Mister-Meeseeks · Oct 16, 2026 · Oct 16, 2026
diff --git a/research/paired-helper-frame-ledger/INPUTS.json b/research/paired-helper-frame-ledger/INPUTS.json
@@ -0,0 +1,105 @@
+{
+  "source_repository": "CrocSwap/integer-mult-bounds",
+  "source_pr": 2917,
+  "source_commit": "224bd5e56041c40078ff6b5fa7393733a215de5c",
+  "files": [
+    {
+      "path": "data/PARENT-base.json.gz",
+      "source_path": "research/paired-helper-extension/data/PARENT-base.json.gz",
+      "git_blob": "6303cfd847033481d1e662e2a2fd467caf5f6429",
+      "sha256": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+      "bytes": 69992
+    },
+    {
+      "path": "data/PARENT-extra.json.gz",
+      "source_path": "research/paired-helper-extension/data/PARENT-extra.json.gz",
+      "git_blob": "38af2b6ea76002df44de3c8045b24ce622782b9f",
+      "sha256": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
+      "bytes": 69989
+    },
+    {
+      "path": "data/TRANSFORM-299.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-299.json",
+      "git_blob": "897a8917195dbcc334293d6509215640a9c852ad",
+      "sha256": "781585f68449c30f63e40ee4bf58d1fa194e4faf8cf4394505437fc15137ba34",
+      "bytes": 2881
+    },
+    {
+      "path": "data/TRANSFORM-304.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-304.json",
+      "git_blob": "e04d29425033122f76dcd7c6658ea95a6cf27d3d",
+      "sha256": "024515c6e47d952dfaf307fcefda9f2106049ccc28875ae620d95241fdec72ed",
+      "bytes": 3084
+    },
+    {
+      "path": "data/TRANSFORM-320.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-320.json",
+      "git_blob": "9c8490c8643214e00eebcc50f45089e4e866d1c4",
+      "sha256": "0e4c0216221ab21c4bf48a11eab34ff6cc245014d664dc1523cfae9d437dc00d",
+      "bytes": 2630
+    },
+    {
+      "path": "data/TRANSFORM-331.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-331.json",
+      "git_blob": "7d35aab299dcd034ec9ecd67877bbe911c1a960c",
+      "sha256": "355bcfd60ffcb672f66882e66bae1b046d1bfb979f725b411b034f811dfb68bb",
+      "bytes": 2812
+    },
+    {
+      "path": "data/TRANSFORM-412.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-412.json",
+      "git_blob": "e62dd449d7ce79fc99cd128855d324ee6b554cd8",
+      "sha256": "54328a8436d7abed6433da5e4384a36ad95b266070479b496e0e96416a5f5a79",
+      "bytes": 2498
+    },
+    {
+      "path": "data/TRANSFORM-424.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-424.json",
+      "git_blob": "4fae6d1bb371f8407a8cd33b47dda8ccd64be7c6",
+      "sha256": "42747fa1332af1ca0827edebfff7490ee761f84f662527f593e975a502400dbc",
+      "bytes": 2399
+    },
+    {
+      "path": "data/TRANSFORM-428.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-428.json",
+      "git_blob": "1593c52045af30bbb15063d29ec1460c79d84ef9",
+      "sha256": "89e8fbd5a5d1d64d386cdc38f257cae18d8e7428e868f618ed1f0be5a22aba3e",
+      "bytes": 2501
+    },
+    {
+      "path": "data/TRANSFORM-499.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-499.json",
+      "git_blob": "7c22cd7a667f9fab088174aae93768d474794061",
+      "sha256": "f86eef40cd96b45c67755903eae6a86432e2aeb6d53812621222db7c062d88f6",
+      "bytes": 3463
+    },
+    {
+      "path": "data/TRANSFORM-511.json",
+      "source_path": "research/paired-helper-extension/data/TRANSFORM-511.json",
+      "git_blob": "7c7bf4b1a18ccdce241d2e8f7d5c1149c5dd3fbe",
+      "sha256": "48e0749f1c82594841c88923a38b0308ed777639631a4c3f2414500617f2e34b",
+      "bytes": 3109
+    },
+    {
+      "path": "data/WORD-base.json.gz",
+      "source_path": "research/paired-helper-extension/data/WORD-base.json.gz",
+      "git_blob": "9be0aa5349dbc8c928a46089a7695e224d0e4d16",
+      "sha256": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+      "bytes": 69818
+    },
+    {
+      "path": "data/WORD-extra.json.gz",
+      "source_path": "research/paired-helper-extension/data/WORD-extra.json.gz",
+      "git_blob": "40b38365ea4b841101405ebd2c4fdcadcb8b9808",
+      "sha256": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+      "bytes": 69814
+    },
+    {
+      "path": "SOURCE-CREDITS.md",
+      "source_path": "research/paired-helper-extension/CREDITS.md",
+      "git_blob": "153868a3ebcf56962716f6222f0f542a9417e502",
+      "sha256": "a4e845cbd7cd430d7b53899b3148fb908c3af1924137412e44f19a9031fdc86a",
+      "bytes": 2337
+    }
+  ]
+}
diff --git a/research/paired-helper-frame-ledger/README.md b/research/paired-helper-frame-ledger/README.md
@@ -0,0 +1,161 @@
+# Independent finite frame ledger for PR2917
+
+**Finite accounting audit; no new κ or supplier admission.** This package checks
+Mason Hale's nine additional paired-helper extractions in
+[PR2917](https://github.com/CrocSwap/integer-mult-bounds/pull/2917), pinned at
+`224bd5e56041c40078ff6b5fa7393733a215de5c`. Both `base` and `extra` providers pass.
+The immediate parent is Jeremy Diviney's [PR2908](https://github.com/CrocSwap/integer-mult-bounds/pull/2908)
+at `51309592971e3b5be935599eed2a95404dc7781e`.
+
+## What this adds
+
+The predecessor `vendor/preload_move.py:frame_report` and
+`vendor/audit_local.py` both use essentially the same pivot-basis and climb
+calculation. Here a frame is its complete subset of `GF(2)^9`: at most 512
+vectors, constructed by XOR closure. Dimensions are obtained from cardinality;
+containment and equality are set operations. No predecessor Python is imported
+or executed. This is a different implementation of the **frame implication**,
+not a claim of independent verification of the whole construction.
+
+The new replay derives every positive climb, every separate centre descent,
+and the terminal climbs from the ordered operations. It checks actual subspaces,
+not merely dimensions, including signed prelude warps, all 512 images of each
+invertible warp map, dual perpendicular transport, lifted frame maps and the
+symplectic identity. It then compares the derived histogram with the word's
+report. It reconstructs nine sequential **frame projections**, checks each
+declared old-frame preimage and candidate index, and compares the final
+frame-bearing sections with the frozen final word. Compensation algebra is not
+part of that projection.
+
+| Derived quantity, for either provider | Parent | Final |
+| --- | ---: | ---: |
+| Paid profile | 2407 H1 + 640 H2 + 262 H3 + 128 H4 + 26 H5 + 8 H8 | 2416 H1 + 640 H2 + 280 H3 + 110 H4 + 26 H5 + 8 H8 |
+| Positive paid events | 3471 | 3480 |
+| Paid rank mass | 5179 | 5170 |
+| Sum of 408 helper widths | 3323 | 3314 |
+| Width inventory | 4:26, 5:2, 7:62, 8:87, 9:231 | 4:26, 5:2, 7:62, 8:96, 9:222 |
+| Private cleanup buffers | 73 | 82 |
+
+The extraction order is `424, 428, 412, 331, 299, 320, 511, 304, 499`.
+Each of the first three steps changes the profile by `3 H1 - 2 H2`; each of
+the last six changes it by `H2 + 3 H3 - 3 H4`. Therefore the net change is
+`9 H1 + 18 H3 - 18 H4`. Each extracted helper changes width from nine to eight;
+all other widths are unchanged.
+
+All **13** declared frame edits satisfy the stronger geometric identity
+`new_frame = old_frame ∩ E_normal`, with `E_normal` the extraction hyperplane.
+Twelve edits lower an A-operation frame from dimension eight to seven. The
+thirteenth lowers helper499's inherited `restore[40]` scale frame from nine to
+eight. Restoring only that frame to FULL makes its later rank-eight touch at
+`restore[114]` illegal, although the scalar operation itself is unchanged.
+
+A useful cross-check telescopes the frame dimensions. Warps preserve dimension;
+ordinary climbs sum to endpoint dimension minus entrance dimension. Centre
+readout descents are charged separately and do not lower the main-word carrier.
+The source/target contribution is `112*8 + 112*8 = 1792`; eight centre descents
+contribute 64. Thus:
+
+```
+parent: 1792 + 3323 + 64 = 5179
+final:  1792 + 3314 + 64 = 5170
+```
+
+The cleanup audit independently constructs the inverse-reverse **syntax** of
+the forward non-target program, omitting the prelude, and substitutes `704+h`
+for every protected helper `h`. It checks every actual cleanup operation,
+reciprocal/negated coefficient, inverse warp identifier, full frame and private
+buffer name. The buffer sets equal exactly `704 + helper_final`, with no direct
+cleanup reference to a protected helper. This does **not** prove that those
+buffers return to zero. Intermediate stage cleanup is derived syntax, not
+comparison against separately stored stage words.
+
+## Reproduce
+
+Python 3.12, standard library only. From repository root:
+
+```sh
+python3.12 -I -B research/paired-helper-frame-ledger/verify.py
+python3.12 -I -B research/paired-helper-frame-ledger/test_verify.py
+python3.12 -I -B -O research/paired-helper-frame-ledger/verify.py
+python3.12 -I -B -O research/paired-helper-frame-ledger/test_verify.py
+python3.12 -B scripts/research_package.py --package research/paired-helper-frame-ledger
+```
+
+Expected marker: `PASS_PAIRED_HELPER_FRAME_LEDGER`. Verification is read-only.
+The local environment, successful commands and reviewed code hashes are recorded
+in [VALIDATION.json](VALIDATION.json); hosted CI is separate.
+`RESULT.json` records both providers, all stage profiles, exact edit locations,
+section histograms and hashes of the derived event ledgers. To inspect every
+paid event and helper width, use `verify.py --details` and redirect stdout to a
+file **outside** the package. This output is freshly calculated, not loaded from
+the frozen receipt. Exact comparison uses canonical JSON so that Boolean and
+floating aliases cannot stand in for integer receipts.
+
+`INPUTS.json` pins the four gzip words, nine transform JSON files and retained
+credit text by SHA256, byte length and Git blob. The wrapper also pins the
+manifest itself. These are immutable source bytes, not regenerated compressed
+outputs. The source commit and original paths were authenticated against Git
+at intake; offline replay checks the frozen source inventory and bytes.
+`SOURCES.json` pins the original catalogue and selected-record provenance;
+they are not live mathematical inputs. The generic metadata check needs that
+base Git history. The standalone replay needs only this directory.
+
+Controls cover equal-rank unequal frames, chronological ordering, warp preimages
+and invertible but wrong maps, omitted endpoint charges, forged inventories,
+the helper499 scale refit, cleanup aliases/inverses/types, transform bindings,
+input corruption and strict JSON. A separate XOR-pivot oracle checks all 128
+generating subsets of the seven nonzero three-bit vectors, their 16 subspaces
+and all 256 ordered containment pairs. Checks remain active under `-O`.
+
+## Scope and overlap
+
+The `independent-moment` card was selected with OS nonce
+`9e2c1aa952cf9f74c87b48ad6e7d6ac1` from priority revision 5 at main
+`8c8bcecb03def61bca701dd3b045932d39c48022`. Its rank-ledger method was refined
+to this new nine-step input. The
+[canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/2612#discussioncomment-18972911)
+records the boundary with mdumitrean's concurrent allocation work on PR2917.
+The entry overlap search covered 476 open PR bodies including drafts, 2657
+local notes/tasks/ledger records, and manually inspected relevant current
+Discussion threads. Cached PR pagination is a non-atomic snapshot; Discussion
+pagination, arbitrary diffs and unpublished work were not exhaustively covered.
+No matches would not certify novelty. See `TASK.json` for exact coverage and
+remaining questions.
+
+This audit does not replay the predecessor's scalar or free-operator identities,
+compensation correctness, 632-column forward/dual audit, native implementation,
+buffer-zero proof, owner allocation, physical stock, precision, moment/root
+calculation, outer admission or all-size/compiler hypotheses. It does not
+change the selected record, any predecessor package, or the frontier. The
+82 cleanup names do not establish an 82-register feasible physical schedule;
+the inherited ambient dimension 73 is a different quantity.
+
+## Open next questions
+
+1. Does the pinned final word, including compensation and cleanup, have the
+   claimed operator endpoint and zero-buffer behavior? A reviewer can first
+   authenticate PR2917's full source closure and replay its declared operator
+   checks. This package supplies only the frame/accounting component; primary
+   success and independent coverage must remain separate.
+2. Does a source-bound native owner allocation for that unchanged word satisfy
+   complete physical-stock, precision and outer-admission obligations? Continue
+   from the current canonical allocation claim, first checking its exact word
+   and allocation pins. A local cap or profile alone cannot discharge those
+   obligations. That work is intentionally left to its active owner.
+
+## Credit
+
+Prepared by ToikY with substantial OpenAI Codex assistance, including separate
+AI implementation, adversarial-test and mathematical-review agents. This is
+not independent human review or proof-assistant verification. New code and
+documentation are Apache-2.0.
+
+Mason Hale contributed the nine extractions and 13 enabling frame edits in
+PR2917. Jeremy Diviney supplied the immediate paired-helper408 construction
+and compensation/cleanup architecture in PR2908. Jeremy Kothe supplied the
+preload and frame chronology in PR2894 (`18d03c447886895ef9abf888398178e0428533ca`)
+and PR2833. Retained upstream attribution, including Yiyang Lu, Dugongue,
+Marius-Paul Dumitrean, Philippe Van Velzen, Tekalign and icekylinx, appears in
+the byte-identical [SOURCE-CREDITS.md](SOURCE-CREDITS.md). Its descriptions of
+the primary package's replay are predecessor statements, not checks claimed
+by this audit. No predecessor executable code is vendored here.