Improve conditional T530 κ through two commuting release retimings

.github/workflows/p112-common-slice.yml

@@ -15,8 +15,6 @@ jobs:
     if: github.repository == 'CrocSwap/integer-mult-bounds'
     runs-on: ubuntu-24.04
     timeout-minutes: 20
-    env:
-      TMPDIR: ${{ runner.temp }}/p112-common-slice
     steps:
       - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
         with:
@@ -25,11 +23,14 @@ jobs:
       - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
         with:
           python-version: '3.12'
+      - name: Configure runner temporary directory
+        run: |
+          mkdir -p "$RUNNER_TEMP/p112-common-slice"
+          printf 'TMPDIR=%s/p112-common-slice\n' "$RUNNER_TEMP" >> "$GITHUB_ENV"
       - name: Install native checker dependencies
         run: |
           sudo apt-get update -qq
           sudo apt-get install -y --no-install-recommends g++ libboost-dev
-          mkdir -p "$TMPDIR"
           g++ --version
           python --version
       - name: Replay the complete slice

research/staged-release-retiming-t530/.gitattributes

@@ -0,0 +1,2 @@
+# Preserve exact bytes of hash-pinned scientific sources and receipts.
+* -text whitespace=blank-at-eol,blank-at-eof,space-before-tab,cr-at-eol

research/staged-release-retiming-t530/CREDITS.md

@@ -0,0 +1,11 @@
+# Credit and provenance
+
+The new contribution is the two commuting release retimings, their independent local proof, changed complete bill, source-bound T530 integration, and the public reproduction package. This work was prepared for GitHub user `roger-sato` with substantial OpenAI Codex assistance, including separate circuit, owner/packing and exact-math review agents. Those agent checks are not independent human peer review. No personal priority over inherited mathematical work is asserted.
+
+- Ross Richardson's [PR3605](https://github.com/CrocSwap/integer-mult-bounds/pull/3605), head `3efbb5de06a49ffeea6684482f2d3fe48cdca3fb`, supplies the staged helpers and both original words. Its lineage includes dcharb78's PR3133 and Jeremy Diviney's PR3148 work.
+- hexapode's [PR3626](https://github.com/CrocSwap/integer-mult-bounds/pull/3626), head `659fd5e7064d9466b668d7188cbb013b333a415a`, supplies the actual T530 allocation, deterministic reconstruction, independent owner audit and complete release machinery. Its manifest and source notices are preserved in the relevant components.
+- Ross Richardson's [PR3630](https://github.com/CrocSwap/integer-mult-bounds/pull/3630), head `bcac7fe04b9b7f7f5d3c27d620561f96c4ae5608`, supplies the fixed-inventory basis/dual argument; PR3531 at `550a660a97308d3aeb3620ee1f4218f77e2c2742` supplies the retained positive-binomial interval engine.
+- [PR3633](https://github.com/CrocSwap/integer-mult-bounds/pull/3633), head `46c5aaca40117a4ca90a3316771ae52cf9a6801e`, is relevant parallel work attaining the old fixed-inventory ceiling. Its allocation is a comparison and possible future composition, not an input to our achieved endpoint.
+- Canonical main at `20ecf2891d80b5acf18d980b2164fb44ea7faa90` supplies the native, owner, outer and release infrastructure. The independent free-operator auditor is preserved from the rank7-coupled-586-588-carrier-fold lineage; its notice credits icekylinx with OpenAI GPT-6 Astra assistance.
+
+All retained notices, licenses and contributor lists remain in their component source trees. The original repository and this derivative package use Apache-2.0. Exact source bytes are retained where pinned; publication adapters are identified by original/public SHA256 provenance maps. Retained computational summaries are distinguished from fresh replay and from general mathematical assumptions.

research/staged-release-retiming-t530/PROOF.md

@@ -0,0 +1,115 @@
+# Proof of the retiming improvement and its conditional transfer
+
+## 1. Claim and dependency boundary
+
+Under the same inherited theorem/implementation hypotheses as the pinned PR3626 release, replacing its two PR3605 staged suppliers by the words in `local-audit/words/` yields
+
+```
+κ = 0.001730394391813963415120 - 10^-46 - 10^-70
+  = 17303943918139634151199999999999999999999998999999999999999999999999
+    / 10000000000000000000000000000000000000000000000000000000000000000000000.
+```
+
+The proof has three distinct parts: an exact algebraic/frame change; a finite complete owner/invoice construction; and a conditional transfer using the inherited compiler and outer assumptions. The last part is not asserted unconditionally. All source pins, original proofs and executable obligations are in the sibling components and their notices.
+
+## 2. Exact word change
+
+Use zero-based B indices. In **both** base and extra words, at indices 591 and 592 replace
+
+```
+640 += 2*644 at P
+496 -= 2*644 at P
+```
+
+by
+
+```
+496 -= 2*644 at P
+640 += 2*644 at Q1.
+```
+
+At indices 641 and 642 replace
+
+```
+656 -= 660 at P
+520 -= 2*660 at P
+```
+
+by
+
+```
+520 -= 2*660 at P
+656 -= 660 at Q2.
+```
+
+Here `L = span(30)`, `P = span(429,30)`, `Q1 = span(423,65,20,10)` and `Q2 = span(427,96,24,6)` are the native GF(2) frame subspaces. Their dimensions are 1, 2, 4 and 4, with `L ⊂ P ⊂ Qi` in each case. These inclusions are checked by exact binary elimination, not numerical rank.
+
+For distinct registers t,u,s, elementary shears `I+c E_ts` and `I+d E_us` commute: both cross products of the two matrix units are zero because neither target is the shared source. This holds over the exact rational scalar model for arbitrary register inputs. Each displayed pair has that form. No warp is crossed and the involved registers have no warp. Moving the first gate after the second therefore preserves the exact operator.
+
+The delayed donor's original frame itinerary is `L → P → Qi`. Inspection of the complete intervening event sequence shows no intermediate contact, and `Qi` is already the next frame used by donor and pivot. The new itinerary is `L → Qi`, while the pivot still pays its existing `P → Qi` transition. Thus there is no frame decrease, uncharged new pivot transition, lost input or changed boundary frame. The independent minimal checker explicitly verifies these conditions and rejects frame, coefficient and interface mutations.
+
+Cleanup is regenerated by the required canonical inverse-reverse order at FULL. Only B, cleanup and the reported local profile change; A, cut, restore, warps, helper identities, entrance/final frames and all external interfaces remain identical. The old cleanup order is itself algebraically equivalent because its inverse shears commute; rejecting it is a canonical-format control, not evidence that its operator is wrong.
+
+## 3. Local recursive bill and exact operator coverage
+
+A frame jump by d dimensions contributes `H_d`. Each direct jump replaces `H1+H2` by `H3`; the two pairs produce
+
+```
+ΔH = -2H1 -2H2 +2H3
+old = {1:2439,2:726,3:224,4:102,5:20,8:8}
+new = {1:2437,2:724,3:226,4:102,5:20,8:8}.
+```
+
+Rank mass remains 5,135, since `-2*1-2*2+2*3=0`. The width inventory remains `{4:26,5:2,6:18,7:52,8:97,9:213}` (408 helpers), and all 91 private zero buffers remain private and zero at exit. For `0<b<1`, the function `x^(1-b)` is strictly subadditive on positive x, so
+
+```
+3^(1-b) < 1 + 2^(1-b).
+```
+
+Consequently the moment strictly decreases throughout that interval. This is an exact structural decrease rather than an improved decimal approximation.
+
+The self-contained replay independently verifies both complete words on all 632 arbitrary live input columns in both orientations and all 91 zero buffers. Separate native runs also check ledger, wrapper, phase and warp contracts, including 512 warp columns and 72 warps. Their largest local prefix sizes are 89 forward bits and 95 backward bits, below the inherited 128-bit reserve. These native runs were fresh in the scientific session; the bounded public verifier authenticates their receipts and freshly reruns the separate free-operator proof, not the entire native implementation.
+
+## 4. Complete T530 construction
+
+The unchanged PR3626 allocation has 530 replicas and 9 invocations per replica. The existing exact integral-network constructor regenerates all 1,946,160 role rows. The independent literal checker verifies their actual provider windows, physical families, chronological compact prefixes, capacity constraints and full invoice. Unchanged helper identities, widths and boundary frames permit this exact ownership construction to be reused with the retimed providers; this implication is verified against both canonical words, not inferred from a local histogram alone.
+
+For `C=4770`, the full profile changes by `C*ΔH`:
+
+| Rank r | Old N_r | New N_r |
+| --- | ---: | ---: |
+| 1 | 11,757,460 | 11,747,920 |
+| 2 | 3,463,020 | 3,453,480 |
+| 3 | 1,102,502 | 1,112,042 |
+| 4 | 486,540 | 486,540 |
+| 5 | 103,690 | 103,690 |
+| 8 | 38,160 | 38,160 |
+| 48 | 202,828 | 202,828 |
+
+The complete rank mass is 34,496,640 = 65,088*530. Live stock is `W=896*530=474880`, physical stock is 475389, and the coverage deficit `W-64*4770` is 169600. The complete global prefix bound is 1479 bits; required reserve is 1512 bits within the paid 2048-bit payload. Retained source, parent, physical, controller and BIT obligations are checked in the full release rather than silently dropped from the bill.
+
+## 5. Exact root and outer transfer
+
+For the displayed *complete* profile define
+
+```
+M(b) = sum_r N_r r^(1-b) / (474880 * 73^(1-b))
+     = sum_r (N_r/474880) (r/73)^(1-b).
+```
+
+Every occupied rank satisfies `0<r<73`; therefore every summand has strictly positive derivative in b, and M is strictly increasing. Two separately implemented rational interval engines establish
+
+```
+M(0.001730394391813963415120) < 1
+M(0.001730394391813963415121) > 1.
+```
+
+They enclose the root between these adjacent exact decimal rationals without floating-point decisions. The lower endpoint with the two inherited strict margins is the stated κ. The source-bound modern outer arithmetic checks 63 strict inequalities and 17 rejection controls plus an independent balance derivation. The complete derivative release binds the changed providers, actual T530 ownership, physical invoice and modern endpoint; its outer gate independently replays 19 exact obligations. An inherited supplier-only intermediate endpoint is not substituted for this final modern endpoint.
+
+The seven scientific stages all completed with exit code 0 and terminal `PASS_RELEASE`. They operated on source-manifest SHA256 `fb47533a401d1d13719be8b9aab91fe5313931ca62d40dba336eab6a96275aa0`. Both the original scientific driver and the subsequently executed public full wrapper reproduced that source identity and completed all seven admission stages. The later wrapper run, at publication commit `abc12f62e4fe9bfcb2e33c84703253c918668351`, is separately recorded in [PUBLIC-FULL-REPLAY.json](PUBLIC-FULL-REPLAY.json). It freshly ran both changed native providers and regenerated the literal ownership construction, while authenticating and reusing the unchanged retained parent and two retained native chains. It adds end-to-end reproduction evidence without changing the algebraic argument, paid profile, endpoint or inherited assumptions. See the README for the limits of normalized recorded-evidence checks, including the omitted runtime archive bytes.
+
+## 6. Conditionality and what remains unproved
+
+This finite result retains the predecessor's all-size dispatcher/compiler assumptions; common-label/mutable-source realization and whole-call hosting; SCALAR/COPY/CLEAR and zero-allocation contracts; uniform coefficient and stock bounds; recursive rounded-precision arguments; bootstrap; tape/recovery; and analytic/BIT H1–H5 premises. Checking finite native instances, exact owner rows and inequalities does not itself prove those general assumptions. No independent human review or formal proof-assistant kernel certification is claimed.
+
+The additional packing certificate checks all 2551 patterns of the stated fixed helper inventory, with 2539 strictly positive reduced costs and 12 symbolic zeros. It bounds that relaxation's root by `0.001730418899766071163805`; it neither supplies a better achieved construction nor excludes improvements that alter the word, inventory or model. Combining this retiming with PR3633 remains an untested next question.

research/staged-release-retiming-t530/PUBLIC-FULL-REPLAY.json

@@ -0,0 +1,130 @@
+{
+  "schema": "public-full-replay-summary/1",
+  "status": "PASS_PUBLIC_FULL_WRAPPER_END_TO_END",
+  "executed_publication_commit": "abc12f62e4fe9bfcb2e33c84703253c918668351",
+  "executed_wrapper_sha256": "9ec43247d2b3af6e4fce61173a4e59aa13b845792776289995cb108285f8aede",
+  "started_at": "2026-10-18T12:37:09.414302+00:00",
+  "finished_at": "2026-10-18T12:58:21.088357+00:00",
+  "wall_seconds": 1271.6689796670107,
+  "exit_code": 0,
+  "package_files_unchanged": true,
+  "environment": {
+    "python": "3.12.14",
+    "implementation": "CPython",
+    "platform": "macOS-27.0-arm64-arm-64bit",
+    "machine": "arm64",
+    "packages": {
+      "numpy": "2.5.4",
+      "scipy": "1.18.1",
+      "sympy": "1.14.0",
+      "mpmath": "1.3.0",
+      "gmpy2": "2.3.2",
+      "psutil": "7.2.2"
+    }
+  },
+  "reproduction_command": "python3.12 -B research/staged-release-retiming-t530/full-admission/reproduce.py --repo . --work /tmp/fresh-retiming-full",
+  "external_allocation_supplied": false,
+  "wrapper_code_modified_for_this_run": false,
+  "source_manifest_sha256": "fb47533a401d1d13719be8b9aab91fe5313931ca62d40dba336eab6a96275aa0",
+  "source_files": 654,
+  "kappa": "17303943918139634151199999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "wrapper_status": "PASS_RETIMER_T530_COMPLETE_CONDITIONAL_RELEASE",
+  "admission_status": "PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE",
+  "release_status": "PASS_RELEASE",
+  "wrapper_stages": [
+    {
+      "name": "original-materialization",
+      "exit_code": 0,
+      "seconds": 0.8973857500241138
+    },
+    {
+      "name": "retiming-source",
+      "exit_code": 0,
+      "seconds": 0.5103864170378074
+    },
+    {
+      "name": "preserved-staged-review",
+      "exit_code": 0,
+      "seconds": 0.22735691699199378
+    },
+    {
+      "name": "new-retiming-review",
+      "exit_code": 0,
+      "seconds": 0.6307750410051085
+    },
+    {
+      "name": "fresh-native",
+      "exit_code": 0,
+      "seconds": 51.058896915987134
+    },
+    {
+      "name": "literal-owners",
+      "exit_code": 0,
+      "seconds": 17.447704249992967
+    },
+    {
+      "name": "full-admission",
+      "exit_code": 0,
+      "seconds": 1195.7171897080261
+    }
+  ],
+  "admission_stages": [
+    {
+      "name": "owners",
+      "exit_code": 0,
+      "seconds": 22.98314816597849
+    },
+    {
+      "name": "parent-lift",
+      "exit_code": 0,
+      "seconds": 45.674995207984466
+    },
+    {
+      "name": "rebind",
+      "exit_code": 0,
+      "seconds": 4.468241333030164
+    },
+    {
+      "name": "discovery",
+      "exit_code": 0,
+      "seconds": 446.7887197919772
+    },
+    {
+      "name": "outer-check_ledger.py",
+      "exit_code": 0,
+      "seconds": 0.1444164999993518
+    },
+    {
+      "name": "outer-independent_check.py",
+      "exit_code": 0,
+      "seconds": 0.0577197500388138
+    },
+    {
+      "name": "release",
+      "exit_code": 0,
+      "seconds": 674.106729666004
+    }
+  ],
+  "fresh_current_native_providers": 2,
+  "reused_retained_native_chains": 2,
+  "fresh_retained_parent": false,
+  "reused_retained_parent": true,
+  "literal_roles": 1946160,
+  "calls": 4770,
+  "replicas": 530,
+  "profile": {
+    "1": 11747920,
+    "2": 3453480,
+    "3": 1112042,
+    "4": 486540,
+    "48": 202828,
+    "5": 103690,
+    "8": 38160
+  },
+  "runtime_manifest_sha256": "9173c368581deec5a97b8be25608289fd9c50627c2041087386d58010b729081",
+  "original_release_receipt_sha256": "cfeb33c43399f1c89c477945e77d6e2b8562ac8341f13ff395381149edcfb173",
+  "fresh_receipts": "full-admission/fresh-replay/",
+  "fresh_evidence_sha256": "a79042409a73bd696bb3ef48655f9c4995de4fe5ef72eeb2b2e6fffbd0bdabaa",
+  "evidence_checker_sha256": "ec3f3d2e2fe6ae8d77399d6e2fa7f3cd834d9cb2e01871f89dbcedb24d260de7",
+  "scope": "A fresh local POSIX execution of the public wrapper from its published commit and a new external work directory, using the existing pinned environment. Both changed providers and the allocation were regenerated; retained native/parent chains were authenticated reuse. New compact receipts are separate from prior scientific and bounded-run records. The public evidence check validates recorded references, not omitted archives or a new scientific run. General inherited theorem assumptions and independent human review remain open."
+}

research/staged-release-retiming-t530/PUBLIC-OWNER-CONTROLS.json

@@ -0,0 +1,68 @@
+{
+  "bounded_result": {
+    "kappa": "17303943918139634151199999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "owner_gate_disable_sensitivity_controls": 5,
+    "owner_semantic_gate_controls": 5,
+    "package_files_unchanged": true,
+    "profile": {
+      "1": 11747920,
+      "2": 3453480,
+      "3": 1112042,
+      "4": 486540,
+      "48": 202828,
+      "5": 103690,
+      "8": 38160
+    },
+    "rejected_recorded_cache_controls": [
+      "empty cache inventory",
+      "empty provider cache subset"
+    ],
+    "scope": "Fresh finite local/operator, regenerated ownership/invoice, exact arithmetic and scoped packing checks; full native/controller/outer admission is retained evidence only in this command. Inherited general assumptions remain.",
+    "stages": [
+      {
+        "exit_code": 0,
+        "seconds": 2.133318333013449,
+        "stage": "local"
+      },
+      {
+        "exit_code": 0,
+        "seconds": 19.608519667002838,
+        "stage": "owner"
+      },
+      {
+        "exit_code": 0,
+        "seconds": 0.29930454201530665,
+        "stage": "numerics"
+      },
+      {
+        "exit_code": 0,
+        "seconds": 1.729215707979165,
+        "stage": "packing"
+      },
+      {
+        "exit_code": 0,
+        "seconds": 0.06904937495710328,
+        "stage": "recorded-summary"
+      }
+    ],
+    "status": "PASS_STAGED_RELEASE_RETIMING_T530_BOUNDED_CHECKS"
+  },
+  "date": "2026-10-19",
+  "finding": "https://github.com/CrocSwap/integer-mult-bounds/pull/3694",
+  "frozen_auditors_and_full_admission_unchanged": true,
+  "platform": "macOS-27.0-arm64-arm-64bit",
+  "prior_head": "044d24f12e74f228dd462c07ae2d7f3ea35e2be9",
+  "python": "3.12.14 (main, Aug 25 2026, 13:50:33) [Clang 22.1.3 ]",
+  "registered_commands_passed": 3,
+  "scope": "Fresh bounded registered package replay including all 1946160 owner rows, five actual production-gate semantic mutations and five gate-disable sensitivities. Old false-expression lambdas are not counted. No new kappa and no new full scientific replay; old complete replay stays separately dated.",
+  "semantic_gate_receipt_sha256": "fafd011475ad59b14d192c03cec3d02c0e46f213602b09352d869585b86e5f2e",
+  "source_sha256": {
+    "VERIFY.json": "2f127bf8cb39b56de040c1353bb462bc16ce5a20c7facd691c5b704822018777",
+    "owner-audit/DERIVATION.json": "a78896e12209bd8bcdb378ba69889f3e63d98ee27e598fbd01c1619f0946828b",
+    "owner-audit/independent_literal.py": "b51c36ad1ae0999547edc4726d698df369fef60daaaac4f5bbea471648c9f628",
+    "owner-audit/run.py": "c1afe53caf696d4f19ae4e515007dd497f85b46cd14aa224be8f32032635cfad",
+    "owner-audit/semantic_gate_controls.py": "5638f9eb05c19be43b6579aa82ab9c01e5648bfeb3d8963042ef6a463dc6e335",
+    "verify.py": "3a77186565cfee7f7b9e3c0bd02072e03c0b133bb9ca43f9e2418af6a17a5fd1"
+  },
+  "status": "PASS_OWNER_SEMANTIC_CONTROL_CORRECTION"
+}