Conditional κ = .00363797977 via a 17-stage signed caller

docs/ci-verification.md

@@ -1,8 +1,25 @@
 # CI verification
 
-## Current selected-family replay: #6030
+## Current selected-family replay: #7000 with #7001
 
 The [selected record](../certificates/selected-result.json) binds conditional
+κ = 0.00363005817 to the [application review](research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md),
+[validation receipts](research/pr-intake-evidence/pr7000-application/VALIDATION.json),
+and [explicit source closure](../certificates/frontier7000-source.json).
+`make frontier7000-verify` follows that exact-source selected replay. The review
+reuses eleven authenticated preceding executions and records seven fresh serial
+application, scalar and complete native-catalogue executions. The earlier
+monolithic timeout is retained separately and is not completed coverage.
+Consult the receipts for exact commands, source heads and limits.
+
+The five inherited framework assumptions remain. No complete uniform word,
+literal multiplier execution, independent human proof or formal-kernel proof
+is asserted. Routine research submissions do not need to rerun this
+selected-family replay. The sections below preserve historical checkpoints.
+
+## Historical selected-family replay: #6030
+
+The [historical checkpoint](../certificates/checkpoints/frontier6030.json) binds conditional
 κ = 0.003125804 to the [proof review](research/pr-intake-evidence/pr6030-audit/PROOF-REVIEW.md),
 [validation receipts](research/pr-intake-evidence/pr6030-audit/VALIDATION.json),
 and [explicit source closure](../certificates/frontier6030-source.json).

research/signed-caller-8x9/APPLICATION.md

@@ -0,0 +1,67 @@
+# Conditional application of the 17-stage signed caller
+
+The exact source is the same 72,143-event #7112 native word used in the
+8+8 application, with canonical SHA256
+3454c4900245ed1814ceeff79a741a45160eb3a93cf8d15f891fe2a67ba036fc.
+The 8+9 caller SHA256 is
+255d89f38cd45e38e5770f559bc43dc217e989032359768cdc7e8cdfd64b47bc.
+Use the five #6030 assumptions listed in [README.md](README.md) and the
+selected BIT backend and fixed-tape construction of the
+[#7000 application review](https://github.com/CrocSwap/integer-mult-bounds/blob/e54523517d0f03e58352e647c403a5af3e525a57/docs/research/pr-intake-evidence/pr7000-application/PROOF-REVIEW.md).
+
+The asymmetric type-B tape closes with five noncommuting quarter turns
+and twelve padding turns in inverse pairs. All required prefix pivots
+are dyadic units. Its grouped idle spaces use a basis over Z[1/30].
+The audited literal 4,783-event caller has 72 output fields. Both the
+rational Laurent replay and a separate integer Laurent engine prove
+the exact same endpoint for all formal central and body variables.
+The 17 distinct eight-axis blocks and nine central axes use ambient
+145. For each invocation the eight complement axes are exchanged with
+its fresh stage block, holding the routed central axis and spectator
+axes fixed. The affine phase-polynomial checks bind these maps in both
+directions. The literal A and B routes apply the commuting stage body
+operators on disjoint blocks. A negative central sign can be reoriented
+by the ordinary square of the central factor. A signed rank-nine idle
+uses one positive rank-nine recursive request and the ordinary
+conjugation and phase that implement the inverse on the protected axis.
+The ordered occurrence receipt binds these completed-child routes. It binds all 13,600 native contacts, 110,638 paid positions,
+22,172 productive fields and 18,428 independently allocated helpers.
+There are 867 reserved native banks and a rank surplus of 1,424.
+The exact 3,047-map native catalogue is reused on identical native
+bytes, including the signed Pauli and absolute phase controls.
+
+Scale the 3,744 raw caller input fields by 675 before this caller and
+divide each of the 3,744 completed main outputs by 675. The integer
+Laurent replay checks the required 3^3 and 5^2 valuations and rejects
+a smaller exponent of either prime, using the safe binary valuation
+381. Every exact normalized main row and pre-ADD product remains
+integral on this odd grid. Substituting the actual Clifford address
+operators introduces only powers of two, so odd divisibility transfers
+to arbitrary complete binary arrays, including all spectators. Within
+each native call, scale all its public fields by the separately audited
+1125 and unscale on return. Fresh helpers use their own independent
+inputs. The native arbitrary-input endpoint ensures that helpers do
+not alter the caller's normalized main-grid invariant. Include both
+scales simultaneously in the unfinished-context mass allowance. The
+new height is 405, context mass exponent 1157 and context allowance
+2314. It is still below 4096, and the same conservative ambient-153
+compiler threshold funds this allowance by the exact bit-length test.
+Use the full-root common-format induction, including fixed padding
+and completed-child returns. Exact finite-state odd division uses the
+retained proof's carry/remainder invariant.
+
+The paid conversion work is included in the 775,153,592 source-unit
+ordinary bound, distinct from the actual physical resource bound.
+Count 41,451,808 scalar services and at most 25,448,575,552
+elementary monomial records per raw occurrence. Numerators in both
+scales and all source scalar instructions stay within 24 bits.
+Substitute these conservative counts and actual owner widths into
+the same fixed-tape stock and primitive movement envelopes, and
+enlarge the eventual cutoffs with the retained positive slacks.
+
+The raw moment crossing lies strictly between .00363797978 and
+.00363797979. The exact interval compiler and 54 strict plus four
+functional outer checks accept candidate .00363797977. The checked
+application is private and conditional. It retains the five named
+assumptions and is not a compiled Turing-machine execution or
+upstream admission.

research/signed-caller-8x9/LICENSE

@@ -0,0 +1,201 @@
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research/signed-caller-8x9/README.md

@@ -0,0 +1,46 @@
+# Conditional κ = .00363797977 with a 17-stage signed caller
+
+This package composes the exact [#7112](https://github.com/CrocSwap/integer-mult-bounds/pull/7112)
+native word with a new asymmetric signed 8+9 caller. The conditional
+claim is `363797977/100000000000`, above #7112 by .000000562650059.
+The raw crossing is between .00363797978 and .00363797979.
+
+The caller uses five noncommuting quarter turns and six inverse pairs.
+Its grouped idles use arithmetic over Z[1/30]. The exact integer replay
+charges caller scale 675 separately from native scale 1125 and rejects
+insufficient powers of 3 and 5. All 72 output fields replay, with 13,600
+physical native contacts, 110,638 paid positions, and 22,172 productive
+fields. See [APPLICATION.md](APPLICATION.md) for the owner, phase,
+precision, and finite-tape bounds.
+
+## Reproduction
+
+```sh
+python3.12 -B scripts/research_package.py --package research/signed-caller-8x9
+```
+
+The replay regenerates the exact caller, verifies rational and integer
+Laurent endpoints, and checks physical binding, precision, ordinary
+work, the compiler and all 58 outer inequalities. It authenticates
+the three completed native catalogue slices on identical word bytes.
+Re-run a slice separately with `short_native_catalogue.py --start START --stop STOP`
+from `replay/supplier7112/short-caller`. The intervals are [0,1000),
+[1000,2000), and [2000,3047). The five inherited assumptions are
+`native_all_columns`, `owned_erasure`, `compiler`, `precision_tape`,
+and `analytic_recovery`, with the selected completed BIT predecessor.
+A compiled multiplier execution and independent maintainer review are
+outside the local checks.
+
+## Open next questions
+
+[TASK.json](TASK.json) records the next source-bound native sign-capacity
+experiment, its relevance and the current obstruction.
+
+## Credit
+
+Rohan Arun with substantial OpenAI Codex assistance. Credits include
+DreamingOfClouds for the native and chain lineage, CubeJerry for the
+shared native, paired BIT and compiler work, ToikY for the signed rank-nine
+caller and #7108–#7110, dillona and Ali Romman for helper splitting and
+#7112, and the #7000 application reviewers. Apache-2.0. Upstream source
+notices are preserved.