Research: independently audit PR #2588's swapped-alias frame bill and lender handoffs

research/t74-swapped-alias-frame-audit/INPUTS.json

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+{
+  "schema_version": 1,
+  "files": [
+    {
+      "pr": 2575,
+      "commit": "921c229b4f030121a1d305de6259e174cd391955",
+      "source_path": "research/gmx-t74-borrow43-handoff/new/borrow/words/BORROW-WORD-43base.json.gz",
+      "local_path": "inputs/pr2575-base.json.gz",
+      "git_blob": "8e24be9d4e9b4d8c62ea008a2e1dc9d99c0198a7",
+      "sha256": "7ded9c8667c123bf0f7833cca78cf7dc79c2dcaca04da405ebfcbbcaf3ebe2ac",
+      "payload_sha256": "94a88069f6b4381127973dc66b6244f072939f21d84c99e2239a74fd768c07b1"
+    },
+    {
+      "pr": 2575,
+      "commit": "921c229b4f030121a1d305de6259e174cd391955",
+      "source_path": "research/gmx-t74-borrow43-handoff/new/borrow/words/BORROW-WORD-43extra.json.gz",
+      "local_path": "inputs/pr2575-extra.json.gz",
+      "git_blob": "e4b2a3c99f0425a36162f3cd80f86fe762bd5a4a",
+      "sha256": "334701c6a6c6d4f67278841412f4deefa72f1b7a28ab7b6ab09ffce98efcad7b",
+      "payload_sha256": "005629c8398da94700cea290c2a80d242eea7a3c13ce464b9e509c591ef732df"
+    },
+    {
+      "pr": 2588,
+      "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+      "source_path": "research/gmx-t74-borrow43-handoff/new/borrow/words/BORROW-WORD-43base.json.gz",
+      "local_path": "inputs/pr2588-base.json.gz",
+      "git_blob": "e319c6e054645846c128b8e1ea85b4eaaf3f9fc4",
+      "sha256": "a94ac54afd0785fe657617094e4d1a2cef4969303247e483c96a09b9c55418d5",
+      "payload_sha256": "d7d8052f795eb5a06b065396b81262760efdb7ce65f3750d1725e34be7ecbf64"
+    },
+    {
+      "pr": 2588,
+      "commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+      "source_path": "research/gmx-t74-borrow43-handoff/new/borrow/words/BORROW-WORD-43extra.json.gz",
+      "local_path": "inputs/pr2588-extra.json.gz",
+      "git_blob": "e38535c9361b14fc58fb82e2761cde00167b55e0",
+      "sha256": "e637086aa54726009405b3c4c42c88d34049699f301dad975bed1b54617e8260",
+      "payload_sha256": "a0923735190ec06eacc5cfdee836f675f88a5c6f2a0db52c967feab44fa758ef"
+    }
+  ],
+  "notice": {
+    "local_path": "inputs/NOTICE",
+    "source_commit": "8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb",
+    "source_path": "research/gmx-t74-borrow43-handoff/NOTICE",
+    "sha256": "a91b93a731f116ae55b3644c88232b4d996e58bb810e2559dec013f9788f5e4b"
+  }
+}

research/t74-swapped-alias-frame-audit/README.md

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+# Independent frame and lender-readiness audit of PR2588's swapped aliases
+
+**Finite certificate and a scoped analytic corollary; no new κ.** On both
+pinned providers, PR2588's substitutions of helpers 596/600 for 648/649 at
+lenders 80/88 have the claimed complete local histogram change
+
+\[
+\Delta n=-2e_1-2e_3+2e_4.
+\]
+
+The audit independently reconstructs all chronological frame charges with
+explicit subsets of the 512-element vector space, and pulls the two moved
+source-partner rows backwards through exact rational, noncommuting operator
+words. All **four moved-handoff rows** (two lenders, two candidate providers) are
+the lender's own arbitrary input. The main contribution is a source-bound
+explanation and independent check of this particular component, including
+failure controls that distinguish frame legality from dirty-state correctness.
+The construction and its improvement belong to Jeremy Kothe and the credited
+predecessors. No defect in the audited component was found.
+
+These are separately implemented, author-run checks, not maintainer review or
+independent human review. They do not certify the complete κ claim.
+
+## Exact sources and task
+
+Base main: `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, priority revision 4.
+The claim is in [discussion #2605](https://github.com/CrocSwap/integer-mult-bounds/discussions/2605).
+Task `complex-new-helper-inventory`, chooser nonce
+`b3b5ee2f84cf3429266e004dacac0b21`, scope key `5868e5281a1e63d41a22`.
+The scope is **changed** from constructing a new helper inventory to auditing
+a changed source binding and its dirty-lender interface. This does not claim
+to meet the original construction card's acceptance gate. See `TASK.json`.
+
+| Source | Exact head | Role |
+|---|---|---|
+| [PR2588](https://github.com/CrocSwap/integer-mult-bounds/pull/2588) | `8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb` | Candidate complete base/extra BORROW-WORD payloads |
+| [PR2575](https://github.com/CrocSwap/integer-mult-bounds/pull/2575) | `921c229b4f030121a1d305de6259e174cd391955` | Comparison complete base/extra payloads |
+| [PR2530](https://github.com/CrocSwap/integer-mult-bounds/pull/2530) | `b4012098048e12500b2d33d2e84be281915a27ac` | Source-partner mechanism credit; no direct code import |
+
+`INPUTS.json` records original paths, Git blobs, compressed SHA256 and
+uncompressed-payload SHA256 for the four verbatim inputs. No predecessor
+builder, elimination routine, frame pricer, scalar replay or stored receipt is
+imported. Only the input word data and its inherited frame-charge contract are
+used. `inputs/NOTICE` preserves the source notice. The selected-result record
+and catalogue in `SOURCES.json` are historical provenance, not mutable inputs
+to this audit.
+
+The closest earlier pricing audit is [PR2359](https://github.com/CrocSwap/integer-mult-bounds/pull/2359),
+which reconstructed the earlier PR2322 handoff bill. This package checks the
+new PR2588 source/helper substitutions and their earlier source-partner cuts.
+The concurrent [discussion #2606](https://github.com/CrocSwap/integer-mult-bounds/discussions/2606)
+audits all eight predecessor source partners and recovery/read ordering; the
+optional content check here is restricted to PR2588's two newly moved cuts.
+[Discussion #2612](https://github.com/CrocSwap/integer-mult-bounds/discussions/2612)
+searches further simultaneous assignments, rather than auditing this fixed swap.
+At the final overlap check, [PR2621](https://github.com/CrocSwap/integer-mult-bounds/pull/2621)
+reported a new order/fill on unchanged PR2588 words. Its global claim is not
+audited here; this package intentionally retains the exact local source pins.
+PR2472 checks entrance Clifford wrappers; PR2478 and PR2508 guard centre-cut
+and helper-index bindings. Their coverage is credited and is not replaced by
+this package. This account's PR2394 checks PR2339's initial native prefix,
+a different component and different word.
+
+## Reconstructed invoice
+
+The following values are independently reproduced for **each** provider:
+
+| Quantity | PR2575 | PR2588 |
+|---|---:|---:|
+| Rank-1 children | 2,369 | 2,367 |
+| Rank-2 children | 632 | 632 |
+| Rank-3 children | 320 | 318 |
+| Rank-4 children | 118 | 120 |
+| Rank-5 children | 26 | 26 |
+| Rank-7 children | 8 | 8 |
+| Total local rank mass | 5,251 | 5,251 |
+| Total charged children | 3,473 | 3,471 |
+| Surviving helpers | 422 | 422 |
+| Helper width mass | 3,395 | 3,395 |
+
+Both inventories are `{4:33, 5:9, 7:62, 8:78, 9:240}`. Each word has
+646 independent live roles, 58 B-phase handoffs, 24 prelude warps and 4,529
+explicit cleanup events. The full local invoice includes prelude raises,
+ordinary A/B climbs, centre COPY descents, restoration and final-frame raises.
+Cleanup touches only full-frame live roles or their full-frame private buffer
+counterparts; no additional local frame climb is hidden there. Buffer values,
+allocation, clearing and global stock charges are separate obligations.
+
+The section delta is particularly useful for review:
+
+| Section | Candidate minus predecessor |
+|---|---|
+| Prelude | `+4 e1` |
+| B | `-6 e1 -2 e3 +2 e4` |
+| Ordinary A, centre COPY, restoration, final raises | zero |
+
+The net four extra prelude raises come from **eight new line-45 target levels**
+(targets 11, 63, 71, 76, 81, 87, 90, 92), while **four line-30 levels disappear**
+(targets 75, 82, 86, 93). Target indices are zero-based, relative to the target
+block. The eight centre descents still split into eight rank-7 and eight rank-1
+children. Thus the net prelude bill must be counted even though the centre bill
+is unchanged.
+
+Only six raw register charge histograms change:
+
+| Register(s) | Delta per register |
+|---|---|
+| Lenders 80, 88 | `-2 e1 + e2` |
+| Helpers 596, 600, newly removed | `-3 e1 -e2 -e3` |
+| Helpers 648, 649, restored to the inventory | `+4 e1 +e4` |
+
+`CERTIFICATE.json` contains their complete before/after charged transitions,
+including event positions and exact subspace incidence masks, all per-role and
+per-section histograms, and full charge/warp trace hashes. It also records all
+twelve target-level changes. Equal per-role histograms need not mean equal
+chronology, so the trace hashes and section charges are retained separately.
+
+## Why this lowers every local moment
+
+For any `0 < p < 1`, both `(1/4)^p > 1/4` and `(3/4)^p > 3/4`.
+Multiplying their sum by `4^p` gives `1 + 3^p > 4^p`. Consequently,
+
+\[
+\sum_r\Delta n_r r^p=2(4^p-3^p-1)<0.
+\]
+
+The rank mass is unchanged because `-2 - 2*3 + 2*4 = 0`. For any fixed
+normalization `m^p W > 0`, the normalized local moment strictly decreases by
+this expression divided by `m^p W`. This is an analytic statement throughout
+the open interval, not a numerical comparison at a chosen saving.
+
+The corollary applies when all other charges are held fixed. It establishes
+neither feasible reuse of a physical owner map nor a global saving or κ.
+The complete swapped construction still needs its native, physical and outer
+checks. No global optimum or new ceiling is claimed.
+
+## Frame and source-state methods
+
+The frame engine expands every generating list by XOR into a literal set.
+Dimensions are the base-two logarithms of set cardinalities; containment is
+set inclusion. Chronological gates require monotone frames, except for the
+explicit zero-rank coordinate changes. Each warp is checked as a permutation
+of all 512 vectors, mapping its source subspace onto its destination. The
+inverse-transpose maps the complementary subspaces correctly. The checker
+also maps all 512 elements of
+`L_U = {(x,x+z): x in U, z in U^perp}` onto `L_E` under
+`(x,y) -> (Gx, Gx + G^-T x + G^-T y)`.
+This verifies the stated geometric interface, not the phase of an emitted
+Gaussian/Clifford circuit.
+
+The scalar checker is a separate reverse-covector calculation. A coefficient
+is a rational linear combination of reduced words in formal invertible warp
+symbols. Pulling a row backward through an ADD adds its coefficient to the
+source; pulling it through a warp multiplies that coefficient **on the right**
+by the warp symbol. Only adjacent inverse symbols cancel. Hence an identity
+in this free algebra holds for any realization of the invertible symbols,
+without assuming that unrelated warps commute.
+
+At the two newly moved handoffs in PR2588, the complete pulled-back row
+is exactly `e_lender` in both providers:
+
+| Lender | PR2588 B cut | Pulled-back row |
+|---|---:|---|
+| 80 | 916 | `e80` |
+| 88 | 931 | `e88` |
+
+A cut `j` means immediately before event `B[j]`, after any earlier same-cut
+warps. The comparison word places these warps at cuts 1062 and 1063; those
+predecessor row identities and its other six source-partner handoffs are left
+to the distinct concurrent audit linked above.
+
+These are forward arbitrary-input readiness statements. For an invertible
+prefix `P`, `e_r^T P=e_r^T` also implies `P^-T e_r=e_r`; that is a dual
+**column** identity, not a claim that the dual row is restored. Complete dual
+word correctness is outside this package.
+
+The readiness checks include the actual prelude, preconditioner, compensation,
+centre-cut scalar gates and all earlier B gates/warps. The pinned words have no
+initial operator-correction terms. No non-target reads a target in A or B.
+Thus no clean-input assumption or omitted target feedback is used.
+
+Two sign faults are especially diagnostic. In each candidate provider,
+flipping B[688]'s `80 += -88` coefficient gives lender 80 the row
+`x80 + 2*x88`. Flipping B[687]'s `88 += x80/2` coefficient gives lender 88
+the row `-x80`. Both mutations leave the **entire independently computed frame
+receipt unchanged** and fail the readiness check. This demonstrates why a
+correct rank ledger alone does not establish the dirty-lender interface.
+
+## Reproduce and controls
+
+CPython 3.12, standard library only, from the repository root:
+
+```sh
+python3 -I -B scripts/research_package.py --package research/t74-swapped-alias-frame-audit
+```
+
+Expected marker, in both normal and optimized modes:
+
+```text
+PASS_T74_SWAPPED_ALIAS_FRAME_AUDIT words=4 providers=2 delta=-2r1-2r3+2r4 helpers=422 handoff_rows=4 frame_controls=18 readiness_controls=4 positive=4 no_new_kappa
+```
+
+The hook compares regenerated mathematical data with `CERTIFICATE.json` and
+writes no package files. For explicit regeneration to a **new** path:
+
+```sh
+python3 -I -B research/t74-swapped-alias-frame-audit/verify.py --write-certificate new-certificate.json
+```
+
+The 18 frame controls cover incorrect reports, singular and wrong-image warps,
+a late handoff, a non-centre cut read, a wrong target room, a wrong inventory,
+a removed-helper touch and a nonzero wrapper frame, on both providers. Four
+additional coefficient-sign mutations preserve the frame receipt but fail
+handoff readiness. Positive controls include equivalent redundant/reordered
+frame generators on both providers, an explicitly noncommuting two-warp
+covector with coefficient `2/3`, and its exact inverse prefix. Runtime guards
+remain active under `python -O`.
+
+## Limits
+
+Not checked: the complete scalar endpoint or cleanup-buffer values, native
+Clifford phases and lowered circuits, physical owner placement and private
+stock, precision/tape costs, the full global moment, outer arithmetic, all-size
+compiler/realization/analytic assumptions, or bit H1–H5. None of these is
+inferred from the local certificate. The maintainer-selected record is unchanged.
+The only selected-record operation used in validation is its binding check,
+not its complete cold replay.
+
+## Open next questions
+
+The structured questions are in `TASK.json`:
+
+1. Test one further pinned lender/helper substitution using these per-role
+   traces and covectors, then its full native and global admission. It needs an
+   actual changed word and complete phase, hosting, stock and precision checks.
+2. Independently replay the complete predecessor supplier and outer packages.
+   This needs their full dependency environment and owner/native sources;
+   the local result here is only one reusable part of that review.
+
+## Credit
+
+Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.
+OpenAI Codex (GPT-6 Astra) performed the derivation, implementation, checking and
+writing. No independent human review is claimed. Apache-2.0.
+
+Jeremy Kothe (jeremykothe2) supplies PR2588's swap and PR2575's integration;
+zxv supplies PR2530's source-partner aliases and restoration schedule; Tekalign
+(tekuuu), PR2436, supplies lifted-target aliases and the prelude mechanism;
+Vlado Vojdanovski, PR2322, supplies coherent handoffs; Cinna Davis
+(1337isnot1337), PR2226, supplies anticipatory dirty borrowing. The T74,
+entrance-raise, native/compiler and supplier lineage retains all source credit.
+Marius-Paul Dumitrean's centre-cut guard, ywz65's helper-index guard and the
+independent pricing/wrapper audits are credited above. The original source
+notice is retained verbatim. The new material is the finite-set interpreter,
+reverse-covector checker, localized delta certificate, analytic corollary and
+semantic controls.

research/t74-swapped-alias-frame-audit/SOURCES.json

@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "e8870e5917057d59b730eb14721a778639eca050",
+      "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7"
+    }
+  ]
+}