load(gzip.open(sys.argv[1], 'rt')); C = json.load(open(sys.argv[2])) +def swaps(sel, dim): + wanted = set(range(len(sel))) + return len(list(zip(sorted(set(sel) - wanted), sorted(wanted - set(sel))))) +n = len(W['initial']); live = set(W['live']); main = live | {r + 112 for r in live} | set(W['hosted']['X2']) | set(W['hosted']['Y2']) +fr = W['frames']; dim = [len(b) for b in fr] +paid = Counter(abs(dim[e[3]] - dim[e[2]]) for e in W['program'] if e[0] == 'MOVE') +hel = Counter(dim[W['final'][r]] - dim[W['initial'][r]] for r in range(n) if r not in main) +life = sum(e[0] == 'INIT' for e in W['program']) +allow = upper = 0 +for e in W['program']: + if e[0] in ('INIT', 'CLEAR'): allow += 2 + elif e[0] == 'SCALE': + q = Q(e[2]); a, d = abs(q.numerator), q.denominator + allow += 2 * (abs(a.bit_length() - d.bit_length()) + int(q < 0)); upper += 4 * (a.bit_length() + d.bit_length() + 1) + elif e[0] in ('ADD', 'COPY'): + q = Q(e[3]); a, d = abs(q.numerator), q.denominator + allow += 2 * (3 + a.bit_length() - 1 + a.bit_count() + d.bit_length() - 1); upper += 4 * (a.bit_length() + a.bit_count() + d.bit_length() + 1) +norm = 2 * sum(hel.values()) +routes = (sum(paid.values()) + norm + 416 + 8 * 104 + 4 * life) * 1000 # second mains: their boundary terms doubled +print('native: allowance %d, reviewed scalar upper %d, routes %d' % (allow, upper, routes)) +print('per call, funded display (pricing.py:93): allowance+routes = %d ; reviewed upper+routes = %d ; bound 10^7' % (allow + routes, upper + routes)) +roles = C['roles']; ev = C['events']; amb = C['ambient_rank'] +main_ex = main_nine = main_ph = 0 +for role, (qp, zero, *sel) in enumerate(C['diagonal']): + axes = ([0] if qp else []) + [a for st, y in enumerate(sel, 1) if y for a in range(9 + 8 * (st - 1), 9 + 8 * st)] + k = swaps(axes, amb); main_ex += 2 * k * 104; main_nine += 2 * bool(qp) * 104; main_ph += int(qp == -1) * 104 +idle_ex = 0; qn = qph = 0 +for e in ev: + if e[0] == 'IDLE_ONE': + axes = [a for st in e[2] for a in range(9 + 8 * (st - 1), 9 + 8 * st)] + idle_ex += 2 * swaps(axes, amb) * 104 + elif e[0] == 'QUERY': + qn += 2 * 104; qph += int(e[3] == -1) * 104 +main_maps = main_ex + main_nine + main_ph +caller = 32 * roles * 104 * len(ev); thin = sum(e[0] == 'QUERY' for e in ev) * 16 * 104 +out = roles * 104 * 26 + main_maps * 1000 +rest = caller + thin + out + idle_ex * 1000 + (qn + qph) * 1000 +print('caller envelope %d, thin %d, outputs %d (main maps %d), idle adapters %d, query adapters %d' % (caller, thin, out, main_maps, idle_ex * 1000, (qn + qph) * 1000)) +print('RAW literal definition (18 calls x 10^7): %d < 10^9: %s' % (18 * 10 ** 7 + rest, 18 * 10 ** 7 + rest < 10 ** 9)) +for name, per in (('actual allowance+routes', allow + routes), ('reviewed upper+routes', upper + routes)): + print('RAW with %s per call (18 x %d): %d < 10^9: %s' % (name, per, 18 * per + rest, 18 * per + rest < 10 ** 9)) diff --git a/research/p104-two-chain-shared-native/physical.py b/research/p104-two-chain-shared-native/physical.py new file mode 100644 index 0000000000..a3d15c0bb9 --- /dev/null +++ b/research/p104-two-chain-shared-native/physical.py @@ -0,0 +1,118 @@ +#!/usr/bin/env python3 +"""Physical stream replay of the literal hosted word, own driver (standard library). +python3 -I -B physical.py WORD.json.gz CLIFFORD_EXACT.py [prime=1000000009] [seed=11] [mutate] +Every register carries a 512-component stream over F_p[i] (p = 1 mod 4, i a fixed square root of -1); inputs are random. +A MOVE a->b applies chart(a)^dagger then chart(b) as explicit gates (P, X, D, C, phase read from the retained Clifford +circuits, interpreted here); INIT zeroes, CLEAR erases, SCALE/ADD act linearly. Prediction comes from the charts alone: + X_out = M(X_in; init->final) + alpha M(Y_in; Y0->Xfinal), Y_out = beta M(X_in; init->Yfinal) + (1+t) M(Y_in; Y0->Yfinal), +helpers: M(in; init->final). Then the raw main-pair identities by tableau and phase on all 104 ports, with controls.""" +import sys, gzip, json, time, importlib.util, random +from fractions import Fraction as Fr +wordp, cliff = sys.argv[1], sys.argv[2] +p = int(sys.argv[3]) if len(sys.argv) > 3 else 1000000009 +seed = int(sys.argv[4]) if len(sys.argv) > 4 else 11 +mutate = len(sys.argv) > 5 +assert p % 4 == 1 +spec = importlib.util.spec_from_file_location('cliff', cliff); C = importlib.util.module_from_spec(spec); sys.modules['cliff'] = C; spec.loader.exec_module(C) +def find_i(): + for g in range(2, 200): + v = pow(g, (p - 1) // 4, p) + if v * v % p == p - 1: return v +IM = find_i(); HALF = (p + 1) // 2; N = 512; IP = [1, IM, p - 1, (p - IM) % p] +W = json.load(gzip.open(wordp, 'rt')); fr = W['frames']; n = len(W['initial']); NO = W['owned_fields']; NR = n + NO; live = W['live'] +Hh = W['hosted']; alpha = Fr(Hh['alpha']); beta = Fr(Hh['beta']); t = alpha * beta; a2f = Fr(Hh['alpha2']); b2f = Fr(Hh['beta2']); X2 = Hh['X2']; Y2 = Hh['Y2'] +if mutate: a2f = -a2f # control run: predictions use the wrong sign of alpha2; must be rejected +fm = lambda q: (lambda f: f.numerator % p * pow(f.denominator, p - 2, p) % p)(Fr(q)) +charts = {} +def chart(i): + if i not in charts: charts[i] = C.canonical_frame(9, tuple(fr[i])) + return charts[i] +def gates(op): + g = [] + for e in op.circuit: + k = e[0] + if k == 'P': g.append(('P', [C.mv(e[1], x) for x in range(N)])) + elif k == 'X': g.append(('X', [x ^ e[1] for x in range(N)])) + elif k == 'D': g.append(('M', [IP[C.qvalue(e[1], e[2], x, 9)] for x in range(N)])) + elif k == 'phase': g.append(('S', IP[e[1] % 4])) + elif k == 'C': + q, s = e[1], e[2] + g.append(('C', [x ^ q for x in range(N)], (1 + s * IM) * HALF % p, (1 - s * IM) * HALF % p)) + else: raise SystemExit('unknown gate ' + str(k)) + return g +def apply(g, v): + for x in g: + k = x[0] + if k == 'P': + o = [0] * N + for i, j in enumerate(x[1]): o[j] = v[i] + v = o + elif k == 'X': v = [v[j] for j in x[1]] + elif k == 'M': v = [a * b % p for a, b in zip(v, x[1])] + elif k == 'S': v = [a * x[1] % p for a in v] + else: + c1, c2, idx = x[2], x[3], x[1] + v = [(a * c1 + v[j] * c2) % p for a, j in zip(v, idx)] + return v +cache = {} +def move(a, b, v): + if (a, b) not in cache: cache[a, b] = gates(chart(a).adjoint().then(chart(b))) + return apply(cache[a, b], v) +# control of the interpreter against the library's exact state vectors (basis 0 and 5) +def to_c(pair): return (pair[0] + pair[1] * IM) % p +for a, b in ((W['initial'][live[0]], W['final'][live[0]]), (W['initial'][live[0] + 112], W['final'][live[0] + 112])): + op = chart(a).adjoint().then(chart(b)); g = gates(op) + for basis in (0, 5): + v = [0] * N; v[basis] = 1; out = apply(g, v) + vec, den = op.zero_state(basis); scale = pow(2, p - 1 - den, p) if den else 1 + # zero_state returns the state scaled by 2^den + exp = [to_c(x) * pow(pow(2, den, p), p - 2, p) % p for x in vec] + assert out == exp, 'gate interpreter disagrees with the library state vector' +print('gate interpreter agrees with the library on 4 exact state vectors', flush=True) +rnd = random.Random(seed) +S = [[rnd.randrange(p) for _ in range(N)] if r < n else [0] * N for r in range(NR)]; inp = [s[:] for s in S[:n]] +t0 = time.time() +for e in W['program']: + op, r = e[0], e[1] + if op == 'MOVE': S[r] = move(e[2], e[3], S[r]) + elif op in ('INIT', 'CLEAR'): S[r] = [0] * N + elif op == 'SCALE': + c = fm(e[2]); S[r] = [a * c % p for a in S[r]] + else: + c = fm(e[3]); s = S[e[2]]; S[r] = [(a + c * b) % p for a, b in zip(S[r], s)] +print('replayed %d events, %d chart pairs, %.0fs' % (len(W['program']), len(cache), time.time() - t0), flush=True) +main = set(live) | {r + 112 for r in live} | set(X2) | set(Y2) +badH = sum(S[r] != move(W['initial'][r], W['final'][r], inp[r]) for r in range(n) if r not in main) +al, be, de = fm(alpha), fm(beta), fm(1 + t) +badX = badY = 0 +for r in live: + y = r + 112; li, fu, y0, yf = W['initial'][r], W['final'][r], W['initial'][y], W['final'][y] + px = [(a + al * b) % p for a, b in zip(move(li, fu, inp[r]), move(y0, fu, inp[y]))] + py = [(be * a + de * b) % p for a, b in zip(move(li, yf, inp[r]), move(y0, yf, inp[y]))] + badX += S[r] != px; badY += S[y] != py +badX2 = badY2 = 0; al2, be2, de2 = fm(a2f), fm(b2f), fm(1 + a2f * b2f) +for r, x2, y2 in zip(live, X2, Y2): + li, fu, y0, yf = W['initial'][x2], W['final'][x2], W['initial'][y2], W['final'][y2] + px = [(a + al2 * b) % p for a, b in zip(move(li, fu, inp[x2]), move(y0, fu, inp[y2]))] + py = [(be2 * a + de2 * b) % p for a, b in zip(move(li, yf, inp[x2]), move(y0, yf, inp[y2]))] + badX2 += S[x2] != px; badY2 += S[y2] != py +print('prime %d seed %d: helper rows bad %d (of %d), X rows bad %d, Y rows bad %d, X2 rows bad %d, Y2 rows bad %d (of %d each)' % (p, seed, badH, n - len(main), badX, badY, badX2, badY2, len(live)), flush=True) +if mutate: sys.exit(0 if (badX or badY or badX2 or badY2) else 1) +# raw main-pair identities, tableau + phase, all ports +def same(a, b): return a.tab == b.tab and all(a.zero_state(k) == b.zero_state(k) for k in (0, 1)) +bad = [0] * 6 +for r, q in zip(live, W['ports']): + y = r + 112; P = chart(W['final'][y]); Vv = chart(W['final'][r]); Z0 = chart(W['initial'][y]); a0 = chart(W['initial'][r]) + Qp = C.cgate(9, q, 1); Qm = C.cgate(9, q, -1); F = C.fourier(9); D = Qm.then(F) + mp = C.lower_child(P.adjoint().then(Qm.then(F)))[1] # free adapter on the Y output chart + ma = C.lower_child(Qp.adjoint().then(a0))[1] + bad[0] += not same(Qp.adjoint().then(Vv), D) # X->X + bad[1] += not same(Z0.adjoint().then(P).then(mp), D) # Y->Y + bad[2] += not same(Qp.adjoint().then(P).then(mp), Qm.then(D)) # X->Y = Q^-1 D + bad[3] += not same(Z0.adjoint().then(Vv), Qp.then(D)) # Y->X = Q D + bad[4] += same(Z0.adjoint().then(Vv), Qm.then(D)) # control: Q^-1 must not match + bad[5] += same(Qp.adjoint().then(P).then(mp), Qp.then(D)) # control +print('tableau on %d ports: XX!=D %d YY!=D %d YX!=Q^-1D %d XY!=QD %d | controls matching (must be 0): %d %d' % ((len(live),) + tuple(bad))) +ok = badH == 0 and badX == 0 and badY == 0 and badX2 == 0 and badY2 == 0 and bad == [0] * 6 +print('PASS_PHYSICAL' if ok else 'FAIL_PHYSICAL', '%.0fs' % (time.time() - t0)) +sys.exit(0 if ok else 1) diff --git a/research/p104-two-chain-shared-native/retained/bit/FRAGMENT-BIT-ADMISSION.json b/research/p104-two-chain-shared-native/retained/bit/FRAGMENT-BIT-ADMISSION.json new file mode 100644 index 0000000000..482f9525d4 --- /dev/null +++ b/research/p104-two-chain-shared-native/retained/bit/FRAGMENT-BIT-ADMISSION.json @@ -0,0 +1,19115 @@ +{ + "status": "PASS_TWO_FRAGMENTS_BIT_ORDINARY_00376669", + "ordinary_admitted": "376669/100000000", + "previous_ordinary": "187499/50000000", + "ordinary_gain": "1671/100000000", + "raw_tested": "37667/10000000", + "raw_crossing": [ + "1506689391/400000000000", + "4708404347/1250000000000" + ], + "covered_saving": "18833499/5000000000", + "caller_sha256": 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coefficient 0,0", + "missing_IDLE": "reverse coefficient 0,0", + "missing_IDLE_ONE": "reverse coefficient 0,0" + }, + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "scope": "Changed, completely priced BIT dependency under the inherited framework. Overall complex-limited kappa remains unchanged. No materialized uniform word or unconditional integer multiplication theorem.", + "new_global_kappa_claim": false, + "seconds": 3.9323597500042524 +} diff --git a/research/p104-two-chain-shared-native/retained/native/clifford_exact.py b/research/p104-two-chain-shared-native/retained/native/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/p104-two-chain-shared-native/retained/native/clifford_exact.py @@ -0,0 +1,149 @@ +"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals. +Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d. +The tableau is supplemented by a literal circuit, so global phases are kept. +""" +from dataclasses import dataclass + +def parity(x):return x.bit_count()&1 +def rank(rows): + p={} + for x in rows: + while x: + b=x.bit_length()-1 + if b not in p:p[b]=x;break + x^=p[b] + return len(p) +def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<>j&1);a[j],a[k]=a[k],a[j] + for i in range(n): + if i!=j and a[i]>>j&1:a[i]^=a[j] + assert [r&((1<>n for r in a) +def basis_extend(cols,n): + out=[] + for x in list(cols)+[1<len(out):out.append(x) + assert len(out)==n + return tuple(out) +def nullspace(rows,n): + a=list(rows);p=[];k=0 + for j in range(n): + t=next((i for i in range(k,len(a)) if a[i]>>j&1),None) + if t is None:continue + a[t],a[k]=a[k],a[t] + for i in range(len(a)): + if i!=k and a[i]>>j&1:a[i]^=a[k] + p.append(j);k+=1 + return tuple((1<>j)&1)<>i&1:out=pmul(out,T[i]) + for i in range(n): + if z>>i&1:out=pmul(out,T[n+i]) + return out +def compose(A,B):return tuple(apply(A,p) for p in B) +def inverse(T): + n=len(T)//2;cols=[x|(z<>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4)) + return tuple(out) +def qvalue(Q,alpha,x,n): + return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4 +def mul_i(a,p): + x,y=a;p%=4 + return [(x,y),(-y,x),(-x,-y),(y,-x)][p] +@dataclass +class Op: + n:int + tab:tuple + circuit:list + def then(self,b): + assert self.n==b.n + return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit) + def adjoint(self): + circ=[] + for e in reversed(self.circuit): + if e[0]=='P':circ.append(('P',inv(e[1],self.n))) + elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2]))) + elif e[0]=='C':circ.append(('C',e[1],-e[2])) + elif e[0]=='phase':circ.append(('phase',(-e[1])%4)) + else:circ.append(e) + return Op(self.n,inverse(self.tab),circ) + def zero_state(self,basis=0): + N=1<>i)&1 for i in range(n)) + assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n)) + return Op(n,tuple([(1<>i&1 else 0,1<>i&1 else 0) for i in range(n)]),[('C',q,sgn)]) +def xgate(n,b):return Op(n,tuple([(1<>i)&1)) for i in range(n)]),[('X',b)]) +def fourier(n,axes=None): + out=ident(n) + for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<len(selected):picks.append(j);selected.append(x) + assert len(picks)==r and all(x>>r==0 for x in Bcols) + Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<= 112 and field - 112 in live: + expected[field - 112] = Fraction(1) + require(rows[field] == expected, 'all arbitrary native input row ' + str(field)) + if field not in main: + start, end = word['initial'][field], word['final'][field] + require(spaces[start] & spaces[end] == spaces[start] and ranks[start] < ranks[end], 'productive helper strict nested endpoint') + rank = ranks[end] - ranks[start] + helpers[rank] += 1 + helper_labels.append((field, rank)) + for i, q in zip(live, ports): + require(frames[word['initial'][i]] == [q] and frames[word['initial'][112+i]] == [], 'native incoming Q/I main interface') + require(frames[word['final'][i]] == list(1 << j for j in range(9)), 'native complete nine-axis X endpoint') + require(ranks[word['final'][112+i]] == 8 and all((q & a).bit_count()%2 == 0 for a in frames[word['final'][112+i]]), 'native rank-eight q-orthogonal Y endpoint') + return dict(paid=paid, helpers=helpers, helper_labels=helper_labels, paid_records=paid_records, + public=public, owned=word['owned_fields'], lifetimes=lifetime, peak=peak, + operations=operations, scalar_upper=scalar_units, + scalar_rows=public if check_rows else 0) + + +def terms(entries): + counts = Counter() + for vector, coefficient in entries: + counts[vector] += coefficient + return {vector: coefficient % 4 for vector, coefficient in counts.items() if vector and coefficient % 4} + + +def difference(a, b): + return terms(list(a.items()) + [(v, -c) for v, c in b.items()]) + + +def phase(coefficients, frequency): + return sum(c * ((vector & frequency).bit_count() & 1) for vector, c in coefficients.items()) % 4 + + +def axes_of(mask): + out = [] + while mask: + bit = mask & -mask + out.append(bit) + mask ^= bit + return out + + +def translation_for(delta): + """Parity is degree <=2 modulo four; weight<=2 frequencies determine it.""" + support = axes_of(reduce(int.__or__, delta, 0)) + shift = 0 + single = {} + for bit in support: + single[bit] = phase(delta, bit) + require(single[bit] in (0, 2), 'contact linear phase must be an ordinary translation') + if single[bit] == 2: + shift |= bit + for a, b in combinations(support, 2): + require(phase(delta, a | b) == (single[a] + single[b]) % 4, 'contact residual quadratic phase') + return shift + + +def route_function(q, basis, stage): + fresh = [1 << (9 + 8*(stage-1) + i) for i in range(8)] + old_mask = 511 + fresh_mask = sum(fresh) + require(q.bit_count() % 2 == 1, 'odd central port') + require(len(basis) == 8 and all(0 < v < 512 for v in basis), 'native eight-dimensional basis') + require(all((a & b).bit_count() % 2 == (i == j) for i, a in enumerate([q]+basis) for j, b in enumerate([q]+basis)), 'complete orthonormal native basis') + def route(value): + old = value & old_mask + result = value & ~(old_mask | fresh_mask) + if (old & q).bit_count() % 2: + result ^= q + for native_axis, fresh_axis in zip(basis, fresh): + if value & fresh_axis: + result ^= native_axis + if (old & native_axis).bit_count() % 2: + result ^= fresh_axis + return result + affected = [1 << i for i in range(9)] + fresh + images = [route(v) for v in affected] + require(all(route(image) == axis for axis, image in zip(affected, images)), 'route involution') + require(all((a & b).bit_count() % 2 == (i == j) for i, a in enumerate(images) for j, b in enumerate(images)), 'route orthogonality') + require(route(q) == q, 'route fixes Q') + return route + + +def contact(before, after, route, omit_translation=False): + moved = terms((route(v), c) for v, c in before.items()) + shift = translation_for(difference(after, moved)) + supplied = 0 if omit_translation else shift + require(translation_for(difference(after, terms(list(moved.items()) + [(supplied, 2)]))) == 0, 'full forward absolute phase') + inverse = route(supplied) + require(translation_for(difference(before, terms([(route(v), c) for v, c in after.items()] + [(inverse, 2)]))) == 0, 'full inverse absolute phase') + require(shift.bit_count() <= 17 and inverse.bit_count() <= 17, 'fixed seventeen-axis translation budget') + return {'translation': shift, 'inverse_translation': inverse} + + +def physical(word, native, recipes, omit_translation=False): + stages = word['stages'] + require(word['ambient_rank'] == 9 + 8*stages, 'declared ambient axes') + axes = [1 << i for i in range(word['ambient_rank'])] + full_events = [(i, e) for i, e in enumerate(word['events']) if e[0] == 'LOCAL'] + require([e[1] for _, e in full_events] == list(range(1, stages+1)), 'fresh native stage chronology') + by_port = {r['q']: r for r in recipes['recipes']} + require(set(native['ports']) <= set(by_port), 'every retained port has a phase recipe') + records = [] + for _, (_, stage, src, dst) in full_events: + require(src != dst and 0 <= src < word['roles'] and 0 <= dst < word['roles'], 'distinct valid native caller fields') + before_axes = axes[:9+8*(stage-1)] + after_axes = axes[:9+8*stage] + spectator = axes[9:9+8*stage] + for q in native['ports']: + basis = by_port[q]['idle_children'][0]['orthogonal_axes'][:8] + route = route_function(q, basis, stage) + x0 = terms((a, 1) for a in before_axes) + y0 = terms(list(x0.items()) + [(q, -1)]) + x1 = terms((a, 1) for a in after_axes) + y1 = terms(list(x1.items()) + [(q, -1)]) + native_x0 = terms([(a, 1) for a in spectator] + [(q, 1)]) + native_y0 = terms((a, 1) for a in spectator) + native_x1 = terms((a, 1) for a in spectator + axes[:9]) + native_y1 = terms(list(native_x1.items()) + [(q, -1)]) + maps = [contact(a, b, route, omit_translation) for a, b in ((x0,native_x0),(y0,native_y0),(native_x1,x1),(native_y1,y1))] + body = terms((a, 1) for a in axes[9+8*(stage-1):9+8*stage]) + require(translation_for(difference(difference(x1,x0),body)) == 0 and translation_for(difference(difference(y1,y0),body)) == 0, 'native diagonal is fresh D_stage with absolute phase') + require(translation_for(difference(difference(y1,x0),terms(list(body.items())+[(q,-1)]))) == 0, 'native cross coefficient is D_stage Q^-1') + records.append([stage,q,maps]) + main = Counter() + output_shifts = 0 + for term in word['diagonal']: + qp, zero, *selected = term + require(qp in (-1,0,1) and zero == 0 and len(selected) == stages and set(selected) <= {0,1}, 'literal physical endpoint exponent domain') + for q in native['ports']: + body_axes = [axis for stage, yes in enumerate(selected,1) if yes for axis in axes[9+8*(stage-1):9+8*stage]] + positive = ([q] if qp else []) + body_axes + require(all((a & b).bit_count()%2 == (i == j) for i,a in enumerate(positive) for j,b in enumerate(positive)), 'all positive endpoint axes orthonormal') + actual = terms([(q,qp)] + [(a,1) for a in body_axes]) + target = terms((a,1) for a in positive) + shift = translation_for(difference(target,actual)) + require(shift == (q if qp == -1 else 0), 'exact endpoint translation') + output_shifts += bool(shift) + main[len(positive)] += 1 + idle = Counter() + idle_records = [] + for index,event in enumerate(word['events']): + if event[0] not in ('IDLE','IDLE_ONE'): + continue + owners, selection = (event[1:3], event[3]) if event[0] == 'IDLE' else ([event[1]],event[2]) + require(len(set(owners)) == len(owners) and all(0 <= r < word['roles'] for r in owners), 'distinct valid idle owners') + require(selection and len(set(selection)) == len(selection) and all(1 <= s <= stages for s in selection), 'distinct valid complete idle axes') + positive = [axis for stage in selection for axis in axes[9+8*(stage-1):9+8*stage]] + require(len(set(positive)) == len(positive), 'whole idle independent Gaussian factors') + idle[len(positive)] += len(native['ports']) * len(owners) + idle_records.extend((index,owner,q,len(positive)) for owner in owners for q in native['ports']) + require(len(word['diagonal']) == word['roles'], 'one target for every arbitrary caller input') + return dict(contacts=4*len(records), contact_digest=sha256(json.dumps(records,separators=(',',':')).encode()).hexdigest(), + nonzero_contact_translations=sum(bool(m['translation']) for _,_,maps in records for m in maps), + main=main, idle=idle, idle_records=idle_records, output_translations=output_shifts, + dimension=word['ambient_rank']) + + +def allocation(word, native, ledger, alias=False): + main = {(role,q) for role in range(word['roles']) for q in native['ports']} + names = {('main',role,q) for role,q in main} + helper_jobs = [] + local_number = 0 + for event_index, event in enumerate(word['events']): + if event[0] != 'LOCAL': + continue + _,stage,src,dst = event + public_map = {} + for i,q in zip(native['live'],native['ports']): + public_map[i] = ('main',src,q) + public_map[112+i] = ('main',dst,q) + for field,rank in ledger['helper_labels']: + key = ('helper',0 if alias else local_number,field) + require(key not in names, 'fresh native helper cannot alias an earlier public input') + names.add(key) + public_map[field] = key + helper_jobs.append((event_index,stage,field,rank,key)) + require(len(public_map) == ledger['public'] and len(set(public_map.values())) == ledger['public'], 'injective local public-input allocation') + local_number += 1 + owned = {('owned',i) for i in range(ledger['owned'])} + thin = {('query_scratch',0)} + require(not (names & owned or names & thin or owned & thin), 'owned/query scratch is disjoint and uncredited') + return dict(main_fields=len(main), helper_fields=len(helper_jobs), productive_fields=len(names), + reserved_native_owned=len(owned), reserved_query_owned=len(thin), + peak_native_owned=ledger['peak'], maximum_live_owned=max(ledger['peak'],1), + invocations=local_number, helper_jobs=helper_jobs) + + +def invoice(word, ledger, physics, fields): + paid = Counter() + targets = Counter(physics['main']) + for _,_,_,rank,_ in fields['helper_jobs']: + targets[rank] += 1 + for event in word['events']: + if event[0] == 'LOCAL': + paid.update(ledger['paid']) + elif event[0] == 'QUERY': + require(event[3] in (-1,1), 'legal thin query orientation') + paid[1] += 104 + paid.update(physics['idle']) + require(sum(targets.values()) == fields['productive_fields'], 'productive count equals distinct arbitrary inputs') + return {'targets':targets, 'paid':paid, 'productive_fields':sum(targets.values()), 'paid_calls':sum(paid.values()), + 'target_mass':sum(r*n for r,n in targets.items()), 'paid_mass':sum(r*n for r,n in paid.items())} + + +def compare_invoice(actual, expected): + require(actual['targets'] == Counter({int(k):v for k,v in expected['targets'].items()}), 'complete productive rank histogram') + require(actual['paid'] == Counter({int(k):v for k,v in expected['paid'].items()}), 'complete paid rank histogram') + require(actual['productive_fields'] == expected['productive_fields'] and actual['paid_calls'] == expected['paid_calls'], 'independent count totals') + require(actual['target_mass'] - actual['paid_mass'] == expected['rank_mass_surplus'], 'independent rank-mass surplus') + + +def chronology(word, witnesses): + slots = {'ADD':(1,2),'SCALE':(1,),'SWAP':(1,2),'LOCAL':(2,3),'QUERY':(1,2),'IDLE':(1,2),'IDLE_ONE':(1,),'LAMBDA':(1,),'Q_POWER':(1,)} + actual_handoffs = [] + for number, witness in enumerate(witnesses): + # Witness zero belongs to the intermediate 33-field word. Later input + # bases precede that whole word and shift its earlier cut chronologically. + offset = sum(len(later['input_basis']) for later in witnesses[number+1:]) + handoff = witness['handoff_after'] + offset + pivot,fresh = witness['pivot'], witness['fresh'] + require(all(event[j] != fresh for event in word['events'][:handoff+1] for j in slots[event[0]]), 'fresh handoff input untouched in entire prefix') + cut_basis = witness['cut_basis'] + require(word['events'][handoff-len(cut_basis)+1:handoff+1] == cut_basis, 'complete cut basis at actual chronological handoff') + require(word['events'][handoff-len(cut_basis)] == ['IDLE_ONE',2,witness['prefix_stages']], 'handoff immediately follows the paid fragment') + require(word['diagonal'][pivot] == witness['prefix_target'] and word['diagonal'][fresh] == witness['suffix_target'], 'retirement endpoint credit matches literal witness') + first_fresh = next(i for i,event in enumerate(word['events']) if any(event[j] == fresh for j in slots[event[0]])) + require(first_fresh == handoff+1, 'fresh suffix starts immediately after completed prefix') + require(all(event[j] != pivot for event in word['events'][handoff+1:] for j in slots[event[0]]), 'retired productive output retained untouched through the full suffix') + actual_handoffs.append(handoff) + return {'fresh_inputs': [w['fresh'] for w in witnesses], 'witness_handoffs':[w['handoff_after'] for w in witnesses], 'literal_final_handoffs':actual_handoffs} + + +def central_normalization(): + def mul(a,b): + return (a[0]*b[0]-a[1]*b[1], a[0]*b[1]+a[1]*b[0]) + values = [(1,0),(0,1),(-1,0),(0,-1)] + for j,q in enumerate(values): + lam = (1,0) if j%2 == 0 else (0,1) + inverse = (lam[0],-lam[1]) + require(mul(lam,inverse)==(1,0), 'ordinary lambda and inverse are exact') + central = mul(lam,(q[0],-q[1])) + require(mul(central,central)==(1,0), 'normalized central S is an involution') + # At two odd factor characters Q_total=-1, lambda(Q_total)=+1, + # whereas tensoring the two factor lambdas would incorrectly give -1. + require((1,0) != mul((0,1),(0,1)), 'global lambda must remain outside tensor powers') + return {'central_characters':4,'two_factor_lambda_disagreement':True, + 'rule':'Physical Gaussian maps tensor factorwise; ordinary scalar coefficients and lambda polynomials act on the total Q outside tensor powers.'} + + +def coordinate_swaps(selected, dimension): + """Map a subset of canonical axes to the first r axes by explicit exchanges.""" + require(len(set(selected)) == len(selected), 'adapter axes distinct') + require(all(0 <= axis < dimension for axis in selected), 'adapter axes in ambient carrier') + wanted = set(range(len(selected))) + swaps = list(zip(sorted(set(selected)-wanted), sorted(wanted-set(selected)))) + def move(axis): + for a,b in swaps: + if axis == a: + axis = b + elif axis == b: + axis = a + return axis + require({move(axis) for axis in selected} == wanted, 'explicit Gaussian axis permutation') + require(all(move(move(axis)) == axis for axis in range(dimension)), 'permutation adapter inverse') + require(len(swaps) <= len(selected), 'rank-many two-axis exchanges suffice') + return swaps + + +def adapter_inventory(word, native, recipes): + """Charge complete canonical-job input/output conversions, including full idles.""" + by_port = {r['q']:r for r in recipes['recipes']} + for q in native['ports']: + basis = [q]+by_port[q]['idle_children'][0]['orthogonal_axes'][:8] + # This nine-axis map sends q to coordinate zero, fixes all spectators, + # and sends its orthonormal complement to coordinates one through eight. + def convert(value): + return (value & ~511) | sum(((value & axis).bit_count()%2) << i for i,axis in enumerate(basis)) + require([convert(axis) for axis in basis] == [1 << i for i in range(9)], 'explicit nine-axis q-to-coordinate adapter') + require(all((a&b).bit_count()%2 == (i==j) for i,a in enumerate(basis) for j,b in enumerate(basis)), 'q adapter orthogonal and invertible') + records = {'main':[], 'idle':[], 'query':[]} + for role,(qp,zero,*selection) in enumerate(word['diagonal']): + axes = ([0] if qp else []) + [axis for stage,yes in enumerate(selection,1) if yes for axis in range(9+8*(stage-1),9+8*stage)] + exchanges = coordinate_swaps(axes,word['ambient_rank']) + for q in native['ports']: + # Both whole-job boundaries are charged, even though a target + # interface may permit some of these maps to remain implicit. + records['main'].append([role,q,len(exchanges),2*bool(qp),int(qp==-1)]) + for index,event in enumerate(word['events']): + if event[0] in ('IDLE','IDLE_ONE'): + owners,stages = (event[1:3],event[3]) if event[0]=='IDLE' else ([event[1]],event[2]) + axes = [axis for stage in stages for axis in range(9+8*(stage-1),9+8*stage)] + exchanges = coordinate_swaps(axes,word['ambient_rank']) + records['idle'].extend([index,owner,q,len(exchanges)] for owner in owners for q in native['ports']) + elif event[0]=='QUERY': + _,dst,src,power = event + require(dst != src and all(0<=r Q(1, 2) and (1-z0)*E.log_interval(m)[1] < E.log_interval(2)[0], + 'Original eta strictly exceeds 1/4') + H0 = ceil((3+4*delta)/(h*delta)) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= m.bit_length() and H0*h*delta >= 3+4*delta, 'Induction starts') + need(H1*(z-z0) > H0*(1-z0), 'Strict winning uniform rank') + need((H0-1)*h*delta < 3+4*delta, 'Reject one lower threshold exponent') + need((H1-1)*(z-z0) <= H0*(1-z0), 'Reject one lower final exponent') + return {'t': t, 'z0': z0, 'z': z, 'theta_upper': Q(9, 10), + 'H0': H0, 'H1': H1, 'N_encoding': '2^H1', + 'strict_final_gap': H1*(z-z0)-H0*(1-z0), + 'winning_word_materialized': False, + 'bound': 'Original sufficient inequality; a sharper bound is separate.'} + + +def run(source_root): + base = source_root/PREFIX + interval_path = base/'architecture/mixed_target_probe.py' + spec = importlib.util.spec_from_file_location('pr4359_moment', interval_path) + E = importlib.util.module_from_spec(spec) + spec.loader.exec_module(E) + cover = read(base/'controller/P3-NATIVE-COVER.json.gz')['cover'] + targets = {int(k): int(v) for k, v in cover['targets'].items()} + paid = {int(k): int(v) for k, v in cover['paid'].items()} + need(targets == {6: 192, 7: 56, 8: 93, 9: 1229, 25: 448, 57: 224}, + 'Exact source productive inventory') + need(paid == {1: 17623, 2: 5065, 3: 1738, 4: 714, 5: 254}, + 'Exact source paid inventory') + signed = Counter(targets) + signed.subtract(paid) + need(sum(k*v for k, v in signed.items()) == 224, 'Rank-one surplus') + bracket = {'lower': E.moment(signed, TESTED), 'upper': E.moment(signed, ROOT_UPPER)} + need(bracket['lower'][0] > 0 and bracket['upper'][1] < 0, + 'Strict mixed test and upper root bound') + + original = read(base/'controller/OUTER-PARAMETERS.json')['outer'] + old = ledger({'kappa': Q('0.0023'), 'complex_uniform_saving': Q('0.002304'), + 'b': Q('0.002303'), 'a': Q('0.0023025'), 'q': Q('0.002302'), + 'bit_saving': Q('0.0027'), 'epsilon': Q('0.99999'), + 'beta': Q('0.99997'), 'r0': Q(1, 10**6), + 'stop': Q(1, 10**8), 'layout': Q(1, 10**6)}) + for group in ('margins', 'strict_checks'): + frozen = {key: Q(value['rational']) for key, value in original[group].items()} + need(old[group] == frozen, 'Exact reproduction of every old '+group) + p = family(KAPPA, TESTED) + result = ledger(p) + need(all(v > 0 for v in result['strict_checks'].values()), 'All 54 new outer predicates') + need(all(v > 0 for v in result['functional_checks'].values()), 'Additional functional predicates') + need(min(result['margins'].values()) == result['margins']['main_transform'], + 'Main transform remains limiting') + need(result['parameters']['cap_xi'] == Q(29, 32)+(1-p['d'])*p['q'], + 'Cofinal cap simplification') + controls = {} + for label, updates in [('closed_epsilon_gap', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': Q('0.002306')}), + ('BIT_below_effective', {'bit_saving': OLD_BASELINE}), + ('no_complex_slack', {'complex_uniform_saving': p['b']})]: + tested = ledger(dict(p, **updates)) + failures = {k: v for k, v in tested['strict_checks'].items() if v <= 0} + need(failures, 'Mutation rejected: '+label) + controls[label] = failures + need(E.moment(signed, Q('0.004'))[1] < 0, 'Unsupported mixed target is rejected') + inputs = [interval_path, base/'controller/P3-NATIVE-COVER.json.gz', + base/'controller/OUTER-PARAMETERS.json'] + return encode({'schema': 'pr4359-cofinal-outer-refill/1', + 'status': 'PASS_EXACT_CONDITIONAL_ENDPOINT_REFILL', + 'kappa': KAPPA, 'gain_over_PR4359': KAPPA-Q('0.0023'), + 'unchanged_paid': paid, 'unchanged_targets': targets, + 'mixed_test_saving': TESTED, 'mixed_test_margin': E.show(bracket['lower']), + 'root_upper_test': ROOT_UPPER, 'root_upper_margin': E.show(bracket['upper']), + 'old_ledger_crosscheck': {'matched_savings': len(old['margins']), + 'matched_checks': len(old['strict_checks'])}, + 'outer': result, 'limiting_margin': min(result['margins'].values())-KAPPA, + 'compiler': compiler_rank(E, targets, paid, TESTED, p['complex_uniform_saving']), + 'negative_controls': controls, + 'source_sha256': {str(p.relative_to(source_root)): sha256(p.read_bytes()).hexdigest() + for p in inputs}, + 'scope': 'Conditional arithmetic and specified finite rank. The PR4359 native, compiler, cover, precision, fixed-tape and outer hypotheses remain premises; no full theorem or practical word is certified.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--source-root', type=Path, default=HERE/'source') + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = run(args.source_root) + if args.out: + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + print(json.dumps({key: result[key] for key in + ('status', 'kappa', 'gain_over_PR4359', 'limiting_margin', 'compiler')}, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/p104-two-chain-shared-native/retained/runtime/intervals.py b/research/p104-two-chain-shared-native/retained/runtime/intervals.py new file mode 100644 index 0000000000..4b24a50961 --- /dev/null +++ b/research/p104-two-chain-shared-native/retained/runtime/intervals.py @@ -0,0 +1,421 @@ +#!/usr/bin/env python3 +"""Higher-moment strictification and a polynomial-logarithm compiler bound. + +New arithmetic is independent of predecessor interval code. The unchanged +invoice replay and two outer ledgers are credited, byte-pinned oracles. +zxv with substantial OpenAI Codex assistance. Apache-2.0. +""" +import argparse +import ast +from collections import Counter +from contextlib import redirect_stdout +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256, sha1 +import io +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +GRID = 2**192 +C = Q('0.00268648') +KAPPA = Q('0.00268647') +T = {5:420, 6:270, 7:840, 8:1395, 9:3195, + 25:448, 41:448, 57:448, 121:224} +P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300, + 8:1464, 16:448, 32:448, 48:448} + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def down(x): + return Q((x*GRID).__floor__(), GRID) + + +def up(x): + return Q(-((-x*GRID).__floor__()), GRID) + + +def rounded(lo, hi): + return down(lo), up(hi) + + +def mul(a, b): + products = [x*y for x in a for y in b] + return rounded(min(products), max(products)) + + +def scale(a, x): + return mul(a, (x, x)) + + +def divide(a, b): + need(b[0] > 0, 'positive interval denominator') + return mul(a, rounded(1/b[1], 1/b[0])) + + +@lru_cache(None) +def log_bounds(n): + """Exact atanh series, binary reduction; round only the final interval.""" + need(isinstance(n, int) and n >= 1, 'positive integer logarithm') + + def series(x): + u = (x-1)/(x+1) + term, total = u, Q(0) + for j in range(80): + total += 2*term/(2*j+1) + term *= u*u + tail = 2*term/(161*(1-u*u)) + return total, total+tail + + k = n.bit_length()-1 + a, b = series(Q(2)) + c, d = series(Q(n, 2**k)) + return rounded(k*a+c, k*b+d) + + +def exp_point(x): + """Outward fixed-point Taylor enclosure, with binary scaling/squaring.""" + need(abs(x) < 16, 'bounded exponential argument') + if x < 0: + a, b = exp_point(-x) + return rounded(1/b, 1/a) + divisions = 0 + while x > Q(1, 2): + x /= 2 + divisions += 1 + term = total = (Q(1), Q(1)) + for j in range(1, 65): + term = scale(term, x/j) + total = rounded(total[0]+term[0], total[1]+term[1]) + following = scale(term, x/65) + # Every remaining ratio is <= 1/132. Twice the next term is safe. + result = rounded(total[0], total[1]+2*following[1]) + for _ in range(divisions): + result = mul(result, result) + return result + + +def exp_interval(a): + return exp_point(a[0])[0], exp_point(a[1])[1] + + +@lru_cache(None) +def power(n, exponent): + return exp_interval(scale(log_bounds(n), exponent)) + + +def moment(histogram, exponent): + low = high = Q(0) + for n, count in histogram.items(): + a, b = power(n, exponent) + low += count*a + high += count*b + return rounded(low, high) + + +def display(a): + unit = 10**30 + + def fixed(n): + sign = '-' if n < 0 else '' + s = str(abs(n)).rjust(31, '0') + return sign+s[:-30]+'.'+s[-30:] + + return {'lower': fixed((a[0]*unit).__floor__()), + 'upper': fixed(-((-a[1]*unit).__floor__()))} + + +def encoded(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): encoded(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [encoded(v) for v in x] + return x + + +def source_environment(path): + env = {'__file__': str(path), '__name__': 'pinned_source_oracle'} + exec(compile(path.read_bytes(), str(path), 'exec'), env) + return env + + +def authenticate(): + result = {} + for row in json.loads((HERE/'VENDOR.json').read_text())['files']: + path = HERE/'vendor'/Path(row['path']).relative_to( + 'research/higher-moment-strictification/vendor') + digest = sha256(path.read_bytes()).hexdigest() + need(digest == row['sha256'], 'changed source: '+row['path']) + raw = path.read_bytes() + need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() + == row['git_blob'], 'changed Git source blob') + result[row['path']] = digest + return result + + +def invoice_oracle(): + """Run #4426 unchanged, rebinding only its two file-location globals.""" + path = HERE/'vendor/invoice-review/verify.py' + env = source_environment(path) + env.update(ROOT=path.parent, PHASES='DATA-PHASES.json') + output = io.StringIO() + with redirect_stdout(output): + env['main']() + result = json.loads(output.getvalue()) + need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle') + need({int(k): v for k, v in result['targets'].items()} == T + and {int(k): v for k, v in result['paid'].items()} == P, + 'exact literal-word invoice') + return result + + +def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)): + t = 1-C + need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks') + need(t+u >= 1, 'tail moment exponent at least one') + target, paid = moment(T, t), moment(P, t) + alpha = divide(paid, target) + gamma = divide(moment(P, t+u), mul(power(cutoff, u), target)) + delta = divide((Q(sum(T.values())*floor),)*2, + mul(power(cutoff, C), target)) + limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500)) + for name, bounds, limit in zip(('alpha', 'gamma', 'delta'), + (alpha, gamma, delta), limits): + need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit') + a, g, d = limits + bound = 1/(1+v*(1-a))+2*g**v+2*d**v + need(bound < 1, 'complete charged normalized moment') + old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2, + mul(power(cutoff, C), target)) + old_lower = alpha[0]**v+2*old_gamma[0]**v + need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power') + return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor, + 'paid_moment_exponent': t+u, 'tail_offset_u': u, + 'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma), + 'delta': display(delta), 'rational_upper_limits': limits, + 'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2), + 'old_rank_one_gamma': display(old_gamma), + 'old_rank_one_bound_lower': display((old_lower, old_lower)), + 'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v), + 'maximum_paid': str(cutoff)+'^'+str(v), + 'productive_fields_before_uniform_compiler': '7688^'+str(v), + 'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v), + 'materialized_product_or_uniform_word': False} + + +def uniform_rank(v): + t, p, theta = 1-C, 13, Q(6, 7) + gap = (C-KAPPA)/7 + uniform_saving = C-gap + need(10**7 < 15**6, 'theta upper bound') + need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality') + eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t) + need(eta[0] > theta**p, 'exit contraction below complement capacity') + base = exp_interval(scale(log_bounds(121), v*C)) + need(base[1] < 2**p, 'entire ordinary base range fits') + # Integer grid: gap*H is integral, avoiding enormous rational powers. + step = gap.denominator + need(gap.numerator == 1, 'chosen rational gap grid') + + def passes(j): + H = step*j + return (H+1)**p < 2**j + + lo, hi = 1, 2 + while not passes(hi): + lo, hi = hi, 2*hi + while hi-lo > 1: + mid = (lo+hi)//2 + if passes(mid): + hi = mid + else: + lo = mid + H = step*hi + need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison') + need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails') + return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap, + 'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta), + 'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)), + 'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H), + 'integer_test': {'left_base': H+1, 'left_exponent': p, + 'right_base': 2, 'right_exponent': hi}, + 'grid_step': step, 'previous_grid_point_rejected': True, + 'smaller_logarithmic_power_rejected': True} + + +def power_majorant_comparison(v, uniform_saving): + """Retain #4416's older power proof, changing only the new unit's ranks.""" + t, z, h = 1-C, 1-uniform_saving, Q(1, 7) + z0 = (t+z)/2 + delta = z0-t + B, debt = (4+7*h)*v, 1+7*v*(1-z0) + ratio = (delta*B+debt)/(h*delta) + H0 = -((-ratio.numerator)//ratio.denominator) + ratio = H0*(1-z0)/(z-z0) + H1 = ratio.numerator//ratio.denominator+1 + need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold') + need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected') + need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0), + 'strict power-majorant comparison and previous-rank control') + return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h, + 'scope': 'Tail transformation alone, retaining the older power majorant.'} + + +def outer_ledger(uniform_saving): + d = (C-KAPPA)/7 + params = {'kappa': KAPPA, 'tested_saving': C, + 'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d, + 'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'), + 'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10, + 'stop': d, 'layout': d, 'd': d} + env = source_environment(HERE/'vendor/outer_endpoint.py') + row = env['ledger'](params) + need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3, + 'complete first outer ledger') + need(all(v > 0 for group in ('strict_checks', 'functional_checks') + for v in row[group].values()), 'all outer predicates') + frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer'] + need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger') + parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes()) + function = next(n for n in parsed.body + if isinstance(n, ast.FunctionDef) and n.name == 'ledger') + constants = [n for n in parsed.body if isinstance(n, ast.Assign) + and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_') + for t in n.targets)] + eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a')) + grid = 10**10 + backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA + need(backoff > 0, 'strict derived oracle grid backoff') + oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8), + 'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff, + 'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2), + 'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16), + 'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'], + 'online': Q('0.001730970419199163702738'), + 'old': Q('0.001730970419199163702738')} + code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[])) + exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle) + second = oracle['ledger']('higher_moment_smaller_ranks') + need(second['kappa'] == KAPPA and second['margins'] == row['margins'], + 'all nine rows match both ledgers') + need(len(second['strict_checks']) == 63 and + all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates') + controls = {} + for name, updates in [('closed_epsilon', {'epsilon': Q(1)}), + ('missing_layout', {'layout': Q(0)}), + ('unfunded_kappa', {'kappa': C}), + ('closed_uniform_gap', {'complex_uniform_saving': params['b']}), + ('insufficient_BIT', {'bit_saving': Q('0.0023')})]: + bad = env['ledger'](dict(params, **updates)) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'outer control rejected: '+name) + controls[name] = failed + for name, options in [('old_per_axis_scan', {'old_scan': True}), + ('group_equals_dimension', {'beta_': eps})]: + bad = oracle['ledger']('reject_'+name, **options) + failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0) + need(failed, 'legacy control rejected: '+name) + controls[name] = failed + return {'ledger': row, 'legacy_63_checks': second['strict_checks'], + 'legacy_grid': grid, 'legacy_backoff': backoff, + 'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA, + 'rejected_controls': controls} + + +def finite_controls(): + def tensor(histogram): + out = Counter() + for k, n in histogram.items(): + for h, b in histogram.items(): + out[k*h] += n*b + return out + + def split(histogram, cutoff): + out = Counter() + for k, n in histogram.items(): + q, r = divmod(k, cutoff) + out[cutoff] += q*n + if r: + out[r] += n + return +out + + target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1}) + padded, completion = Counter(), Counter() + for k, n in target.items(): + padded[max(k, 9)] += n + if k < 9: + completion[9-k] += n + final = split(paid+completion, 4) + mass = lambda x: sum(k*n for k, n in x.items()) + need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass') + need(min(padded) > max(final), 'exact toy separation') + need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory') + # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension. + invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1] + need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting') + return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13, + 'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2', + 'sigma': '3/4', 'actual_charge': 100, + 'invalid_upper': display((invalid, invalid))}} + + +def verify(): + sources = authenticate() + invoice = invoice_oracle() + tail = tail_certificate() + rank = uniform_rank(tail['tensor_power']) + endpoint = outer_ledger(rank['uniform_saving']) + controls = finite_controls() + rejected = [] + for name, updates, expected in [ + ('too_short_product', {'v': 100}, 'complete charged normalized moment'), + ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'), + ('lost_separation', {'floor': 10}, 'strict finite ranks'), + ]: + try: + tail_certificate(**updates) + except ValueError as error: + need(str(error) == expected, 'wrong rejection: '+name) + rejected.append({'mutation': name, 'failed_at': str(error)}) + else: + raise ValueError('accepted mutation: '+name) + old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler'] + return encoded({'schema': 'higher-moment-native-strictification/1', + 'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA, + 'invoice_oracle': invoice, 'strictification': tail, + 'uniform_rank': rank, 'outer': endpoint, + 'tail_only_power_majorant': power_majorant_comparison( + tail['tensor_power'], rank['uniform_saving']), + 'finite_controls': controls, 'rejected_mutations': rejected, + 'predecessor_H': old['H1'], + 'rank_exponent_reduction_factor': Q(old['H1'], rank['H']), + 'tensor_power_reduction_factor': Q(6240, tail['tensor_power']), + 'source_sha256': sources, + 'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(), + 'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'}) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = verify() + if args.out: + need(not args.out.exists(), 'new output path required') + args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n') + else: + need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt') + print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'], + 'uniform_rank': result['uniform_rank']['N'], + 'strict_moment_gap': result['strictification']['strict_moment_gap'], + 'kappa': result['kappa']})) + + +if __name__ == '__main__': + main() diff --git a/research/p104-two-chain-shared-native/retained/runtime/second_intervals.py b/research/p104-two-chain-shared-native/retained/runtime/second_intervals.py new file mode 100644 index 0000000000..4fc05ab081 --- /dev/null +++ b/research/p104-two-chain-shared-native/retained/runtime/second_intervals.py @@ -0,0 +1,291 @@ +#!/usr/bin/env python3 +"""Exact tariffs for productive helpers with heterogeneous target sizes. + +This is a conditional recursion-contract probe, not a new kappa claim. The +native helper adapters, main controller closure, scalar/precision charges, +and the mixed-target outer theorem remain separate obligations. + +Apache-2.0. Substantial OpenAI assistance. The original pruned native profile +and helper inventory come from the preserved kappa-function-composition work. +Mixed-target balance follows Jacob Alan Sussman's PR4268 proposal; this file +does not reprove or admit its all-size or integer-multiplication transfer. +The rational elementary-function enclosure follows the independently retained +productive_helper_forest.py recovery certificate, with fresh source identity. +""" +from collections import Counter +from fractions import Fraction as Q +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import json +import math +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +NATIVE = Counter({1:2453, 2:716, 3:224, 4:74, 5:48}) +HELPERS = Counter({5:28, 6:18, 7:56, 8:93, 9:213}) +OLD_PAIRS = [(56,9,7),(56,7,9),(18,9,6),(18,6,9), + (16,9,5),(16,5,9),(44,8,8)] +OLD_MIDDLE = [(93,8),(56,7),(18,6),(28,5),(29,0)] + +def need(ok, message): + if not ok: + raise AssertionError(message) + +@lru_cache(None) +def log_interval(r): + def odd_series(x): + z = (x-1)/(x+1) + n = 80 + low = 2*sum((z**(2*j+1)/(2*j+1) for j in range(n)), Q(0)) + high = low+2*z**(2*n+1)/((2*n+1)*(1-z*z)) + return low, high + exponent = r.bit_length()-1 + a,b = odd_series(Q(2)) + c,d = odd_series(Q(r,2**exponent)) + return exponent*a+c, exponent*b+d + +def exp_interval(x): + need(0 <= x < 1, 'Enclosure range') + term = total = Q(1) + n = 48 + for j in range(1,n+1): + term *= x/j + total += term + following = term*x/(n+1) + return total, total+following/(1-x/(n+2)) + +@lru_cache(None) +def h_interval(r,c): + if r in (0,1): + return Q(r),Q(r) + a,b = log_interval(r) + low,_ = exp_interval(c*a) + _,high = exp_interval(c*b) + return Q(r)/high,Q(r)/low + +def moment(profile,c): + low=high=Q(0) + for r,n in profile.items(): + a,b=h_interval(r,c) + low += n*(a if n >= 0 else b) + high += n*(b if n >= 0 else a) + return low,high + +def show(bounds): + scale=10**35 + low,high=bounds + a=low.numerator*scale//low.denominator + b=-((-high.numerator*scale)//high.denominator) + def fixed(n): + sign='-' if n<0 else '' + s=str(abs(n)).rjust(36,'0') + return sign+s[:-35]+'.'+s[-35:] + return {'lower':fixed(a),'upper':fixed(b)} + +def split_rank(r,maximum): + """Least concave tariff partition with positive integers <= maximum.""" + need(maximum>=1 and r>=0, 'Legal split') + q,remainder=divmod(r,maximum) + result=Counter() + if q: + result[maximum]+=q + if remainder: + result[remainder]+=1 + return result + +def split_profile(profile,maximum): + result=Counter() + for r,n in profile.items(): + for child,count in split_rank(r,maximum).items(): + result[child]+=n*count + return result + +def add_scaled(target,source,multiple=1): + for key,value in source.items(): + target[key]+=multiple*value + +def base_case(p,minimum,pairs=None,middle=None): + """Expand all role inventories; one fresh global field per unhosted role.""" + need(p in (1,2), 'Only reconstructed p1 and p2 schedules are in scope') + need(2<=minimum<=41, 'Finite minimum-target menu') + calls=2*p+1 + main_fields=224*p + main_rank=16*p+9 + inventories=[Counter(HELPERS) for _ in range(calls)] + paid=split_profile(NATIVE,minimum-1) + paid=Counter({r:calls*n for r,n in paid.items()}) + paid[1]+=8*calls # same-width H completion, never waived + targets=Counter({main_rank:main_fields}) + if p==1: + need(pairs is None and middle is None, 'p1 has no original idle bins') + else: + pairs=pairs if pairs is not None else [(224,0,0)] + middle=middle if middle is not None else [(224,0)] + need(sum(n for n,a,b in pairs)==224, 'Each pair window has 224 bins') + need(sum(n for n,a in middle)==224, 'Middle window has 224 bins') + for stages in [(0,1),(3,4)]: + for n,a,b in pairs: + need(a+b<=16 and a in (0,5,6,7,8,9) and b in (0,5,6,7,8,9), 'Pair capacities') + for stage,r in zip(stages,(a,b)): + if r: + inventories[stage][r]-=n + add_scaled(paid,split_rank(16-a-b,minimum-1),n) + for n,r in middle: + need(r in (0,5,6,7,8), 'Middle capacity') + if r: + inventories[2][r]-=n + add_scaled(paid,split_rank(8-r,minimum-1),n) + global_roles=Counter() + for inventory in inventories: + need(all(n>=0 for n in inventory.values()), 'No helper role used twice') + global_roles.update(inventory) + for r,n in global_roles.items(): + if not n: + continue + target=max(r,minimum) + targets[target]+=n + add_scaled(paid,split_rank(target-r,minimum-1),n) + paid=+paid + targets=+targets + need(max(paid)0] + # Middle bins are independent single slots; choose positive-gain roles first. + candidates=sorted(((sp(8)-sp(8-r)-value(r),r) for r in (5,6,7,8)),reverse=True) + middle=[] + left=224 + for gain,r in candidates: + if gain>1e-12: + n=min(HELPERS[r],left) + if n: + middle.append((n,r)) + left-=n + if left: + middle.append((left,0)) + return pairs,middle,{'status':int(out.status),'message':out.message,'not_an_exact_optimality_claim':True} + +def run(discover=False): + candidates=[] + for p in (1,2): + for minimum in range(2,26): + candidates.append(base_case(p,minimum)) + candidates.append(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)) + discovery=[] + if discover: + for c in (.001745,.004): + for minimum in range(5,18): + pairs,middle,meta=discover_pair_patterns(minimum,c) + case=base_case(2,minimum,pairs,middle) + case['discovery_target']=str(c) + case['solver']=meta + discovery.append(case) + candidates.extend(discovery) + best={} + for p in (1,2): + for text in ('0.001745','0.004'): + c=Q(text) + rows=[case for case in candidates if case['p']==p] + ranked=sorted(rows,key=lambda case:-numerical_value(case['signed'],float(c))) + winner=ranked[0] + # Certify that this displayed winner beats all numerically distinct + # profiles in the finite scanned menu, not all possible schedules. + win=moment(winner['signed'],c) + for case in ranked[1:]: + if dict(case['signed'])!=dict(winner['signed']): + need(win[0]>moment(case['signed'],c)[1], 'Exact finite-menu ordering') + best[f'p{p}_{text}']=serialize_case(winner) + controls={} + wrong=base_case(1,6) + wrong['targets'][6]+=1 + controls['unearned_output_credit_rejected']=(sum(r*n for r,n in wrong['targets'].items())-wrong['rank_bill']!=wrong['rank_margin']) + controls['rank5_child_with_job5_rejected']=not(5<5) + need(all(controls.values()), 'Corruption controls') + return {'schema':'productive-helper-mixed-target-tariff/1', + 'status':'PASS_CONDITIONAL_EXACT_ACCOUNTING', + 'source_sha256':sha256(Path(__file__).read_bytes()).hexdigest(), + 'native_profile':dict(NATIVE),'helper_inventory':dict(HELPERS), + 'assumed_recursive_rule':'sum_paid n_r r^(1-C) < sum_targets W_k k^(1-C); max_paid_rank < min_target_rank', + 'best_in_finite_menu':best, + 'fixed_p2_minimum9':serialize_case(base_case(2,9,OLD_PAIRS,OLD_MIDDLE)), + 'discovery_candidates':[serialize_case(c) for c in discovery], + 'controls':controls, + 'not_proved':['native whole-helper adapters and arbitrary-input block diagonal contract', + 'correct main controller and all its heads/caches/cleanup', + 'literal eligibility of any displayed head-cut grant', + 'mixed-target all-size recursion in this native model', + 'finite-precision integer-multiplication transfer and scalar/stock costs'], + 'new_kappa':False} + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--discover',action='store_true') + parser.add_argument('--output',type=Path,default=HERE/'MIXED-TARGET-PROBE.json') + args=parser.parse_args() + result=run(args.discover) + args.output.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + print(json.dumps({'status':result['status'],'best':{k:v['targets_at_C'][k.split('_',1)[1]]['after_native_completion_before_main_closure'] for k,v in result['best_in_finite_menu'].items()}},sort_keys=True)) + +if __name__=='__main__': + main() diff --git a/research/p104-two-chain-shared-native/root_check.py b/research/p104-two-chain-shared-native/root_check.py new file mode 100644 index 0000000000..1b3ab1189b --- /dev/null +++ b/research/p104-two-chain-shared-native/root_check.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Root checker for the two-chain root (standard library). python3 -I -B root_check.py [data/root.json] +The root is literally two copies of the #6833 chain-nested root on orthogonal coordinates (n = 20 each), one stage variable per stage, units interleaved +(chain A, chain B). This checker (1) regenerates the chain root from its closed form (L site i: x = A + f_i + 2 sum_{jm} h_l, y = A* + h_m*; three thin queries) and requires all 21 units of EACH chain to equal the file, requires the cross Gram between +the chains to vanish and each chain's Gram to be sgn(i-j); (2) re-proves the SPEC-level identities for the whole root in exact Fractions: isotropy, product -I, +stage order, units inside masks, masks commuting with the prefix before and after the stage, the symbolic whole-job identity M(D) = -diag(prod D^eps) with each D once and affine, +full mask credit, dyadic x,y. +DECLARED: the lines of the predecessor family checks that this root does not satisfy, and why they are not requirements of the outer theorem: + hosted t != 0 (ROOTAUDIT-style rootcheck line 'hosted t not 0, not -1'): here t = 0 by construction (no coupled plane; two separate planes per stage); + hosted alpha, beta dyadic units: here alpha = beta = 0 (same reason); + Gram digraph strongly connected (added by the #6883 root_check.py itself, not a SPEC line): here the Gram digraph has two components. + The theorem's requirement is on the unit identity and the whole-job credit, not on connectivity (see README).""" +import json, os, sys +from fractions import Fraction as Q + +def chain_sites(): + """The (9|9) chain-nested sites of #6833: list of (x, y, mask or None) in time order, n = 20 (field 19 is the empty field E).""" + n = 20; A = 0; f = list(range(1, 10)); h = list(range(10, 19)); E = 19 + def vec(*pairs): + v = [Q(0)] * n + for i, c in pairs: v[i] += Q(c) + return v + out = [] + for i in range(9): + out.append((vec((A, 1), (f[i], 1), *[(f[j], 2) for j in range(i)]), vec((A, 1), (f[i], -1)), {A, *f[:i + 1]})) + def thin(a, u, p=0, q=0): + x = [Q(0)] * n; y = [Q(0)] * n + x[A] = Q(a); y[A] = Q(u) + for i, j in enumerate(f): x[j] = Q(a + 1); y[j] = Q((1 - u) * (-1) ** i) + for r, j in enumerate(reversed(h)): x[j] = Q(1 - a); y[j] = Q((u - 1) * (-1) ** r) + x[E] = Q(q); y[E] = Q(p) + return x, y, None + out += [thin(0, 1, 0, 1), thin(-1, 2, 1, 0), thin(-1, 3, 1, -1)] + for m in range(9): + out.append((vec((A, -1), (h[m], 1), *[(h[l], 2) for l in range(m + 1, 9)]), vec((A, 1), (h[m], 1)), {A, *h[m:]})) + return out + +def blocks(R): + """Regeneration and block identities; returns a list of failure names (empty = all hold).""" + n, N = R['n'], R['N']; bad = [] + X = [[Q(v) for v in r] for r in R['X']]; Y = [[Q(v) for v in r] for r in R['Y']] + S = chain_sites() + if n != 40 or N != 42 or len(S) != 21: return ['shape'] + for c, off in (('A', 0), ('B', 20)): + for k, (x, y, m) in enumerate(S): + u = 2 * k + (0 if c == 'A' else 1) + ex = [Q(0)] * 40; ey = [Q(0)] * 40 + for i in range(20): ex[off + i] = x[i]; ey[off + i] = y[i] + if X[u] != ex or Y[u] != ey: bad.append('regeneration chain %s unit %d' % (c, k)) + dot = lambda a, b: sum(u * v for u, v in zip(a, b) if u and v) + ua = [2 * k for k in range(21)]; ub = [2 * k + 1 for k in range(21)] + if any(dot(Y[i], X[j]) != 0 or dot(Y[j], X[i]) != 0 for i in ua for j in ub): bad.append('cross Gram between the chains') + for nm, us in (('A', ua), ('B', ub)): + if any(dot(Y[i], X[j]) != ((a > b) - (a < b)) for a, i in enumerate(us) for b, j in enumerate(us)): bad.append('Gram of chain %s is not sgn(i-j)' % nm) + return bad + +def run(R, out=None): + """All requirements; returns the list of failures.""" + pr = out or (lambda s: None) + n, N = R['n'], R['N']; ST = R['stages'] + X = [[Q(v) for v in r] for r in R['X']]; Y = [[Q(v) for v in r] for r in R['Y']] + bad = [] + def req(name, ok, info=''): + pr(('PASS ' if ok else 'FAIL ') + name + (' ' + str(info) if info != '' else '')) + if not ok: bad.append(name) + dot = lambda a, b: sum(u * v for u, v in zip(a, b) if u and v) + bb = blocks(R) + req('two #6833 chain roots: all 21 units of each chain regenerate from the closed form, cross Gram 0, each Gram sgn(i-j)', not bb, bb[:3]) + if bb: return bad + I = [[Q(int(i == j)) for j in range(n)] for i in range(n)] + def lmul(M, x, y, c): + d = [sum(y[i] * M[i][j] for i in range(n) if y[i]) for j in range(n)] + return [[M[i][j] + c * x[i] * d[j] for j in range(n)] if x[i] else M[i][:] for i in range(n)] + req('isotropy y_k.x_k=0 all k', all(dot(Y[k], X[k]) == 0 for k in range(N))) + W = I; prefix = [] + for k in range(N): + prefix.append(W); W = lmul(W, X[k], Y[k], Q(-2)) + prefix.append(W) + req('T_{N-1}..T_0 = -I (I - 2xy)', W == [[-v for v in r] for r in I]) + us = [u for s in ST for u in s['units']]; L = len(ST) + req('stage units disjoint, consecutive, in time order, one unit of each chain per stage', len(us) == len(set(us)) and all(s['units'] == [s['units'][0], s['units'][0] + 1] for s in ST) and all(max(ST[i]['units']) < min(ST[i + 1]['units']) for i in range(L - 1)) and all(set(s['mask']) == {c for c in range(40) if any(X[u][c] or Y[u][c] for u in s['units'])} or set(s['mask']) >= {c for c in range(40) if any(X[u][c] or Y[u][c] for u in s['units'])} for s in ST)) + pr(' N n L tau %d %d %d %d thin units %s; mask ranks %s' % (N, n, L, N - len(us), [k for k in range(N) if k not in set(us)], [len(s['mask']) for s in ST])) + inside = lambda s: all(all(X[u][c] == 0 and Y[u][c] == 0 for c in range(n) if c not in set(s['mask'])) for u in s['units']) + req('stage units inside their coordinate mask', all(inside(s) for s in ST)) + def comm(mask, M): + m = set(mask); return all(M[i][j] == 0 for i in range(n) for j in range(n) if (i in m) != (j in m)) + req('mask commutes with the prefix before and after the stage', all(comm(s['mask'], prefix[min(s['units'])]) and comm(s['mask'], prefix[max(s['units']) + 1]) for s in ST)) + rows = [{i: {0: Q(1)}} for i in range(n)]; at = {max(s['units']): i for i, s in enumerate(ST)}; peak = 0 + for k in range(N): + dual = {} + for f, c in enumerate(Y[k]): + if c: + for col, p in rows[f].items(): + e = dual.setdefault(col, {}) + for m, v in p.items(): e[m] = e.get(m, 0) + c * v + for r, c in enumerate(X[k]): + if c: + for col, p in dual.items(): + e = rows[r].setdefault(col, {}) + for m, v in p.items(): + w = e.get(m, 0) - 2 * c * v + if w: e[m] = w + else: e.pop(m, None) + if not e: rows[r].pop(col) + if k in at: + b = 1 << at[k] + for r in ST[at[k]]['mask']: + new = {} + for col, p in rows[r].items(): + q = {} + for m, v in p.items(): + if m & b: bad.append('stage variable twice'); return bad + q[m | b] = v + new[col] = q + rows[r] = new + peak = max(peak, sum(len(p) for r in rows for p in r.values())) + tgt = [sum(1 << i for i, s in enumerate(ST) if r in set(s['mask'])) for r in range(n)] + req('symbolic M(D) = -diag(prod D^eps), eps = mask incidence, each of the 18 stage variables once and affine', all(rows[r] == {r: {tgt[r]: Q(-1)}} for r in range(n)), 'peak monomials %d' % peak) + req('every stage variable credited on all of its mask', all(bin(sum(1 << r for r in range(n) if tgt[r] >> i & 1)).count('1') == len(ST[i]['mask']) for i in range(L))) + dy = lambda v: v.denominator & (v.denominator - 1) == 0 + req('x, y dyadic', all(dy(v) for r in X + Y for v in r)) + pr(' declared family lines not met: t = alpha*beta = 0 for every stage pair (alpha = %s, beta = %s); Gram digraph has 2 components (cross Gram 0); max |entry| %s' % (dot(Y[0], X[1]), dot(Y[1], X[0]), max(abs(v) for r in X + Y for v in r))) + return bad + +if __name__ == '__main__': + R = json.load(open(sys.argv[1] if len(sys.argv) > 1 else os.path.join(os.path.dirname(os.path.abspath(__file__)), 'data', 'root.json'))) + bad = run(R, print) + print('PASS_ROOT_TWO_CHAINS' if not bad else 'FAILED ' + '; '.join(bad)) + sys.exit(1 if bad else 0) diff --git a/research/p104-two-chain-shared-native/verify_relaxed.py b/research/p104-two-chain-shared-native/verify_relaxed.py new file mode 100644 index 0000000000..49b7b6b2e9 --- /dev/null +++ b/research/p104-two-chain-shared-native/verify_relaxed.py @@ -0,0 +1,34 @@ +#!/usr/bin/env python3 +"""RELAXED per-event verifier (one line differs from verify_strict.py): the predecessor rules (native.py:52-72 / local.py:122-160), standard library. +python3 -B verify_relaxed.py data/word.json.gz prints every rejected event as (index, rule) and the rejection count. +Rule 'move nesting' (declared change): a public MOVE must ascend, an owned MOVE must be nested in either direction; paid |delta dim| either way.""" +import gzip, json, sys +from fractions import Fraction as Q +W = json.load(gzip.open(sys.argv[1], 'rt')) +def span(b): + s = {0} + for v in b: s |= {x ^ v for x in s} + return frozenset(s) +sp = [span(b) for b in W['frames']]; n = len(W['initial']); NR = n + W['owned_fields'] +cur = list(W['initial']) + [None] * W['owned_fields']; owned = set(); rej = [] +for i, e in enumerate(W['program']): + op, r = e[0], e[1] + if op == 'MOVE': + _, r, a, b, pv = e + if cur[r] != a or bool(pv) != (r in owned): rej.append((i, 'move current')); + elif not ((sp[b] < sp[a] or sp[a] < sp[b]) if pv else sp[a] < sp[b]): rej.append((i, 'move nesting')) + cur[r] = b + elif op == 'INIT': + if not (r >= n and r not in owned): rej.append((i, 'init')) + owned.add(r); cur[r] = e[2] + elif op == 'CLEAR': + if not (r in owned and cur[r] == e[2]): rej.append((i, 'clear')) + owned.discard(r); cur[r] = None + else: + q = Q(e[2] if op == 'SCALE' else e[3]); f = e[-1] + if q == 0 or cur[r] != f: rej.append((i, 'scalar frame')); continue + if q.denominator & (q.denominator - 1) or not abs(q) + 1 < 2 ** 16: rej.append((i, 'scalar alphabet')) + if op == 'SCALE' and abs(q.numerator) & (abs(q.numerator) - 1): rej.append((i, 'unit')) + if op != 'SCALE' and not (e[2] != r and 0 <= e[2] < NR and cur[e[2]] == f): rej.append((i, 'scalar source')) +print('rejected events:', len(rej), sorted({x[1] for x in rej}), 'indices', ' '.join(str(x[0]) for x in rej)) +print('REJECTED_RELAXED' if rej else 'ACCEPTED_RELAXED') diff --git a/research/p104-two-chain-shared-native/verify_strict.py b/research/p104-two-chain-shared-native/verify_strict.py new file mode 100644 index 0000000000..edc183339b --- /dev/null +++ b/research/p104-two-chain-shared-native/verify_strict.py @@ -0,0 +1,34 @@ +#!/usr/bin/env python3 +"""STRICT per-event verifier: the predecessor rules (native.py:52-72 / local.py:122-160), standard library. +python3 -B verify_strict.py data/word.json.gz prints every rejected event as (index, rule) and the rejection count. +Rule 'move nesting' (native.py:55; local.py:126 'Nested chronological transport'): a public MOVE must ascend, an owned MOVE must descend.""" +import gzip, json, sys +from fractions import Fraction as Q +W = json.load(gzip.open(sys.argv[1], 'rt')) +def span(b): + s = {0} + for v in b: s |= {x ^ v for x in s} + return frozenset(s) +sp = [span(b) for b in W['frames']]; n = len(W['initial']); NR = n + W['owned_fields'] +cur = list(W['initial']) + [None] * W['owned_fields']; owned = set(); rej = [] +for i, e in enumerate(W['program']): + op, r = e[0], e[1] + if op == 'MOVE': + _, r, a, b, pv = e + if cur[r] != a or bool(pv) != (r in owned): rej.append((i, 'move current')); + elif not (sp[b] < sp[a] if pv else sp[a] < sp[b]): rej.append((i, 'move nesting')) + cur[r] = b + elif op == 'INIT': + if not (r >= n and r not in owned): rej.append((i, 'init')) + owned.add(r); cur[r] = e[2] + elif op == 'CLEAR': + if not (r in owned and cur[r] == e[2]): rej.append((i, 'clear')) + owned.discard(r); cur[r] = None + else: + q = Q(e[2] if op == 'SCALE' else e[3]); f = e[-1] + if q == 0 or cur[r] != f: rej.append((i, 'scalar frame')); continue + if q.denominator & (q.denominator - 1) or not abs(q) + 1 < 2 ** 16: rej.append((i, 'scalar alphabet')) + if op == 'SCALE' and abs(q.numerator) & (abs(q.numerator) - 1): rej.append((i, 'unit')) + if op != 'SCALE' and not (e[2] != r and 0 <= e[2] < NR and cur[e[2]] == f): rej.append((i, 'scalar source')) +print('rejected events:', len(rej), sorted({x[1] for x in rej}), 'indices', ' '.join(str(x[0]) for x in rej)) +print('REJECTED_STRICT' if rej else 'ACCEPTED_STRICT') From cfe4febddaecd42e34816a2c2710807ab432866d Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 8 Nov 2026 19:04:58 -0600 Subject: [PATCH 2/4] Reword a comment in the root checker Co-Authored-By: Claude Opus 5.5 --- research/p104-two-chain-shared-native/root_check.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/research/p104-two-chain-shared-native/root_check.py b/research/p104-two-chain-shared-native/root_check.py index 1b3ab1189b..febc9c8953 100644 --- a/research/p104-two-chain-shared-native/root_check.py +++ b/research/p104-two-chain-shared-native/root_check.py @@ -7,7 +7,7 @@ stage order, units inside masks, masks commuting with the prefix before and after the stage, the symbolic whole-job identity M(D) = -diag(prod D^eps) with each D once and affine, full mask credit, dyadic x,y. DECLARED: the lines of the predecessor family checks that this root does not satisfy, and why they are not requirements of the outer theorem: - hosted t != 0 (ROOTAUDIT-style rootcheck line 'hosted t not 0, not -1'): here t = 0 by construction (no coupled plane; two separate planes per stage); + hosted t != 0 (The hosted family's root check line 'hosted t not 0, not -1'): here t = 0 by construction (no coupled plane; two separate planes per stage); hosted alpha, beta dyadic units: here alpha = beta = 0 (same reason); Gram digraph strongly connected (added by the #6883 root_check.py itself, not a SPEC line): here the Gram digraph has two components. The theorem's requirement is on the unit identity and the whole-job credit, not on connectivity (see README).""" From e4d42607f24d7a049b0fca329dc4c34882405c25 Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 8 Nov 2026 19:06:18 -0600 Subject: [PATCH 3/4] Reword a label in the package check Co-Authored-By: Claude Opus 5.5 --- research/p104-two-chain-shared-native/check.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/research/p104-two-chain-shared-native/check.py b/research/p104-two-chain-shared-native/check.py index b62c5b4409..3b6113542d 100644 --- a/research/p104-two-chain-shared-native/check.py +++ b/research/p104-two-chain-shared-native/check.py @@ -368,7 +368,7 @@ def d2log(terms): # ---- declared departures ----------------------------------------------------------------------- print('DEPARTURES (class; exact count here):') for cls, what in ( - ('new family: reducible root', 'the root is literally two #6833 chain roots on orthogonal coordinates, t = 0 at every stage, Gram digraph with two components; the family lines t != 0 (ROOTAUDIT-style rootcheck line "hosted t not 0, not -1"), alpha and beta dyadic units, and "Gram digraph strongly connected" (added by the #6883 root_check.py, not a SPEC line) do not hold. What the outer theorem requires is the unit identity and whole-job credit, which root_check.py re-proves (SPEC-level lines all pass).'), + ('new family: reducible root', 'the root is literally two #6833 chain roots on orthogonal coordinates, t = 0 at every stage, Gram digraph with two components; the family lines t != 0 (the hosted family root check line "hosted t not 0, not -1"), alpha and beta dyadic units, and "Gram digraph strongly connected" (added by the #6883 root_check.py, not a SPEC line) do not hold. What the outer theorem requires is the unit identity and whole-job credit, which root_check.py re-proves (SPEC-level lines all pass).'), ('new event', 'HOST2: one native contact per stage that serves both chains (18 events, forward contact q^-1 on the first plane, q on the second, 124 LAMBDA events with the second chain flipped).'), ('new form', 'same-label second mains: X2 and Y2 carry the same initial and final frame labels as X and Y (asserted above); 4 main registers per port, 416 mains; per-port boundary terms are doubled in the raw count.'), ('convention (A6, load-bearing)', 'owned ascent: 23 owned rises (rank mass 56) against native.py:55 / local.py:126; peak owned 30; 8 owned reads of Y2 (events %s). No ascent, no word.' % oy), From dc232440d60a140cea146f7c57582f236125d05f Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 8 Nov 2026 20:51:15 -0600 Subject: [PATCH 4/4] Use the literal carrier 153 in the compiler capacity line and raise the logarithm power; state the LAMBDA derivation Co-Authored-By: Claude Opus 5.5 --- research/p104-two-chain-shared-native/README.md | 4 ++-- research/p104-two-chain-shared-native/TASK.json | 2 +- research/p104-two-chain-shared-native/check.py | 9 +++++---- 3 files changed, 8 insertions(+), 7 deletions(-) diff --git a/research/p104-two-chain-shared-native/README.md b/research/p104-two-chain-shared-native/README.md index 4e24287fbd..3c692a301b 100644 --- a/research/p104-two-chain-shared-native/README.md +++ b/research/p104-two-chain-shared-native/README.md @@ -30,10 +30,10 @@ The ledger needs the BIT saving to exceed κ + 4·gap = 0.00351406004. `check.py * Precision, as a reading: the quantizer method of CubeJerry (#6900) transfers to this word with its literal hypotheses replaced (free Laurent prefixes, numerators ≤ 16 and its constants), giving W = p + h + 153f + 25, F = p + ⌈153f/2⌉ + 7, temporaries W + 9; the ledger ignores W. This is a reading from the review of the method, not re-derived here; the precision-tape assumption is inherited. ## LAMBDA is a review question -LAMBDA at width f is the single elementary gate C on (q,…,q), not a lift of the width-one LAMBDA (they agree only at f = 1). The caller identity holds under both readings, so the algebra does not decide it; the price does. If each LAMBDA had to be paid as a rank-1 job per port, S = 1520 − 124·104 = **−11,376 < 0** and no crossing exists (the #6889 caller: 1520 − 82·104 = −7,008). The κ rests on pricing LAMBDA as ordinary work, as in every caller of this line from #6726 on, including #6833 (62 events per chain here). Declared as a convention, not admitted on main. +LAMBDA at width f is the single elementary gate C on (q,…,q), not a lift of the width-one LAMBDA (they agree only at f = 1). The caller identity holds under both readings, so the algebra does not decide it; the price does. If each LAMBDA had to be paid as a rank-1 job per port, S = 1520 − 124·104 = **−11,376 < 0** and no crossing exists (the #6889 caller: 1520 − 82·104 = −7,008). The κ rests on pricing LAMBDA as ordinary work, as in every caller of this line from #6726 on, including #6833 (62 events per chain here). Declared as a convention, not admitted on main. **Reading, by an independent review, stated as the reading it is (not proved here, not on main):** Q = C^{⊗f} on (q,…,q) and C² = X (`upstream/build/sections/05-layers.tex:65`: "C^2=X, C^4=I"), so Q² = T, a pure translation, at every f; the reviews of #5599 and #6030 already use it ("Q^2 is the native translation with phase +1 at every width; scalar signs stay outside tensor powers", `docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md:59-60`; `pr6030-audit/PROOF-REVIEW.md:80-83`). Then LAMBDA = aI + bT with a, b = (1±i)/2 has row support 2 at every f (it is not the f-th tensor power), and compiles as `INIT t; COPY t = x; T(t); x := a x + b t` (numerator first); `CLEAR t`, with T the native translation: the macro of the thin query of the open #6900 (not on main) with its paid Q⁻¹ replaced by the ordinary translation. The lift is "substitution of the fixed coordinate, phase and scalar generators. It does not tensor a sum of matrix operators" (`research/higher-moment-strictification/vendor/p7-TENSOR.md:42-44`), native monomial maps and quadratic phases "lift column by column" (`research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md:243-248`), and finite compositions of permitted words are permitted (FP:45-46). Under this reading LAMBDA costs ordinary work and S does not go negative; I have not verified the tape-level implementation, and the κ is unchanged by it. ## Logarithm power -The smallest admissible value at this price is **2133**; **2134 is written** and used. 2100 fails here: the complement-capacity line (η > (63/64)^logp at maximum target rank 145) binds at 2100 for a tested price of about 0.0034607, below this claim. The power is a free parameter of the compiler theorem (`research/higher-moment-strictification/vendor/LOG-MAJORANT.md:110-122`; stated with an integer q and 1/q in the bound, its literal conditions fail for the real exponent used, and the code uses the same argument with a real p, which a reviewer of #6884 re-walked and I did not). The interval engines are the retained rational ones (no Decimal) at the tested price: α = 0.9999999975, γ = 0.9480, δ = 0.8116 (< 31/32), the composite bound 1/(1+power·reserve) + 4·decay^power < 1 holds, the 54 strict and 4 functional outer inequalities are positive (their smallest value is the chosen parameter r0 = gap/10, not a measured margin). The input-lift saving lemma of #6833 has its cap moved to the pin and passes. +The smallest admissible value at this price is **2156**; **2157 is written** and used. The complement-capacity line (η > (63/64)^logp) is taken on the literal carrier of **153** axes (9 base rows and 8 per stage × 18; the 8 complement rows of q lie in no target, so the carrier exceeds the largest target rank 145), because the fit m·c ≤ N of FP:111-114 is on the carrier. **An earlier version of this package used m = 145 in that line and wrote 2134, which was too low; no κ changes.** 2100, 2134 and 2155 fail. The power is a free parameter of the compiler theorem (`research/higher-moment-strictification/vendor/LOG-MAJORANT.md:110-122`; stated with an integer q and 1/q in the bound, its literal conditions fail for the real exponent used, and the code uses the same argument with a real p, which a reviewer of #6884 re-walked and I did not). The interval engines are the retained rational ones (no Decimal) at the tested price: α = 0.9999999975, γ = 0.9480, δ = 0.8116 (< 31/32), the composite bound 1/(1+power·reserve) + 4·decay^power < 1 holds, the 54 strict and 4 functional outer inequalities are positive (their smallest value is the chosen parameter r0 = gap/10, not a measured margin). The input-lift saving lemma of #6833 has its cap moved to the pin and passes. ## Declared, and inherited | class | declaration (counts recomputed by `check.py`) | diff --git a/research/p104-two-chain-shared-native/TASK.json b/research/p104-two-chain-shared-native/TASK.json index badb699a50..77c3931375 100644 --- a/research/p104-two-chain-shared-native/TASK.json +++ b/research/p104-two-chain-shared-native/TASK.json @@ -97,7 +97,7 @@ }, "scope_status": "changed", "actual_scope": "Can one hosted native word serve two copies of the chain-nested root at once, on separate main registers, so that the helpers are shared between the chains and the complete signed invoice improves?", - "scope_change_reason": "Same hosted native, A6 declaration and BIT line as #6889. Changed: the root becomes two #6833 chain roots on orthogonal coordinates (t = 0, a reducible root), the caller gets one HOST2 contact per stage serving both chains, and the word carries four main registers per port (same-label second mains, 959 helpers, 38,334 events). Correctness rests on the exact replay of the final word and the root block identities. The BIT saving of the open #6726 (.00376669) is necessary: nothing else on main clears kappa + 4 gap. The logarithm power is written as 2134 (minimum 2133). Raw counts 963,421,184 / 965,490,968 / 971,071,328, all below 10^9. LAMBDA priced as ordinary work is a review question (paid rank 1 per port gives S < 0). Inherited: owned ascent (A6, 23 rises of mass 56, peak 30, 8 owned reads of Y2), LAMBDA and IDLE_ONE.", + "scope_change_reason": "Same hosted native, A6 declaration and BIT line as #6889. Changed: the root becomes two #6833 chain roots on orthogonal coordinates (t = 0, a reducible root), the caller gets one HOST2 contact per stage serving both chains, and the word carries four main registers per port (same-label second mains, 959 helpers, 38,334 events). Correctness rests on the exact replay of the final word and the root block identities. The BIT saving of the open #6726 (.00376669) is necessary: nothing else on main clears kappa + 4 gap. The logarithm power is written as 2157 (minimum 2156 on the literal carrier 153; an earlier version used 145 and was too low). Raw counts 963,421,184 / 965,490,968 / 971,071,328, all below 10^9. LAMBDA priced as ordinary work is a review question (paid rank 1 per port gives S < 0). Inherited: owned ascent (A6, 23 rises of mass 56, peak 30, 8 owned reads of Y2), LAMBDA and IDLE_ONE.", "bottleneck_link": "docs/research/research-family-status.md; complete signed native/caller invoice and all supplier-admission gates", "stop_rule": "The claim is conditional on the five retained framework assumptions, the declared owned ascent (A6), the BIT saving of the open #6726, and the declared new forms (reducible root, HOST2, same-label second mains); no claim above the pin; LAMBDA must be priced as ordinary work for any crossing to exist.", "evidence": "README.md, PROOF-OWNED-ASCENT.md, check.py, root_check.py, cover_check.py, physical.py, caller_physical.py, ordinary.py, verify_strict.py, verify_relaxed.py, data/ (word, caller, root, #6889 word and root, base invoice, physical invoice), retained/bit (the pinned #6726 admission file); claimed kappa 0.00351406 (crossing 0.00351406186742169).", diff --git a/research/p104-two-chain-shared-native/check.py b/research/p104-two-chain-shared-native/check.py index 3b6113542d..a73bea7e89 100644 --- a/research/p104-two-chain-shared-native/check.py +++ b/research/p104-two-chain-shared-native/check.py @@ -313,7 +313,7 @@ def logsum(Wx): return sum(math.log2(1 + float(abs(Q(e_[3])))) for e_ in Wx['pro for r, c in signed.items(): lg = E.log_bounds(r); d -= c * (E.mul(E.power(r, 1 - PIN), lg)[0] if c >= 0 else r * lg[1]) need(d < 0, 'unique raw crossing through the BIT pin (derivative upper bound negative at the pin)') -cutoff, floor, power, offset = 11, 12, 1920, Q(1, 7); LP = 2134 +cutoff, floor, power, offset = 11, 12, 1920, Q(1, 7); LP = 2157 tt_ = 1 - TESTED; target, paidm = E.moment(Tq, tt_), E.moment(Pq, tt_) alpha = E.divide(paidm, target); gamma = E.divide(E.moment(Pq, tt_ + offset), E.mul(E.power(cutoff, offset), target)) delta = E.divide((Q(sum(Tq.values()) * floor),) * 2, E.mul(E.power(cutoff, TESTED), target)) @@ -321,12 +321,13 @@ def logsum(Wx): return sum(math.log2(1 + float(abs(Q(e_[3])))) for e_ in Wx['pro need(alpha[1] < 1 - reserve and gamma[1] < decay and delta[1] < decay, 'tail ratios (interval engine): alpha %.12f gamma %.4f delta %.4f (cutoff 11, floor 12, offset 1/7, power 1920)' % (float(alpha[1]), float(gamma[1]), float(delta[1]))) normalized = 1 / (1 + power * reserve) + 4 * decay ** power need(normalized < 1, 'composite bound (predecessor pricing.py:211): 1/(1+power*reserve) + 4*decay^power < 1 at power 1920 (excess over the first term %.2e)' % float(4 * decay ** power)) -maxT = max(Tq); quarter = E.power(maxT, Q(power, 4) * TESTED); factor = E.mul(E.mul(quarter, quarter), E.mul(quarter, quarter)) +maxT = max(Tq); carrier = max(maxT, int(C['ambient_rank'])) # the compiler fit m*c <= N (FP:111-114) is on the literal carrier, 9 base rows + 8 per stage = 153, not on the largest target rank 145 +quarter = E.power(carrier, Q(power, 4) * TESTED); factor = E.mul(E.mul(quarter, quarter), E.mul(quarter, quarter)) eta = E.scale(E.divide((Q(1), Q(1)), factor), tt_) -need(eta[0] > Q(63, 64) ** LP and factor[1] < 2 ** LP and cutoff ** 64 < floor ** 63 and 2 * (cutoff ** power) ** 64 <= (maxT ** power) ** 63, 'compiler complement capacity and shifted exits at logarithm power %d (max target rank %d)' % (LP, maxT)) +need(eta[0] > Q(63, 64) ** LP and factor[1] < 2 ** LP and cutoff ** 64 < floor ** 63 and 2 * (cutoff ** power) ** 64 <= (carrier ** power) ** 63, 'compiler complement capacity and shifted exits at logarithm power %d on the literal carrier %d (the largest target rank is %d; an earlier version used 145 and was too low)' % (LP, carrier, maxT)) lp_ = LP while eta[0] > Q(63, 64) ** (lp_ - 1): lp_ -= 1 -need(lp_ == 2133 and Q(63, 64) ** 2100 > eta[0], 'logarithm power: the smallest admissible value at this price is %d, written as %d (2100 FAILS here: it is a free parameter, LOG-MAJORANT.md:110-122, and the wall of 2100 is at a tested price near .0034607, below this claim)' % (lp_, LP)) +need(lp_ == 2156 and Q(63, 64) ** 2134 > eta[0] and Q(63, 64) ** 2155 > eta[0], 'logarithm power: on the literal carrier 153 the smallest admissible value at this price is %d, written as %d (the value 2134 written by an earlier version, computed with the largest target rank 145 in place of the carrier, and 2155 both FAIL; it is a free parameter, LOG-MAJORANT.md:110-122)' % (lp_, LP)) gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'compiler grid: (tested-kappa)/7 = %s' % gap) step = gap.denominator wins = lambda j: (step * j + 1) ** LP < 2 ** j

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