From a3d665bf170a0a3ebc5ea60354ae9e19a199388d Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 8 Nov 2026 17:42:45 -0600 Subject: [PATCH] Conditional kappa 0.003452786: choose X and Y merges of the hosted mirror jointly with the shared helpers Co-Authored-By: Claude Opus 5.5 --- research/p104-hosted-joint-merge/LICENSE | 201 + research/p104-hosted-joint-merge/NOTICE | 3 + .../PROOF-OWNED-ASCENT.md | 33 + research/p104-hosted-joint-merge/README.md | 72 + research/p104-hosted-joint-merge/SOURCES.json | 46 + research/p104-hosted-joint-merge/TASK.json | 149 + research/p104-hosted-joint-merge/VERIFY.json | 60 + .../caller_physical.py | 59 + research/p104-hosted-joint-merge/check.py | 434 + .../p104-hosted-joint-merge/cover_check.py | 115 + .../data/base_invoice.json | 61 + .../p104-hosted-joint-merge/data/caller.json | 1 + .../data/control_root_ungauged.json | 1 + .../data/invoice_check.json | 40 + .../data/prior_word.json.gz | Bin 0 -> 708696 bytes .../data/prior_word_6884.json.gz | Bin 0 -> 908508 bytes .../data/prior_word_6886.json.gz | Bin 0 -> 552255 bytes .../p104-hosted-joint-merge/data/root.json | 1 + .../p104-hosted-joint-merge/data/word.json.gz | Bin 0 -> 680179 bytes research/p104-hosted-joint-merge/ordinary.py | 48 + research/p104-hosted-joint-merge/physical.py | 112 + .../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 + .../p104-hosted-joint-merge/root_check.py | 137 + .../p104-hosted-joint-merge/verify_relaxed.py | 34 + .../p104-hosted-joint-merge/verify_strict.py | 34 + 32 files changed, 22438 insertions(+) create mode 100644 research/p104-hosted-joint-merge/LICENSE create mode 100644 research/p104-hosted-joint-merge/NOTICE create mode 100644 research/p104-hosted-joint-merge/PROOF-OWNED-ASCENT.md create mode 100644 research/p104-hosted-joint-merge/README.md create mode 100644 research/p104-hosted-joint-merge/SOURCES.json create mode 100644 research/p104-hosted-joint-merge/TASK.json create mode 100644 research/p104-hosted-joint-merge/VERIFY.json create mode 100644 research/p104-hosted-joint-merge/caller_physical.py create mode 100644 research/p104-hosted-joint-merge/check.py create mode 100644 research/p104-hosted-joint-merge/cover_check.py create mode 100644 research/p104-hosted-joint-merge/data/base_invoice.json create mode 100644 research/p104-hosted-joint-merge/data/caller.json create mode 100644 research/p104-hosted-joint-merge/data/control_root_ungauged.json create mode 100644 research/p104-hosted-joint-merge/data/invoice_check.json create mode 100644 research/p104-hosted-joint-merge/data/prior_word.json.gz create mode 100644 research/p104-hosted-joint-merge/data/prior_word_6884.json.gz create mode 100644 research/p104-hosted-joint-merge/data/prior_word_6886.json.gz create mode 100644 research/p104-hosted-joint-merge/data/root.json create mode 100644 research/p104-hosted-joint-merge/data/word.json.gz create mode 100644 research/p104-hosted-joint-merge/ordinary.py create mode 100644 research/p104-hosted-joint-merge/physical.py create mode 100644 research/p104-hosted-joint-merge/retained/bit/FRAGMENT-BIT-ADMISSION.json create mode 100644 research/p104-hosted-joint-merge/retained/native/clifford_exact.py create mode 100644 research/p104-hosted-joint-merge/retained/physical-review/NOTICE create mode 100644 research/p104-hosted-joint-merge/retained/physical-review/verify.py create mode 100644 research/p104-hosted-joint-merge/retained/runtime/DATA-PHASES.json create mode 100644 research/p104-hosted-joint-merge/retained/runtime/endpoint.py create mode 100644 research/p104-hosted-joint-merge/retained/runtime/intervals.py create mode 100644 research/p104-hosted-joint-merge/retained/runtime/second_intervals.py create mode 100644 research/p104-hosted-joint-merge/root_check.py create mode 100644 research/p104-hosted-joint-merge/verify_relaxed.py create mode 100644 research/p104-hosted-joint-merge/verify_strict.py diff --git a/research/p104-hosted-joint-merge/LICENSE b/research/p104-hosted-joint-merge/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/PROOF-OWNED-ASCENT.md b/research/p104-hosted-joint-merge/PROOF-OWNED-ASCENT.md new file mode 100644 index 0000000000..7929b21a81 --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/README.md b/research/p104-hosted-joint-merge/README.md new file mode 100644 index 0000000000..139eea4270 --- /dev/null +++ b/research/p104-hosted-joint-merge/README.md @@ -0,0 +1,72 @@ +# Conditional κ = 0.003452786 (+0.685% over #6886): joint merges of the hosted mirror + +**Result.** The exact-kernel crossing of the complete signed invoice is **0.00345278688457739788**, which is **+0.6852% over #6886** (0.00342928953721633; exactly 0.685196%) and **+1.5546% over #6883** (0.00339993013239573), the base of the hosted line of work; also +1.0759% over #6884 and +2.4019% over #6833. +The claim for the outer statement is **κ = 0.003452786** with tested price 0.0034527867 (grid 10⁻¹⁰), both strictly below the raw crossing, which lies in (0.003452786884577, 0.003452786884578). +The package keeps the root, caller and hosted pair (α, β) = (−1, 1/2), t = −1/2 of #6883 and the 24-pad word of #6886 as its comparison; only the native word changes (`data/word.json.gz`, a single input). + +**Conditional statement.** The result holds under the five framework assumptions of #6833; under assumption A6 (owned ascent) as declared in #6883; and under a BIT saving that is not admitted by anything on main, for which the pin used is the 0.00376669 of the open #6726. +**What the BIT line needs numerically.** Only that the saving exceeds κ + 4·gap (here 0.0034527864) and the tested price; `check.py` runs the ledger at eight values: 0.0034 (main's admitted saving), 0.00343, 0.0034363538396 (main's ordinary stock) and #5421's 0.00344412 fail; #4760's 0.0034597, #4814's 0.003475458, #5512's 0.003483969976 and #6726's 0.00376669 pass all 54 + 4 inequalities, with margins over the tested price of 6.9e-6, 2.3e-5, 3.1e-5 and 3.139e-4. The claim is above main's admitted saving and ordinary stock. The values of #4760, #4814, #5512 and #5421 are read from `docs/research/pr-ledger.json` at the base commit (titles, status `merged_for_archive_only`; "Archival publication does not admit a supplier" in `pr-intake-decisions.json`), so none of them is an admitted saving; #6726 is open. #6726 is therefore a choice with the largest margin, not a numerical necessity, and the claim stays conditional on whichever saving is adopted. 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; #6726, #6883, #6884 and #6886 are open pull requests. +Margins of the #6726 file, as read: the raw BIT tested saving 0.0037667 exceeds the pin by 1.0e-8, and the raw BIT crossing lower bound exceeds the raw BIT tested saving by 2.3e-8. + +## What changed against the #6886 word (counted on the words by `cover_check.py`) +Correctness rests only on the exact replay of the final word, with the physical and caller replays below. The builders' truncation argument (a pad is needed only where the forward network both writes X and reads Y; Law H, applied per time segment) is a hand argument; it is not used and not cited as a bound. +* Public registers 1371 → 1363, MOVEs 6634 → 6518, core ADDs 6719 → 6722, core SCALEs 730 → 715; owned lifetimes (54) and COPY unchanged; no silent helper. The builders report 339 deletions (#6884: 342) and the core has 3 more ADDs than the #6886 word; which events differ was not traced. +* **Direct reads of Y by helpers** (the mirror reads the forward network's Y register itself): 210 → 245, changing on 42 ports (30 gain, 12 lose). **Direct writes into X by helpers:** 436 → 553 on 51 ports (50 gain, 1 loses). Helper reads of X change on 1 port; helper writes into Y on none. +* The builders report 6 joint Y components on 12 ports (the #6886 word had 24 pad-less ports), 6 X units on 12 ports, 118 shared helpers, 40 Y tails and 37 X heads. These counts are not recoverable from the words alone; what is counted above is their effect, and what is checked is that the endpoint is exact. The 51 ports whose direct X writes change are the 12 unit ports and 37 head ports plus 2 more, X registers 41 (one more write: helper 401, coefficient 2, frame id 1090) and 79 (one write fewer: helper 269, coefficient −1, frame id 73), traced here against the builders' port lists; neither is a head or a unit, and both are single-event differences consistent with the different deletion set; the replay governs. +* Gate blocks are solved per word and split so that every coefficient stays in the alphabet: events before the core 69,980 → 90,770, after 39,688 → 39,677; total events 123,860 → 144,511. +* Exactly one owned register reads a main Y register: event 98540, `ADD 1394 134 -2` at frame id 595 (`check.py` asserts it); the #6886 word had two such reads, the second now reads a helper. Declared with A6. Peak owned fields 25. +* Controls (replay): a wrong weight (×2), a missing event and an event taken twice, each on 6 sampled direct Y reads and 6 sampled direct X writes of the changed ports, are all rejected; so are removing the first core ADD and removing any of 12 sampled core ADDs. +* Owned ascent is unchanged: 23 events, rank mass 56, 19 lifetimes with rises (3 read before the rise, 3 with contacts between rises, none both rising and falling, same start frames), so the list of what goes beyond the P112 precedent does not change. The hosted pair is unchanged: T[Y,X] = 1/2, Tinv[X,Y] = 1, block determinant 1, helpers identity, and XX = YY = D, YX = Q⁻¹D, XY = QD on all 104 ports. +* Targets: 38×104 diagonal fields plus 1155 helpers per call (#6886: 1163); 6518 paid moves per call; dD per hosted call 7284.61 (#6886: 7451.30); S = 656 + 48·18 = 1520, net of 56 per hosted call. New = 2 × base + 29774.0 − 29737.7 = +36.25 at the crossing. + +## Raw bound +* Literal definition (18 × 10⁷ + caller, thin, output and adapter terms): 948,952,288 < 10⁹. +* With the actual per-call work (18 × 11,874,748 + the same terms): **982,697,752 < 10⁹**, margin 17,302,248 (1.7%). +* With the review's conservative count (reviewed scalar upper 4,434,656 + routes 9,668,000, 18 × 14,102,656): **1,022,800,096, which exceeds 10⁹ by 2.28%.** The same formula gives 983,664,136 / 1,019,551,024 for #6883, 999,138,736 / 1,052,149,312 for #6884 and 975,554,380 / 1,006,146,280 for #6886, so the conservative line has been over 10⁹ since #6883. +* Substitution (FP:278-283): events 144,511; scalar allowance 2,206,748 or reviewed upper 4,434,656; routes 9,668,000; per call 11,874,748 or 14,102,656 (both above the displayed 10⁷ of pricing.py:93); caller envelope 258,618,880. The growth bound written for the precision contract is **2^(1,022,800,096 + 347,996·f)** on the conservative count (2^(982,697,752 + 347,996·f) on actual work), R = 347,996 the paid rank mass, as in FP:278-283 and `OUTER-TRANSFER-AUDIT.md:382,390`. +* No term of the outer ledger reads this number (`check.py` verifies that the ledger source has none). That it is not load-bearing is a reading of the texts, not a proof; the precision and tape contract (`research/p104-productive-controller/PROOF.md` section 5) is inherited and not examined; the only packages above 10⁹, on the conservative line, are the open #6883, #6884, #6886 and this one. + +## Growth of the scalar updates (productive-controller PROOF.md section 5: fewer than 26,000 events, |q|+1 < 2¹⁶, local bound 2^(16·26000) = 2^416000) +* Events: 144,511 here; all four words are above 26,000 (read literally the bound is 2^(16·events)). +* Sum of log2(1+|q|) over the ADD coefficients, the actual local growth exponent per call: 246,857 here, 171,846 in #6886, 309,379 in #6884, 196,440 in #6883, against 416,000: below it in every word. +* This word: peak |row entry| on any prefix 2^23.2 (#6886: 2^15.5), peak row denominator 2^21 (#6886: 2^17), coefficient bits at most 28 (numerator) and 17 (denominator), largest |q| 62,224, so |q|+1 stays 3,311 below 2¹⁶. +* Alphabet: no event has |q|+1 ≥ 2¹⁶ (0 of the ADD and COPY events; the largest is event 108841, `ADD 188 1148 -62224`), and 489 ADDs have |q| ≥ 2¹². But the gate blocks were split so that this holds per event: there are 41 clusters of adjacent ADDs on one register pair and frame, and 31 of them add up to |sum|+1 ≥ 2¹⁶ (234 pieces). The largest true combined coefficient is −2,689,024, in 83 pieces at events 108873-108955. The rule (local.py:90) is per event, so each event is legal; a reader should know the true combined coefficients. Ten further adjacent clusters, eight of them exact cancelling pairs, are harmless and removable (the review that found them lists the events; not recounted here). +* The conservative raw count 1,022,800,096 is above #6883's conservative count 1,019,551,024, as well as above 10⁹. +* `check.py` computes these on the word it is given. + +## The outer statement +Cutoff 11, floor 12, offset 1/7, power 1920 hold unchanged: α = 0.99999999977, γ = 0.9475, δ = 0.8516 (< 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); both interval engines bracket the crossing. The input-lift saving lemma of #6833 (pricing.py:128-156) has its cap moved to the pin and passes. +**Logarithm power.** The smallest admissible value at this price is **2096**; 2100 is used. With 2100 the complement-capacity line (η > (63/64)^logp at maximum target rank 145) binds at a tested price of about 0.0034607, 7.9e-6 above the tested price used: this is the wall near 0.00346, and this claim is close to it. The power is a free parameter of the compiler theorem (`research/higher-moment-strictification/vendor/LOG-MAJORANT.md:110-122` is stated with an integer q and 1/q in the bound, its literal conditions (3) and (4) fail for the real exponent used, and the code uses the same argument with 1/q replaced by a real p; a reviewer of #6884 re-walked that replacement, I did not); a larger power moves the wall. + +## Inherited, stated here +**A6, owned ascent (load-bearing: no ascent, no word):** an owned nested rise costs one paid H_r plus rank-0 adapters, no credit, on arbitrary contents, factorwise at every width, with CLEAR at any frame under owned_erasure. The one-line rule change, both verifiers (the strict one rejects this word at exactly the 23 events), the direction-free cost argument and the evidence read at the base commit 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. + +| class | departure (recomputed by `check.py`) | +|---|---| +| convention (A6) | owned ascent, native.py:55 / local.py:126: 23 events, rank mass 56; one owned read of a main Y register (above) | +| verifier | endpoint literal native.py:75-77 / local.py:168: the hosted target replaces `X = x, Y = x + y` on the 104 main pairs | +| verifier | events 144,511, public 1363, owned roles 51, 54 lifetimes, peak 25 (local.py:52,54,103; pricing.py:84-87) | +| verifier | per-call scalar work 11,874,748 against the displayed 10⁷ (pricing.py:93) | +| verifier | caller coefficient height 9 and 8 bits against 8 and 7 (pricing.py:96-97) | +| convention | LAMBDA: 82 caller events, a two-term scalar pass at width ≥ 2, inherited from the open callers #6726 and #6763; no compiler list names it and it is not on main; the text does not decide whether it is a scalar or a routing pass. Verified algebraically by the composition replay, counted in ordinary work, no physical contact check | +| convention | root family N = n + 2, two units per stage (chain_root.py:79,82,83,98; check_root.py:26,133,141-145) | +| convention | one-site idles: a rank-8 one-field idle is a whole job by the compiler definition (FP:23-26); IDLE_ONE comes from the open #6716 and #6726. The 36×104 are paid whole H8 idles in P[8]; targets get nothing for them. Priced as eight rank-1 jobs each, κ would be 0.003024 | +| assumption | dirty owned erasure (the existing owned_erasure assumption) | + +## Check +`check.py` (about 45 s): exact event replay; strict and relaxed verifiers with the rejection control; root checker; composition at four central characters with the pair read from the root and controls; invoice rebuilt from word, root and caller, with the #6886, #6884, #6883 and #6833 words as comparison controls; the three raw figures; growth figures; the owned read of Y; interval engines; the BIT pin and the failures at the pins that need no open pull request; input-lift lemma; logarithm power and its wall; strictification, compiler and outer ledger; departures. +`ordinary.py` (seconds): the raw figures. `cover_check.py` (about 30 s): the counts and controls above. `physical.py` (about 30 s): all events as 512-component streams over F_p[i] (p = 10⁹+9), chart predictions, raw main-pair identities by tableau and phase on all 104 ports, with controls. `caller_physical.py` (about 15 s): the caller's physical replay through the retained independent physical audit (one declared line changed for A6): 7488 contact phases, reverse cross term, main targets, whole idles on every owner and port, field map and alias control, invoice, adapters, controls. + +## 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. Not independently examined: the adjoint (transpose) physical replay of this word; which events differ in the deletion set (339 reported against 342) and why 3 more core ADDs remain; streams at tensor width 2 or more (width 3, Q = −i, not run); the BIT verifiers (the admission is read, not re-run); the builders' derivation of the truncation weights; the compiler texts beyond the parts quoted in `PROOF-OWNED-ASCENT.md`. 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` (counts, event numbers, raw figures) are the ones to update. + +## Open next questions +1. Is owned ascent (A6), with the owned read of a main Y register, accepted for the native verifier, as it is in the P112 native? +2. Which BIT saving is adopted for the outer statement? The ledger needs only more than κ + 4·gap: the open #6726's 0.00376669 (margin 3.1e-4) or the archive-only values of #4760, #4814 or #5512 (margins 6.9e-6 to 3.1e-5), none of which is admitted; main's admitted 0.0034 and its ordinary stock 0.00343635 do not suffice. +3. Does the conservative raw count 1,022,800,096 matter for the precision and tape contract, or can the gates be rebuilt a little smaller so that it falls under 10⁹? +4. Are the single-field idle (IDLE_ONE) and the two-term LAMBDA pass of the open callers admitted to the compiler's job list? + +## Credit +Builds on #6883 (hosted pair at every call of the chain-nested root: root, caller and checks), #6884 (shared cover and deletions), #6886 (the 24-pad word, whose package this one extends), #6833 (chain-nested root, invoice and outer ledger), #6726 (zxv, two-pair root caller; 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), 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-hosted-joint-merge/SOURCES.json b/research/p104-hosted-joint-merge/SOURCES.json new file mode 100644 index 0000000000..1de4f0ee51 --- /dev/null +++ b/research/p104-hosted-joint-merge/SOURCES.json @@ -0,0 +1,46 @@ +{ + "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" + }, + "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-hosted-joint-merge/TASK.json b/research/p104-hosted-joint-merge/TASK.json new file mode 100644 index 0000000000..49a3ef09a8 --- /dev/null +++ b/research/p104-hosted-joint-merge/TASK.json @@ -0,0 +1,149 @@ +{ + "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 the mirror of the hosted native be merged jointly with the forward network on more ports (Y components, X units, Y tails, X heads, shared helpers), with the complete signed invoice improving?", + "scope_change_reason": "Same root, caller, hosted pair, deletions and BIT pin as #6886 (built on #6883 and #6884). Changed: the word. Direct reads of Y by mirror helpers change on 42 ports and direct writes into X on 51 ports, 8 fewer public registers, 116 fewer MOVEs, gate blocks rebuilt. Correctness rests on the exact replay of the final word. The claim is above main's admitted BIT saving and ordinary stock; the pin used is .00376669 of the open #6726, which the ledger needs only to exceed kappa + 4 gap (archive-only values .0034597, .003475458 and .003483969976 also pass). Raw count 982,697,752 on actual work (under 10^9) and 1,022,800,096 on the conservative count (over, as since #6883); the growth bound is written. Inherited: owned ascent (A6, 23 events of rank mass 56, one owned read of a main Y register), the endpoint literal, LAMBDA and IDLE_ONE, the root family, the idle pricing.", + "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), and a BIT saving above kappa + 4 gap that main has not admitted (the pin used is .00376669 of the open #6726; archive-only values of #4760, #4814 and #5512 also pass the ledger); no claim above the pin; the conservative raw count is over 10^9 and is stated.", + "evidence": "README.md, PROOF-OWNED-ASCENT.md, check.py, cover_check.py, physical.py, caller_physical.py, verify_strict.py, verify_relaxed.py, root_check.py, data/ (word, #6886, #6884 and #6883 words, root, caller, wrong-gauge control root, base invoice), retained/bit (the pinned #6726 admission file); claimed kappa 0.003452786 (crossing 0.00345278688457739788).", + "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, inherited from #6883: 23 owned rises, rank mass 56, 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": "Which BIT saving is adopted for the outer statement? The ledger needs only more than kappa + 4 gap: the open #6726's .00376669 or the archive-only values of #4760, #4814 or #5512; main's admitted .0034 and ordinary stock .00343635 do not suffice.", + "why_it_matters": "None of these savings is admitted on main.", + "first_step": "Merge or re-verify the #6726 BIT admission (retained/bit/FRAGMENT-BIT-ADMISSION.json) and replace the pin accordingly.", + "blocked_by": "#6726 is an open pull request; its BIT admission is read here from the pinned file and not re-derived." + }, + { + "question": "Are the single-field idle (IDLE_ONE) and the two-term LAMBDA pass of the open callers admitted to the compiler's job list?", + "why_it_matters": "The invoice prices the hosted-stage idles as whole H8 jobs; priced as eight rank-1 jobs each, kappa would fall to 0.002995.", + "first_step": "Locate the opcodes in the compiler's job list, or have them added with the substitution of constants written.", + "blocked_by": "Neither opcode is named on main." + }, + { + "question": "Does the conservative raw count 1,022,800,096 (above 10^9; the actual-work count 982,697,752 is below) matter for the retained precision and tape contract?", + "why_it_matters": "The growth bound 2^(10^9 + R f) would take the larger figure; the conservative line has been above 10^9 since #6883.", + "first_step": "Substitute the written constants into the precision contract, or rebuild the gates a little smaller.", + "blocked_by": "The precision-tape assumption text is not examined here." + } + ], + "research_context": { + "base": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "builds_on": [ + "#6883 hosted pair at every call of the chain-nested root (the base)", + "#6884 shared cover and deletions", + "#6886 24-pad word", + "#6833 chain-nested root", + "#6824 native word", + "#6805 helper recount", + "#6702 native source", + "#6726 BIT admission (pin)", + "#6868 chain optimality" + ], + "credit": "The prior work above; #6883 is the base." + }, + "selected_frontier_changed": false +} diff --git a/research/p104-hosted-joint-merge/VERIFY.json b/research/p104-hosted-joint-merge/VERIFY.json new file mode 100644 index 0000000000..24615a3dca --- /dev/null +++ b/research/p104-hosted-joint-merge/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 172166-event hosted word (frame law, endpoint, T and Tinv structure), extended root check, caller composition at all four central characters with the pair read from the root plus wrong-gauge and wrong-pair controls, invoice rebuilt from word, root and caller with the predecessor invoice rebuilt by the same code, exact kernel kappa, both interval engines, strictification, compiler and outer ledger, declared departures. Also: the #6883 word through the same code as a comparison control, the BIT pin read from the pinned #6726 admission file, the input-lift saving lemma with its cap at the pin, and the logarithm power." + }, + { + "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-hosted-joint-merge/caller_physical.py b/research/p104-hosted-joint-merge/caller_physical.py new file mode 100644 index 0000000000..9c0ac6c20f --- /dev/null +++ b/research/p104-hosted-joint-merge/caller_physical.py @@ -0,0 +1,59 @@ +#!/usr/bin/env python3 +"""Physical replay of the literal hosted caller (standard library): every HOST 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 HOST is read as the LOCAL contact (stage, source, destination). +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 forward cross coefficient, +the reverse cross coefficient D_stage Q^+1 that the hosted native adds, main-target exponents and translations, whole-idle rank and axis disjointness on every owner and port, +the field map (injective, fresh helpers, owned/query scratch disjoint) with the aliased-helper control, the complete invoice from the caller, 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] == 'HOST' else e for e in shim['events']] +need(sum(e[0] == 'LOCAL' for e in shim['events']) == 18, 'the caller has 18 hosted native contacts (HOST 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())))) +# reverse cross coefficient of the hosted native (X_out over Y_in = D_stage Q^+1), with the control Q^-1 +dim = C['ambient_rank']; axes = [1 << i for i in range(dim)]; bad = ctl = cnt = 0 +for e in C['events']: + if e[0] != 'HOST': 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 at %d stage-port pairs (control Q^-1 matches %d)' % (cnt, ctl)) +led = P.native_ledger(W, check_rows=False) +dm = [len(b) for b in W['frames']]; mn = set(W['live']) | {r + 112 for r in W['live']} +helc = Counter(dm[W['final'][r]] - dm[W['initial'][r]] for r in range(len(W['initial'])) if r not in mn) +NH = sum(helc.values()) +need(led['helpers'] == helc and led['public'] == len(W['initial']), 'native ledger of the hosted word: %d helpers, %d public (endpoint rows checked separately in check.py)' % (NH, len(W['initial']))) +fld = P.allocation(shim, W, led) +need(fld['invocations'] == 18 and fld['productive_fields'] == C['roles'] * 104 + 18 * NH and fld['main_fields'] == C['roles'] * 104, 'field map: %d productive fields, every native helper a distinct fresh field per call, injective public allocation, owned and query scratch disjoint' % fld['productive_fields']) +try: P.allocation(shim, W, led, alias=True); al = False +except ValueError: al = True +need(al, 'control: aliasing helpers across calls is rejected') +bill = P.invoice(shim, led, ph, fld) +inv = json.load(open(HERE + '/data/invoice_check.json')) +need(dict(bill['targets']) == {int(k): v for k, v in inv['T'].items()} and dict(bill['paid']) == {int(k): v for k, v in inv['P'].items()}, 'complete invoice from the physical audit equals the check.py invoice (targets and paid)') +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') +# controls: a swapped native chronology and a deleted idle are rejected +def rejected(f): + try: f(); return False + except (ValueError, SystemExit): return True +sw = copy.deepcopy(shim); idx = [i for i, e in enumerate(sw['events']) if e[0] == 'LOCAL']; sw['events'][idx[0]][1], sw['events'][idx[1]][1] = 2, 1 +need(rejected(lambda: P.physical(sw, 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')] +need(P.invoice(de, led, P.physical(de, W, recipes), fld)['paid'] != bill['paid'], 'control: deleting one idle job changes the invoice (so the idle layout is bound to the bill)') +print('PASS_CALLER_PHYSICAL') diff --git a/research/p104-hosted-joint-merge/check.py b/research/p104-hosted-joint-merge/check.py new file mode 100644 index 0000000000..b5d64d6974 --- /dev/null +++ b/research/p104-hosted-joint-merge/check.py @@ -0,0 +1,434 @@ +#!/usr/bin/env python3 +"""Exact replay of the hosted native word, the hosted chain-nested root, the complete invoice and the outer constants. +Standard library only. python3 -I -B check.py (writes nothing) +Steps: (1) event-by-event exact replay of data/word.json.gz; (2) root_check.py; (3) invoice rebuilt from the word and the root, +and the #6833 invoice rebuilt by the same code; (4) caller recount; (5) outer conditions with the retained interval engines. +Prints PASS_P104_HOSTED_CHAIN_ROOT. (physical.py, run as a second command, replays the 512-component physical streams.)""" +import gzip, json, os, sys, subprocess, importlib.util, random, hashlib, math +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) + +# ---- (1) replay of the word ------------------------------------------------------------------- +W = json.load(gzip.open(data('word.json.gz'), 'rt')) +def span(b): + s = {0} + for v in b: + need_ = isinstance(v, int) and 0 < v < 512 and v not in s + if not need_: 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): + o = subprocess.run([sys.executable, '-I', '-B', os.path.join(HERE, name), data('word.json.gz')], capture_output=True, text=True).stdout + return o +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') +al, be = Q(W['hosted']['alpha']), Q(W['hosted']['beta']); t = al * be +live = W['live']; X = set(live); Y = {r + 112 for r in live} +need(len(live) == len(W['ports']) == 104 and t == Q(-1, 2) and 1 + t != 0, 'hosted pair alpha=%s beta=%s t=%s, 1+t != 0' % (al, be, t)) +bad = 0 +for r in range(NR): + if r >= n: ex = {} + elif r in X: ex = {r: Q(1), r + 112: al} + elif r in Y: ex = {r - 112: be, r: 1 + t} + else: ex = {r: Q(1)} + bad += row[r] != ex +need(bad == 0, 'endpoint exact on all %d public and owned rows: X=x+alpha y, Y=beta x+(1+t) y, helpers identity, owned empty' % NR) +need(all(row[y].get(y - 112) == be for y in Y), 'T[Y,X]=beta on all 104 ports; Tinv[X,Y]=-alpha (block det 1)') +for r, q in zip(live, W['ports']): + 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') +need(True, '104 literal central ports, full X final frame, empty Y initial frame, literal output hyperplane') +main = X | Y +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)') +print(' events', len(W['program']), 'public', n, 'owned roles', NO, 'peak owned', peak, 'owned lifetimes', life, 'dirty owned erasures', dirty, 'max |coefficient|', maxq) + +def logsum(Wx): + return sum(math.log2(1 + float(abs(Q(e[3])))) for e in Wx['program'] if e[0] in ('ADD', 'COPY')) +l83 = logsum(json.load(gzip.open(data('prior_word.json.gz'), 'rt'))); l84 = logsum(json.load(gzip.open(data('prior_word_6884.json.gz'), 'rt'))) +print(' GROWTH (productive-controller PROOF.md section 5: fewer than 26000 events, |q|+1 < 2^16, local scalar growth bound 2^(16*26000) = 2^416000):') +print(' events: #6883 word 172166, #6884 word 222128, this word %d (all above the 26000 events of that text; its bound read literally is 2^(16*events) = 2^%d for this word)' % (len(W['program']), 16 * len(W['program']))) +print(' sum of log2(1+|q|) over the ADD coefficients (the actual local growth exponent per call): #6883 %d, #6884 %d, this word %d, against 416000' % (round(l83), round(l84), round(logq))) +print(' peak |row entry| on any prefix 2^%.1f; peak row denominator 2^%d; coefficient bits: numerator up to %d, denominator up to %d; largest |q| %s (|q|+1 < 2^16 = 65536)' % (math.log2(float(pmax)), dmaxb, nbits, dbits, maxq)) +l86 = logsum(json.load(gzip.open(data('prior_word_6886.json.gz'), 'rt'))) +need(round(l83) == 196440 and round(l84) == 309379 and round(l86) == 171846, 'sum of log2(1+|q|) of the #6883, #6884 and #6886 words: 196440, 309379 and 171846 (below 416000, but their event counts already exceed 26000)') +big_ = sum(1 for e_ in W['program'] if e_[0] in ('ADD', 'COPY') and abs(Q(e_[3])) >= 2 ** 12) +cl_ = []; i_ = 0; Pg = W['program'] +while i_ < len(Pg): + e_ = Pg[i_] + if e_[0] == 'ADD': + j_ = i_; s_ = Q(0) + while j_ < len(Pg) and Pg[j_][0] == 'ADD' and Pg[j_][1] == e_[1] and Pg[j_][2] == e_[2] and Pg[j_][4] == e_[4]: s_ += Q(Pg[j_][3]); j_ += 1 + if j_ - i_ > 1: cl_.append((i_, j_, s_)) + i_ = j_ + else: i_ += 1 +over_ = [c_ for c_ in cl_ if abs(c_[2]) + 1 >= 2 ** 16]; top_ = max(over_, key=lambda c_: abs(c_[2])) +need(big_ == 489 and len(over_) == 31 and sum(j_ - i_ for i_, j_, _ in over_) == 234 and top_ == (108873, 108956, Q(-2689024)), + 'alphabet: every event has |q|+1 < 2^16 (largest %s), but adjacent events on one register pair and frame add up: %d adjacent clusters, %d of them with |sum|+1 >= 2^16 (234 pieces; the largest true coefficient is %s over events %d-%d, %d pieces); %d ADDs have |q| >= 2^12 (declared; legal per event, the rule being per event)' % (maxq, len(cl_), len(over_), top_[2], top_[0], top_[1] - 1, top_[1] - top_[0], big_)) +oy = [i_ for i_, e_ in enumerate(W['program']) if e_[0] == 'ADD' and e_[1] >= n and e_[2] in Y] +oy4 = [i_ for i_, e_ in enumerate(json.load(gzip.open(data('prior_word_6884.json.gz'), 'rt'))['program']) if e_[0] == 'ADD' and e_[1] >= 1385 and e_[2] in Y] +need(oy == [98540] and list(W['program'][98540]) == ['ADD', 1394, 134, '-2', 595] and oy4 == [], 'owned registers reading a main Y register: %d events (event numbers %s; %s) in this word, none in the #6884 word; they replace pad reads and are declared with A6; peak owned fields %d' % (len(oy), oy, [list(W['program'][i_]) for i_ in oy], peak)) +# ---- (2) root ---------------------------------------------------------------------------------- +out = subprocess.run([sys.executable, '-I', '-B', os.path.join(HERE, 'root_check.py'), data('root.json')], capture_output=True, text=True).stdout +need(out.strip().endswith('PASS_ROOT_HOSTED') and 'FAIL' not in out, 'extended root checker: PASS_ROOT_HOSTED (relaxations declared in its header)') +R = json.load(open(data('root.json'))) + +# ---- (3) 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 outer(F, thin): + 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(18): + if hc[k] > 2: P[8] += 104 * (hc[k] - 2) + P[1] += 104 * thin + return T, P +def invoice(hel_, paid_, F, thin): + T, P = outer(F, thin) + for r, k in hel_.items(): T[r] += 18 * k + for r, k in paid_.items(): P[r] += 18 * k + return T, P +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)] + [([], [])] +Tb, Pb = invoice({int(k): v for k, v in bi['helpers'].items()}, {int(k): v for k, v in bi['local_paid'].items()}, chain, 3) +need(+Tb == T0 and +Pb == P0, 'same code rebuilds the #6833 invoice term for term') +kb = kappa(T0, P0) +need(abs(kb - D(bi['kappa_literal'])) < D('1e-17'), 'base kappa %s' % str(kb)[:20]) +ST = R['stages']; F = [] +for c in range(R['n']): + ms = [k for k, s in enumerate(ST) if c in set(s['mask'])] + F.append((ms, [k for k in ms if any(Q(R['Y'][u][c]) != 0 for u in ST[k]['units'])])) +thin = R['N'] - sum(len(s['units']) for s in ST) +Tn, Pn = invoice(hel, paid, F, thin) +kn = kappa(Tn, Pn) +need(abs(kn - D('0.0034527868845774')) < D('1e-16'), 'new kappa %s' % str(kn)[:22]) +# comparison control: the #6883 word (data/prior_word.json.gz) through the same code +Wp = json.load(gzip.open(data('prior_word.json.gz'), 'rt')); mp_ = set(Wp['live']) | {r + 112 for r in Wp['live']}; dp_ = [len(b) for b in Wp['frames']] +hel_p = Counter(dp_[Wp['final'][r]] - dp_[Wp['initial'][r]] for r in range(len(Wp['initial'])) if r not in mp_) +paid_p = Counter(abs(dp_[e[3]] - dp_[e[2]]) for e in Wp['program'] if e[0] == 'MOVE') +Tp, Pp = invoice(hel_p, paid_p, F, thin); kp = kappa(Tp, Pp) +need(abs(kp - D('0.00339993013239573')) < D('1e-17'), 'control: the #6883 word through the same code gives %s (its published kappa)' % str(kp)[:22]) +need(abs(kb - D(bi['kappa_literal'])) < D('1e-17'), 'secondary control: #6833 rebuilt, kappa %s' % str(kb)[:22]) +W4 = json.load(gzip.open(data('prior_word_6884.json.gz'), 'rt')); m4 = set(W4['live']) | {r + 112 for r in W4['live']}; d4 = [len(b) for b in W4['frames']] +h4 = Counter(d4[W4['final'][r]] - d4[W4['initial'][r]] for r in range(len(W4['initial'])) if r not in m4); p4 = Counter(abs(d4[e[3]] - d4[e[2]]) for e in W4['program'] if e[0] == 'MOVE') +T4_, P4_ = invoice(h4, p4, F, thin); k4 = kappa(T4_, P4_) +need(abs(k4 - D('0.00341603288178402')) < D('1e-17'), 'control: the #6884 word through the same code gives %s (its published kappa)' % str(k4)[:22]) +W6 = json.load(gzip.open(data('prior_word_6886.json.gz'), 'rt')); m6_ = set(W6['live']) | {r + 112 for r in W6['live']}; d6 = [len(b) for b in W6['frames']] +h6 = Counter(d6[W6['final'][r]] - d6[W6['initial'][r]] for r in range(len(W6['initial'])) if r not in m6_); p6 = Counter(abs(d6[e[3]] - d6[e[2]]) for e in W6['program'] if e[0] == 'MOVE') +T6_, P6_ = invoice(h6, p6, F, thin); k6 = kappa(T6_, P6_) +need(abs(k6 - D('0.00342928953721633')) < D('1e-17'), 'control: the #6886 word through the same code gives %s (its crossing)' % str(k6)[:22]) +print(' gain over #6886: %.6f%% (exactly kappa_new / kappa_6886 - 1 = %s); over #6883: %.4f%%; over #6884: %.4f%%; over #6833: %.4f%%' % (100 * float(kn / k6 - 1), str(100 * (kn / k6 - 1))[:9], 100 * float(kn / kp - 1), 100 * float(kn / k4 - 1), 100 * float(kn / kb - 1))) +S = sum(r * (Tn.get(r, 0) - Pn.get(r, 0)) for r in set(Tn) | set(Pn)) +need(S == 656 + 48 * 18 and D(PIN.numerator) / D(PIN.denominator) > kn, 'rank-mass surplus S=%d (656+48h, already net of the 56 owned-ascent mass per host); kappa above the retained .0034 pin and below the .00376669 pin by %s' % (S, str(D(PIN.numerator) / D(PIN.denominator) - kn)[:10])) + +# ---- (4) caller, composition, recount --------------------------------------------------------- +C = json.load(open(data('caller.json'))); Tc = Counter(); Pc = Counter(); nh = 0 +for e in C['events']: + if e[0] == 'HOST': 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 hosted native calls, 4 thin queries, one-site idle jobs)') +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 root_pairs(root): + """(alpha,beta) of every hosted stage, read from the root's own units: alpha=y_u.x_v, beta=y_v.x_u.""" + dot = lambda a_, b_: sum(Q(u) * Q(v) for u, v in zip(a_, b_) if Q(u) and Q(v)) + out = {} + for k, s_ in enumerate(root['stages']): + u, v = s_['units']; out[k + 1] = (dot(root['Y'][u], root['X'][v]), dot(root['Y'][v], root['X'][u])) + return out +def replay(Wc, qv, D, pairs): + """caller events over F_p at central character qv (q^4=1) and random stage values D; HOST uses the pair read from the ROOT, not from the event.""" + n_ = Wc['roles']; Rm = [[int(i == j) for j in range(n_)] for i in range(n_)]; qi = pow(qv, pM - 2, pM) + 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 * D[k] % pM + Rm[e[1]] = [a_ * c % pM for a_ in Rm[e[1]]] + elif o == 'HOST': + st, src, dst = e[1:4]; a_, b_ = fm(pairs[st][0]), fm(pairs[st][1]); tt_ = a_ * b_ % pM; d = D[st] + ns = [(x + a_ * qv % pM * y) % pM * d % pM for x, y in zip(Rm[src], Rm[dst])] + nd = [(b_ * qi % pM * x + (1 + tt_) * y) % pM * d % pM for x, y in zip(Rm[src], Rm[dst])] + Rm[src], Rm[dst] = ns, nd + else: raise SystemExit('FAIL unknown caller event ' + o) + 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 * D[k + 1] % pM + bad += sum(Rm[i][j] != (c if i == j else 0) for j in range(n_)) + return bad +rp = root_pairs(R) +need(set(rp.values()) == {(al, be)} and len(rp) == 18, 'every one of the 18 hosted stages of the root has the word\'s pair (alpha,beta)=(%s,%s)' % (al, be)) +need(all(e[4] == str(al) and e[5] == str(be) for e in C['events'] if e[0] == 'HOST'), 'every HOST event carries the word\'s pair') +need(all(bool(C['diagonal'][c][2 + k]) == (c in set(ST[k]['mask'])) for c in range(R['n']) for k in range(18)), 'caller target exponents equal the root mask incidence (field by field, stage by stage)') +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, rp); cnt += 1 +need(tot == 0, 'composition: caller with the hosted native replays to the diagonal root target at all four central characters, random stage values (%d evaluations, 0 bad of %d coefficients each)' % (cnt, R['n'] ** 2)) +R0 = json.load(open(data('control_root_ungauged.json'))); rp0 = root_pairs(R0) +bad0 = replay(C, IM, {s_: rnd.randrange(2, pM) for s_ in range(1, 19)}, rp0) +need(set(rp0.values()) != {(al, be)} and bad0 > 0, 'control: the same root in the other gauge (pairs (-1/2,1) at the right stages) is rejected: %d bad coefficients' % bad0) +muts = [] +for name, fn in (('alpha sign', lambda x: x.__setitem__(0, -x[0])), ('beta sign', lambda x: x.__setitem__(1, -x[1])), ('swapped', lambda x: x.reverse())): + pm = {k: list(v) for k, v in rp.items()}; fn(pm[13]); muts.append(replay(C, IM, {s_: rnd.randrange(2, pM) for s_ in range(1, 19)}, pm)) +need(all(muts), 'controls: wrong alpha sign / beta sign / swapped pair at one stage are rejected (bad %s)' % muts) +# departures that are counted rather than pinned +nums = [abs(Q(e[3] if e[0] == 'ADD' else e[2])) for e in C['events'] if e[0] in ('ADD', 'SCALE')] +hb = (max(x.numerator.bit_length() for x in nums), max(x.denominator.bit_length() for x in nums)) +scal = 0 +for e in W['program']: + if e[0] in ('INIT', 'CLEAR'): scal += 2 + elif e[0] == 'SCALE': + q = Q(e[2]); scal += 2 * (abs(q.numerator.bit_length() - q.denominator.bit_length()) + int(q < 0)) + elif e[0] in ('ADD', 'COPY'): + q = Q(e[3]); scal += 2 * (3 + abs(q.numerator).bit_length() - 1 + bin(abs(q.numerator)).count('1') + q.denominator.bit_length() - 1) +routes = (sum(paid.values()) + 2 * sum(hel.values()) + 208 + 4 * 104 + 4 * life) * 1000 +print('DEPARTURES (class; exact count here):') +for cls, what in ( + ('convention (A6, load-bearing)', 'owned ascent: 23 owned MOVEs rise in frame (rank mass 56); the predecessor native.py:55 / local.py:126 lets owned moves only descend. A6: an owned nested rise costs one paid H_r plus rank-0 adapters, no credit, on arbitrary contents, factorwise at every width, with CLEAR at any frame under owned_erasure. No ascent, no word; kappa is conditional on A6.'), + ('verifier', 'endpoint literal: the predecessor native.py:75-77 / local.py:168 expect X=x, Y=x+y; the hosted target is X=x-y, Y=(x+y)/2 on 104 ports (proved exactly above and physically in physical.py).'), + ('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 (the predecessor word already exceeds the 26000 cap; counts are recounted, not pinned).' % (len(W['program']), n, NO, life, peak)), + ('verifier', 'per-call scalar work %d against the displayed pricing.py:93 bound 10^7 (word scalar %d + routes %d); the outer ledger has no scalar-work term.' % (scal + routes, scal, routes)), + ('verifier', 'coefficient height of the caller: numerators up to %d bits, denominators up to %d bits against the predecessor 8 and 7 bits (pricing.py:96-97).' % hb), + ('convention', 'LAMBDA: 82 caller events (two-term two-sided scalar pass at width >= 2) inherited from the open predecessor callers (#6726, #6763); no compiler list names it and it is not on main; the text does not decide whether it is a scalar or a routing pass. It is checked algebraically by the composition replay at four central characters and counted in ordinary work, not by a physical contact check.'), + ('convention', 'root family: N=n+2 and two units per stage instead of the shortest root with one full site per child (chain_root.py:79,82,83,98; check_root.py:26,133,141-145); the SPEC-level identities are re-proved in root_check.py.'), + ('convention', 'pricing: the 36x104 one-site idle jobs at the hosted stages are PAID whole H8 idles (P[8]); targets get nothing for them. kappa rests on pricing them as whole H8 idles (the line construction attains that exactly); priced as 8 rank-1 jobs each, kappa would be 0.003024.'), + ('assumption', 'owned erasure of dirty owned content (%d erasures, predecessor 45): the owned_erasure assumption of the predecessor, unchanged.' % dirty)): + print(' [%s] %s' % (cls, what)) +need(True, 'departures listed') + +# ---- (4b) ordinary (non-recursive) raw bound: definition of the predecessor review ordinary() and pricing.py:93,102-113 ------ +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 +per_call = scal + routes +raw_lit, raw_act = 18 * 10 ** 7 + rest, 18 * per_call + rest +print(' raw bound pieces: caller+thin+outputs+idle adapters+query adapters = %d; per call (word scalar + routes) = %d against the displayed 10^7' % (rest, per_call)) +need(raw_lit < 10 ** 9, 'raw bound, literal definition (18 calls x 10^7 + terms): %d < 10^9' % raw_lit) +need(raw_act < 10 ** 9, 'raw bound with the ACTUAL per-call work (18 x %d + terms): %d < 10^9, margin %d (%.1f%%)' % (per_call, raw_act, 10 ** 9 - raw_act, 100 * (1 - raw_act / 10 ** 9))) +print(' NOTE: per-call %d exceeds the displayed per-call bound 10^7 (pricing.py:93); the literal raw uses 10^7 per call, so only the actual-work total is self-consistent. The per-call work feeds raw only in that second total.' % per_call) +upper_rev = 0 +for e in W['program']: + if e[0] == 'SCALE': + q = Q(e[2]); upper_rev += 4 * (abs(q.numerator).bit_length() + q.denominator.bit_length() + 1) + elif e[0] in ('ADD', 'COPY'): + q = Q(e[3]); upper_rev += 4 * (abs(q.numerator).bit_length() + bin(abs(q.numerator)).count('1') + q.denominator.bit_length() + 1) +raw_rev = 18 * (upper_rev + routes) + rest +need(raw_rev > 10 ** 9, 'raw bound with the reviewed scalar upper (18 x %d + terms): %d EXCEEDS 10^9 by %.2f%%; stated plainly: the conservative count is over, the actual-work count is under' % (upper_rev + routes, raw_rev, 100 * (raw_rev / 10 ** 9 - 1))) +def raw_of(Wx): + nx = len(Wx['initial']); lx = set(Wx['live']); mx = lx | {r_ + 112 for r_ in lx}; dx = [len(b_) for b_ in Wx['frames']] + al = up = 0; ndh = 0; pm = Counter(); lt = 0 + for e_ in Wx['program']: + if e_[0] in ('INIT', 'CLEAR'): al += 2; lt += e_[0] == 'INIT' + elif e_[0] == 'MOVE': pm[abs(dx[e_[3]] - dx[e_[2]])] += 1 + elif e_[0] == 'SCALE': + q_ = Q(e_[2]); a_, d_ = abs(q_.numerator), q_.denominator + al += 2 * (abs(a_.bit_length() - d_.bit_length()) + int(q_ < 0)); up += 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 + al += 2 * (3 + a_.bit_length() - 1 + bin(a_).count('1') + d_.bit_length() - 1); up += 4 * (a_.bit_length() + bin(a_).count('1') + d_.bit_length() + 1) + nh = sum(1 for r_ in range(nx) if r_ not in mx) + rt = (sum(pm.values()) + 2 * nh + 208 + 4 * 104 + 4 * lt) * 1000 + return 18 * (al + rt) + rest, 18 * (up + rt) + rest +r86 = raw_of(json.load(gzip.open(data('prior_word_6886.json.gz'), 'rt'))) +r83 = raw_of(json.load(gzip.open(data('prior_word.json.gz'), 'rt'))); r84 = raw_of(json.load(gzip.open(data('prior_word_6884.json.gz'), 'rt'))) +need(r86 == (975554380, 1006146280) and r83 == (983664136, 1019551024) and r84 == (999138736, 1052149312), 'same formula on the #6883, #6884 and #6886 words: (actual, reviewed upper) = %s, %s and %s; the reviewed-upper line was already over 10^9 at #6883' % (r83, r84, r86)) +print(' CONSTANT SUBSTITUTION (FINITE-PRECOMPILATION.md:278-283): events %d; scalar allowance %d; reviewed scalar upper %d; routes %d; per call %d (allowance) or %d (reviewed upper); caller envelope %d; raw upper %d (allowance) or %d (reviewed upper) against 10^9.' % (len(W['program']), scal, upper_rev, routes, per_call, upper_rev + routes, 32 * roles * 104 * len(evs), raw_act, raw_rev)) +Rm = sum(r_ * v_ for r_, v_ in Pn.items()) +print(' PRECISION BOUND SUBSTITUTION: paid rank mass R = %d; growth bound 2^(raw + R*f): raw %d (allowance total) or %d (reviewed upper) in place of 10^9, with the same R' % (Rm, raw_act, raw_rev)) +print(' [statement] raw bound: %d on actual work (under 10^9 by %d), %d with the reviewed scalar upper (over 10^9 by %.2f%%); the growth bound written for the precision contract is 2^(%d + %d f) with R = %d the paid rank mass, per FP:278-283 and OUTER-TRANSFER-AUDIT:382,390 (the figure %d replaces 10^9; %d if the reviewed upper is taken). Whether raw is load-bearing is a reading of the texts, not a proof, the precision contract is inherited and not examined, and the only packages above 10^9 so far are the open #6883 and #6884 on the reviewed-upper line.' % (raw_act, 10 ** 9 - raw_act, raw_rev, 100 * (raw_rev / 10 ** 9 - 1), raw_rev, Rm, Rm, raw_act, raw_rev)) +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: the raw bound is a parameter of the precompilation constants, not an input of the 54+4 inequalities') +# net accounting: new = 2 x base + word part + lines +tk = kn; ex = lambda r_: (D(r_).ln() * (1 - tk)).exp() +mom = lambda H_: sum(v * ex(r_) for r_, v in H_.items()) +bh = {int(k): v for k, v in bi['helpers'].items()}; bp = {int(k): v for k, v in bi['local_paid'].items()} +word_part = 18 * ((mom(hel) - mom(paid)) - 2 * (mom(bh) - mom(bp))); lines_part = -36 * 104 * ex(8) +net = (sum((Tn.get(r_, 0) - Pn.get(r_, 0)) * ex(r_) for r_ in set(Tn) | set(Pn)) - 2 * sum((T0.get(r_, 0) - P0.get(r_, 0)) * ex(r_) for r_ in set(T0) | set(P0))) +need(abs((word_part + lines_part) - net) < D('1e-6'), 'net accounting at the crossing: new = 2 x base %+.1f (hosted word vs 2 x predecessor native, 18 calls) %+.1f (36 whole H8 idle jobs per port) = net %+.2f' % (word_part, lines_part, net)) + +# ---- (5) outer conditions ---------------------------------------------------------------------- +def ld(name): + s = importlib.util.spec_from_file_location(name, os.path.join(HERE, 'retained', 'runtime', name + '.py')); m = importlib.util.module_from_spec(s); sys.modules[name] = m; s.loader.exec_module(m); return m +E, SE, OUT = ld('intervals'), ld('second_intervals'), ld('endpoint') +KAPPA, TESTED = Q('.003452786'), Q('.0034527867') +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'])) +need(Q(BITF['raw_crossing'][0]) > Q(BITF['raw_tested']) > PIN > TESTED, 'BIT side: raw crossing > raw tested saving 0.0037667 > pin > tested complex price') +Tq = Counter({r: v for r, v in Tn.items() if v}); Pq = Counter({r: v for r, v in Pn.items() if v}) +for name, k, pos in (('lower', Q('.003452786884577'), 1), ('upper', Q('.003452786884578'), -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: sign of the margin at the %s price endpoint' % name) +ORD = Q(8590884599, 2500000000000) +need(KAPPA > ORD and TESTED > ORD, 'the claim %s is above main\'s ordinary BIT stock %.8f (by %.2e); the admitted BIT saving of main, 0.0034, is lower still' % (float(KAPPA), float(ORD), float(TESTED - ORD))) +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'])))) +need(TESTED < PIN and Q('.003452786884577') > TESTED, 'tested price below the raw crossing and below the BIT pin .00376669') +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) +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: alpha %.12f gamma %.4f delta %.4f (cutoff 11, floor 12, offset 1/7, power 1920)' % (float(alpha[1]), float(gamma[1]), float(delta[1]))) +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) ** 2100 and factor[1] < 2 ** 2100 and cutoff ** 64 < floor ** 63 and 2 * (cutoff ** power) ** 64 <= (maxT ** power) ** 63, 'compiler complement capacity and shifted exits (max target rank %d)' % maxT) +normalized = 1 / (1 + power * reserve) + 4 * decay ** power +need(normalized < 1 and normalized == 1 / (1 + power * reserve) + 4 * decay ** power, '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)) +gap = (TESTED - KAPPA) / 7; need(gap.numerator == 1, 'compiler grid: (tested-kappa)/7 = %s' % gap) +step = gap.denominator +wins = lambda j: (step * j + 1) ** 2100 < 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' % (step * hi_)) +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') +need(any(v <= 0 for v in OUT.ledger(dict(params, bit_saving=Q('.0027')))['strict_checks'].values()), 'insufficient BIT budget is rejected') +PINS = [('main admitted', Q('.0034'), False), ('.00343', Q('.00343'), False), ('main ordinary stock', Q('.0034363538396'), False), ('#5421', Q('.00344412'), False), + ('#4760', Q('.0034597'), True), ('#4814', Q('.003475458'), True), ('#5512', Q('.003483969976'), True), ('#6726 (the pin used)', PIN, True)] +for lab_, pin_, want_ in PINS: # the ledger needs bit_saving > kappa + 4 gap, nothing else; the last four values are archive-only or open, none is admitted + 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 is rejected') +# second hidden .0034: the input-lift saving lemma of the predecessor (pricing.py:128-156) with its cap moved to the pin +plus = [(7, 1), (3, 1), (5, 1)]; minus = [(9, 1), (4, 1), (1, 2)] +need(sum(x * c for x, c in plus) == sum(x * c for x, c in minus), 'input-lift saving: equal local rank mass 15 = 15') +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: g prime negative on 1-pin..1 (the predecessor cap .0034 moved to the pin; its crude bound holds to about .0037765)') +for nm, k_ in (('claim', KAPPA), ('tested', TESTED)): + tl_ = 1 - k_; tot = lambda terms_, sgn: (sum(c * E.power(x, tl_)[0] for x, c in terms_), sum(c * E.power(x, tl_)[1] for x, c in terms_)) + gl = tot(plus, 1)[0] - tot(minus, 1)[1] + need(gl > 0 and k_ * (-d1[1]) - k_ * k_ * Mq / 2 > 0, 'input-lift saving positive at the %s price' % nm) +# logarithm power: minimum for this tested price against the 2100 used +lp_ = 2100 +while eta[0] > Q(63, 64) ** (lp_ - 1): lp_ -= 1 +lo_t, hi_t = 0.0, 0.01 +for _ in range(60): + mid_t = (lo_t + hi_t) / 2 + if math.log(1 - mid_t) - 1920 * mid_t * math.log(maxT) > 2100 * math.log(63 / 64): lo_t = mid_t + else: hi_t = mid_t +need(lp_ <= 2100, 'logarithm power: the smallest admissible value at this price is %d (2100 used, a free parameter, LOG-MAJORANT.md:110-122); with 2100 the complement-capacity line binds at a tested price of about %.7f, %.1e above the tested price used' % (lp_, lo_t, lo_t - float(TESTED))) +print('PASS_P104_HOSTED_JOINT_MERGE') diff --git a/research/p104-hosted-joint-merge/cover_check.py b/research/p104-hosted-joint-merge/cover_check.py new file mode 100644 index 0000000000..c9b6f5925f --- /dev/null +++ b/research/p104-hosted-joint-merge/cover_check.py @@ -0,0 +1,115 @@ +#!/usr/bin/env python3 +"""What changed against the #6883 and #6884 words, measured on the two words (standard library). python3 -I -B cover_check.py +The core of a word is the span from its first to its last MOVE; the gates before and after it are rebuilt per word and are not compared. +Reports: ADD events of the core (the #6883 word minus this word = the deleted ADDs), silent helpers, registers, MOVEs, peak owned fields; +checks that dropping silent helpers leaves the invoice unchanged; and controls on a random-evaluation replay (mod 2^61-1) that the endpoint +is destroyed by removing one more ADD, by duplicating an ADD (a wrongly restored one), and by removing sampled ADDs that are not in the deleted set.""" +import gzip, json, os, random, sys +from collections import Counter +from decimal import Decimal as D, getcontext +from fractions import Fraction as Q +getcontext().prec = 50 +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')) +def census(W): + n = len(W['initial']); live = set(W['live']); main = live | {r + 112 for r in live} + touched = set() + for e in W['program']: + if e[0] in ('ADD', 'COPY'): touched |= {e[1], e[2]} + elif e[0] == 'SCALE': touched.add(e[1]) + silent = [r for r in range(n) if r not in main and r not in touched] + P = W['program']; mv = [i for i, e in enumerate(P) if e[0] == 'MOVE']; lo, hi = mv[0], mv[-1] + core = Counter(e[0] for e in P[lo:hi + 1]); own = set(); peak = 0 + for e in P: + if e[0] == 'INIT': own.add(e[1]); peak = max(peak, len(own)) + elif e[0] == 'CLEAR': own.discard(e[1]) + return dict(n=n, silent=silent, core=core, lo=lo, hi=hi, moves=sum(e[0] == 'MOVE' for e in P), peak=peak, events=len(P), main=main) +old, mid, m6, new = load('prior_word.json.gz'), load('prior_word_6884.json.gz'), load('prior_word_6886.json.gz'), load('word.json.gz') +co, cm, c6, cn = census(old), census(mid), census(m6), census(new) +for nm, c in (('#6883 word', co), ('#6884 word', cm), ('#6886 word', c6), ('this word ', cn)): + print(' %s: events %d, public %d, silent helpers %d, MOVEs %d, core ADDs %d, core SCALEs %d, gate events before/after the core %d/%d, peak owned %d' % (nm, c['events'], c['n'], len(c['silent']), c['moves'], c['core']['ADD'], c['core']['SCALE'], c['lo'], c['events'] - c['hi'] - 1, c['peak'])) +need(co['core']['ADD'] - cm['core']['ADD'] == 342, 'the #6884 word loses exactly 342 core ADD events against the #6883 word (the deletions of #6884)') +need(c6['silent'] == [] and c6['n'] == cm['n'] - 14 and c6['moves'] == cm['moves'] - 45 and cm['core']['ADD'] - c6['core']['ADD'] == 48 and cm['core']['SCALE'] - c6['core']['SCALE'] == 12, + 'the #6886 word against the #6884 word: 14 fewer public registers, 45 fewer MOVEs, 48 fewer core ADDs, 12 fewer core SCALEs') +need(cn['silent'] == [] and cn['n'] == c6['n'] - 8 and cn['moves'] == c6['moves'] - 116 and cn['core']['ADD'] - c6['core']['ADD'] == 3 and c6['core']['SCALE'] - cn['core']['SCALE'] == 15 and all(c6['core'][k] == cn['core'][k] for k in ('INIT', 'CLEAR', 'COPY')), + 'this word against the #6886 word: 8 fewer public registers, 116 fewer MOVEs, 3 more core ADDs, 15 fewer core SCALEs, same owned lifetimes and COPY, no silent helper') +need(c6['lo'] == 69980 and cn['lo'] == 90770 and c6['events'] - c6['hi'] - 1 == 39688 and cn['events'] - cn['hi'] - 1 == 39677, 'the gate blocks are rebuilt (events before the core 69,980 -> 90,770, after 39,688 -> 39,677; they are solved per word and split so every coefficient stays inside the alphabet)') +# the joint structure, as counted on the words: direct reads of Y and direct writes into X by helpers inside the core +def port_counts(W, kind): + P = W['program']; live = W['live']; Yr = {r + 112 for r in live}; Xr = set(live); n = len(W['initial']); mn = Xr | Yr + mv = [i for i, e in enumerate(P) if e[0] == 'MOVE']; out = [] + for i, e in enumerate(P[mv[0]:mv[-1] + 1], mv[0]): + if e[0] != 'ADD': continue + if kind == 'yread' and e[2] in Yr and e[1] < n and e[1] not in mn: out.append((i, e, e[2])) + if kind == 'xwrite' and e[1] in Xr and e[2] < n and e[2] not in mn: out.append((i, e, e[1])) + if kind == 'xread' and e[2] in Xr and e[1] < n and e[1] not in mn: out.append((i, e, e[2])) + if kind == 'ywrite' and e[1] in Yr and e[2] < n and e[2] not in mn: out.append((i, e, e[1])) + return out +def diff(kind): + a_, b_ = port_counts(m6, kind), port_counts(new, kind); ca, cb = Counter(p for _, _, p in a_), Counter(p for _, _, p in b_) + d_ = {k: cb[k] - ca[k] for k in set(ca) | set(cb) if ca[k] != cb[k]} + return a_, b_, d_ +ya, yb, yd = diff('yread'); xa, xb, xd = diff('xwrite'); xra, xrb, xrd = diff('xread'); ywa, ywb, ywd = diff('ywrite') +need((len(ya), len(yb), len(yd), sum(v > 0 for v in yd.values())) == (210, 245, 42, 30) and (len(xa), len(xb), len(xd), sum(v > 0 for v in xd.values())) == (436, 553, 51, 50) and len(xrd) == 1 and not ywd, + 'joint structure counted on the words: direct reads of Y by helpers 210 -> 245 on 42 ports (30 more, 12 fewer); direct writes into X by helpers 436 -> 553 on 51 ports (50 more, 1 fewer); helper reads of X change on 1 port; helper writes into Y on none') +gain = {y: v for y, v in yd.items() if v > 0}; xgain = {x_: v for x_, v in xd.items() if v > 0} +rn_ = [(i, e) for i, e, _ in yb] +# dropping silent helpers: same rise in targets and in paid, so the invoice is unchanged (checked on the #6883 word, which still has them) +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(200): + m = (lo + hi) / 2 + if e(m) > 0: lo = m + else: hi = m + return lo +dim = [len(b) for b in old['frames']] +sil = set(co['silent']); mvs = Counter(); rise = {} +for e in old['program']: + if e[0] == 'MOVE' and e[1] in sil: mvs[e[1]] += 1 +for r in sil: rise[r] = dim[old['final'][r]] - dim[old['initial'][r]] +need(all(mvs[r] == 1 for r in sil) and all(rise[r] > 0 for r in sil), 'each of the %d silent helpers of the #6883 word is one single MOVE with rank equal to its target rank, so removing it removes the same job from targets and paid' % len(sil)) +# control: random-evaluation replay +M = (1 << 61) - 1; inv2 = pow(2, M - 2, M) +al, be = Q(new['hosted']['alpha']), Q(new['hosted']['beta']); t = al * be +fm = lambda q: (lambda f: f.numerator % M * pow(f.denominator, M - 2, M) % M)(Q(q)) +live = new['live']; X = set(live); Y = {r + 112 for r in live} +def endpoint_ok(W, prog, K=2, seed=3): + n = len(W['initial']); NR = n + W['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(W['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)] + a_, b_, d_ = fm(al), fm(be), fm(1 + t) + for r in range(NR): + if r >= n: ex = [0] * K + elif r in X: ex = [(v0[r][k] + a_ * v0[r + 112][k]) % M for k in range(K)] + elif r in Y: ex = [(b_ * v0[r - 112][k] + d_ * v0[r][k]) % M for k in range(K)] + else: ex = v0[r] + if v[r] != ex: return False + return True +P = new['program']; lo, hi = cn['lo'], cn['hi'] +need(endpoint_ok(new, P), 'random-evaluation replay accepts the word (endpoint exact on every public and owned row)') +yidx = [i for i, e, p in yb if p in gain]; xidx = [i for i, e, p in xb if p in xgain] +rnd = random.Random(9); smp = rnd.sample(yidx, 6) + rnd.sample(xidx, 6); bw = bm = bd = 0 +for i in smp: + e = list(P[i]); e[3] = str(Q(e[3]) * 2) + bw += not endpoint_ok(new, P[:i] + [e] + P[i + 1:]) # wrong weight + bm += not endpoint_ok(new, P[:i] + P[i + 1:]) # missing read or write + bd += not endpoint_ok(new, P[:i + 1] + [P[i]] + P[i + 1:]) # taken twice +need(bw == bm == bd == len(smp), 'controls on 6 sampled direct Y reads and 6 sampled direct X writes of the changed ports: a wrong weight (x2), a missing event and an event taken twice are all rejected') +adds = [i for i in range(lo, hi + 1) if P[i][0] == 'ADD'] +need(not endpoint_ok(new, 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(new, 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 (the deletions of #6884 are removable only jointly or alone with the gates absorbing them)' % broke) +print('PASS_COVER_CHANGES') diff --git a/research/p104-hosted-joint-merge/data/base_invoice.json b/research/p104-hosted-joint-merge/data/base_invoice.json new file mode 100644 index 0000000000..f2a6958ee2 --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/data/caller.json b/research/p104-hosted-joint-merge/data/caller.json new file mode 100644 index 0000000000..f82451bb54 --- /dev/null +++ b/research/p104-hosted-joint-merge/data/caller.json @@ -0,0 +1 @@ +{"schema": "hosted-root-caller/1", "roles": 38, "stages": 18, "ambient_rank": 153, "events": [["ADD", 2, 3, "-2"], ["ADD", 1, 3, "1"], ["ADD", 0, 3, "2"], ["ADD", 1, 2, "1"], ["ADD", 0, 2, "1"], ["ADD", 0, 1, "-2"], ["SCALE", 1, "256"], ["ADD", 3, 1, "-1/128"], ["ADD", 2, 1, "1/128"], ["SCALE", 0, "128"], ["ADD", 3, 0, "-1/128"], ["ADD", 2, 0, "1/64"], ["ADD", 1, 0, "1"], ["LAMBDA", 0, -1], ["HOST", 1, 1, 0, "-1", "1/2"], ["LAMBDA", 0, 1], ["IDLE_ONE", 2, [1]], ["IDLE_ONE", 3, [1]], ["ADD", 4, 5, "-2"], ["ADD", 2, 5, "-2"], ["ADD", 1, 5, "-256"], ["ADD", 0, 5, "-128"], ["ADD", 3, 4, "1"], ["ADD", 2, 4, "-2"], ["ADD", 1, 4, "-256"], ["ADD", 1, 3, "256"], ["ADD", 0, 3, "-128"], ["ADD", 0, 2, "-128"], ["ADD", 3, 2, "1"], ["ADD", 0, 1, "1/2"], ["SCALE", 1, "-1"], ["ADD", 5, 1, "-1/128"], ["ADD", 4, 1, "1/128"], ["ADD", 3, 1, "1/128"], ["ADD", 2, 1, "1/128"], ["SCALE", 0, "-1"], 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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} +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 + 208 + 4 * 104 + 4 * life) * 1000 +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-hosted-joint-merge/physical.py b/research/p104-hosted-joint-merge/physical.py new file mode 100644 index 0000000000..f4086b3172 --- /dev/null +++ b/research/p104-hosted-joint-merge/physical.py @@ -0,0 +1,112 @@ +#!/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'] +alpha = Fr(W['hosted']['alpha']); beta = Fr(W['hosted']['beta']); t = alpha * beta +if mutate: alpha = -alpha # control run: predictions use the wrong sign; 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} +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 +print('prime %d seed %d: helper rows bad %d (of %d), X rows bad %d, Y rows bad %d (of %d each)' % (p, seed, badH, n - len(main), badX, badY, len(live)), flush=True) +if mutate: sys.exit(0 if (badX or badY) 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 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-hosted-joint-merge/retained/bit/FRAGMENT-BIT-ADMISSION.json b/research/p104-hosted-joint-merge/retained/bit/FRAGMENT-BIT-ADMISSION.json new file mode 100644 index 0000000000..482f9525d4 --- /dev/null +++ b/research/p104-hosted-joint-merge/retained/bit/FRAGMENT-BIT-ADMISSION.json @@ -0,0 +1,19115 @@ +{ + "status": 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{ + "missing_input_basis": "reverse coefficient 6,7", + "missing_first_handoff": "reverse coefficient 4,4", + "missing_second_handoff": "reverse coefficient 0,2", + "missing_output_basis": "reverse coefficient 32,7", + "missing_LOCAL": "reverse coefficient 0,0", + "missing_QUERY": "reverse 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-hosted-joint-merge/retained/native/clifford_exact.py b/research/p104-hosted-joint-merge/retained/native/clifford_exact.py new file mode 100644 index 0000000000..166841a037 --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/retained/runtime/intervals.py b/research/p104-hosted-joint-merge/retained/runtime/intervals.py new file mode 100644 index 0000000000..4b24a50961 --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/retained/runtime/second_intervals.py b/research/p104-hosted-joint-merge/retained/runtime/second_intervals.py new file mode 100644 index 0000000000..4fc05ab081 --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/root_check.py b/research/p104-hosted-joint-merge/root_check.py new file mode 100644 index 0000000000..dec810d167 --- /dev/null +++ b/research/p104-hosted-joint-merge/root_check.py @@ -0,0 +1,137 @@ +#!/usr/bin/env python3 +"""Extended root checker for the hosted chain-nested root. Standard library only. python3 -I -B root_check.py [data/root.json] +It re-proves, in exact Fractions, the root identity the caller needs, and DECLARES the relaxations of the #6833 root checkers: + chain_root.py:79 need(n%2==0 and len(S)==n+1) -> here N=n+2 (two thin units beyond the shortest root), rank G=n instead + chain_root.py:82 sign Gram y_i.x_j=sgn(i-j) -> not required (consequence of 79) + chain_root.py:83 alternating sum of x vanishes -> not required (consequence of 79) + chain_root.py:98 one full site per child -> here every stage hosts a pair of consecutive units (two units per stage) + independent/check_root.py:26 odd/odd family -> not required + independent/check_root.py:133 shortest root N=n+1 -> N=n+2 + independent/check_root.py:141-145 chain target formulas for the stage masks -> replaced by the whole-job test below (symbolic M(D)=-diag(prod D^eps) from the mask incidence) +Everything SPEC-level is kept: unit square-zero reflections, product -I, masks commuting with the prefix, units inside masks, multilinear symbolic endpoint. +Added here: dyadic x,y; each stage's pair has t=alpha*beta=-1/2 (1+t != 0) and dyadic alpha,beta; Gram digraph strongly connected (absolute irreducibility). +Prints PASS_ROOT_HOSTED on success.""" +import json,sys +from fractions import Fraction as Q +import os +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')));n,N=R['n'],R['N'] +X=[[Q(v) for v in r] for r in R['X']];Y=[[Q(v) for v in r] for r in R['Y']];ST=R['stages'] +assert len(X)==N==len(Y) and all(len(r)==n for r in X+Y) +bad=[] +def req(name,ok,info=''): + print(('PASS ' if ok else 'FAIL ')+name+(' '+str(info) if info!='' else ''),flush=True) + if not ok:bad.append(name) +dot=lambda a,b:sum(u*v for u,v in zip(a,b) if u and v) +I=[[Q(int(i==j)) for j in range(n)] for i in range(n)] +def lmul_unit(M,x,y,c): + """(I+c x y^T) M""" + 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)] +# 1 isotropy, nonzero +req('isotropy y_k.x_k=0 all k',all(dot(Y[k],X[k])==0 for k in range(N))) +req('units nonzero',all(any(X[k]) and any(Y[k]) for k in range(N))) +# 2 product identity +W=I;prefix=[] # prefix[k]=T_{k-1}..T_0 +for k in range(N): + prefix.append(W);W=lmul_unit(W,X[k],Y[k],Q(-2)) +prefix.append(W) +req('T_{N-1}..T_0=-I (ROOTTHM order, I-2xy)',W==[[-v for v in r] for r in I]) +# 3 stage partition +us=[u for s in ST for u in s['units']] +req('stage units disjoint',len(us)==len(set(us))) +req('each stage units consecutive',all(sorted(s['units'])==list(range(min(s['units']),max(s['units'])+1)) for s in ST)) +L=len(ST);thin=[k for k in range(N) if k not in set(us)] +hosted=[s for s in ST if len(s['units'])==2] +print(' N n L tau h',N,n,L,len(thin),len(hosted),'thin units',thin) +req('stages ordered in time',all(max(ST[i]['units'])>i&1)).count('1')==len(ST[i]['mask']) for i in range(L))) +# 6 hosts: frame-free t, plane +def t_of(u,v):return dot(Y[u],X[v])*dot(Y[v],X[u]) +print(' hosted pairs (u,v,alpha,beta,t,1+t):',[(s['units'][0],s['units'][1],str(dot(Y[s['units'][0]],X[s['units'][1]])),str(dot(Y[s['units'][1]],X[s['units'][0]])),str(t_of(*s['units'])),str(1+t_of(*s['units']))) for s in hosted]) +req('every hosted pair has alpha=-1, beta=1/2 (the pair the native realises)',all((dot(Y[x['units'][0]],X[x['units'][1]]),dot(Y[x['units'][1]],X[x['units'][0]]))==(-1,Q(1,2)) for x in hosted)) +req('all 18 stages host',len(hosted)==18) +req('hosted t not 0, not -1',all(t_of(*s['units']) not in (0,-1) for s in hosted)) +# path frame t for adjacent pair with q=+1 frame U=I+x y equals root frame t +# 7 dyadic +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)) +def odd(v): + v=abs(v.numerator) + while v and v%2==0:v//=2 + return v +req('hosted alpha,beta dyadic units (plane projector dyadic)',all(odd(dot(Y[s['units'][0]],X[s['units'][1]]))==1 and odd(dot(Y[s['units'][1]],X[s['units'][0]]))==1 for s in hosted)) +print(' max |entry|',max(abs(v) for r in X+Y for v in r),' t values odd parts',{str(t_of(*s['units'])) for s in hosted}) +# 8 Gram rank, irreducible exactly +def rank(A): + A=[r[:] for r in A];rk=0 + if not A:return 0 + for c in range(len(A[0])): + p=next((i for i in range(rk,len(A)) if A[i][c]),None) + if p is None:continue + A[rk],A[p]=A[p],A[rk] + for i in range(rk+1,len(A)): + if A[i][c]: + f=A[i][c]/A[rk][c];A[i]=[a-f*b for a,b in zip(A[i],A[rk])] + rk+=1 + return rk +G=[[dot(Y[i],X[j]) for j in range(N)] for i in range(N)] +req('rank G=n',rank(G)==n);req('N-n=rho',True,N-n) +Om=[[Q(1) if i==j else (G[i][j] if i>j else -G[i][j]) for j in range(N)] for i in range(N)] +print(' rank(sign-twisted Gram) =',rank(Om),'; rank in other twist',rank([[Q(1) if i==j else (-G[i][j] if i>j else G[i][j]) for j in range(N)] for i in range(N)])) +req('x span, y span',rank(X)==n and rank(Y)==n) +# strongly connected digraph on G!=0 (proof: W invariant, w!=0, some y_k w!=0 since y span => x_k in W; G_jk!=0 => x_j in W; x span => W=F^n) +def reach(s,fw): + seen={s};st=[s] + while st: + u=st.pop() + for v in range(N): + if v not in seen and (G[v][u] if fw else G[u][v]):seen.add(v);st.append(v) + return seen +req('Gram digraph strongly connected => absolutely irreducible over Q [P]',len(reach(0,True))==N and len(reach(0,False))==N) +print('PASS_ROOT_HOSTED' if not bad else 'FAILED '+'; '.join(bad)) +sys.exit(1 if bad else 0) diff --git a/research/p104-hosted-joint-merge/verify_relaxed.py b/research/p104-hosted-joint-merge/verify_relaxed.py new file mode 100644 index 0000000000..49b7b6b2e9 --- /dev/null +++ b/research/p104-hosted-joint-merge/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-hosted-joint-merge/verify_strict.py b/research/p104-hosted-joint-merge/verify_strict.py new file mode 100644 index 0000000000..edc183339b --- /dev/null +++ b/research/p104-hosted-joint-merge/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')