Independently audit #2979's joint rank-seven frame paths

research/rank7-joint-frame-audit/README.md

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+# Independent joint rank-seven frame audit
+
+Both #2979 providers pass a code-disjoint chronological frame recount. The
+five isolated groups sum to its stage-one invoice. No finite frame defect was
+found. This is a partial audit, not supplier admission or a new kappa.
+
+## Shared overhead, with losing controls
+
+For V45, keep the group's 61 gate-frame edits fixed and lower any `k` of
+helpers `{249,251,265,267}` from rank eight to rank seven. All 16 endpoint
+subsets pass the literal frame and unchanged cleanup-syntax checks. Their
+exact paid-profile difference from the parent is
+
+```text
+Delta(k) = (2-k) H1 + 10 H2 + 6 H3 - 10 H4,  0 <= k <= 4.
+```
+
+Here `Hr` means one rank-`r` child, not a numerical tariff. Thus the partner
+cost is paid once and each additional endpoint saves exactly `H1`. The result
+holds for any additive rank tariff on these fixed paths. It does not optimize
+frames for the proper subsets or prove a global single-lowering bound.
+
+Substituting the source's integer surrogate prices and its approximate
+2,091,300-unit width guide gives the following margins:
+
+| Lowered endpoints | Number of subsets | Guide margin per subset |
+|---:|---:|---:|
+| 0 | 1 | -78,512 |
+| 1 | 4 | -53,141 |
+| 2 | 6 | -27,770 |
+| 3 | 4 | -2,399 |
+| 4 | 1 | +22,972 |
+
+These reproduce the source's comparison, but **the guide is not a certified
+physical idle tariff**. A positive guide margin does not establish a complete
+supplier saving. The symbolic identity above is independent of the guide.
+
+## Whole stage and final boundary
+
+The checker partitions all 139 edits by their unique containing group space,
+checks each old gate and frame, and reconstructs each group independently.
+No scalar, operator, entrance or cleanup gate changes in stage one.
+
+| Group | Exact paid-profile delta | Gate-frame edits |
+|---|---|---:|
+| V45 | `-2 H1 +10 H2 +6 H3 -10 H4` | 61 |
+| A | `-H1 +20 H2 -14 H3 +2 H4 -2 H5` | 21 |
+| B | `-H1 +20 H2 -14 H3 +2 H4 -2 H5` | 21 |
+| C | `20 H2 -14 H3 +2 H4 -2 H5` | 18 |
+| D | `20 H2 -14 H3 +2 H4 -2 H5` | 18 |
+
+Their sum is `-4 H1 +90 H2 -50 H3 -2 H4 -8 H5`. Paid rank mass falls
+5,166 to 5,144, and helper-width mass falls 3,310 to 3,288. Both providers
+also reproduce the shipped final local profile, of mass 5,139, and its
+six-width inventory, of mass 3,283. The 408 live helpers remain present.
+
+The inverse-cleanup syntax and endpoint/buffer bijection give 86 private names
+before and after stage one, and 91 in the final word. This counts names; it
+neither proves their zero return nor supplies physical storage admission.
+
+The actual dispatch has 250 base and 416 extra calls. Multiplying the checked
+final local profiles by those counts leaves
+`17310 H1 +4956 H3 +1728 H5 +28190 H48` when subtracted from the source's
+claimed complete invoice. `RESULT.json` labels this remainder conditional:
+this check does not reconstruct owner geometry or establish that subtraction
+as an independently certified idle bill. [#2987](https://github.com/CrocSwap/integer-mult-bounds/pull/2987)
+is the separate chronological-packing audit, not a substitute for native or
+physical admission.
+
+## Evidence and reproduction
+
+Exact source [#2979](https://github.com/CrocSwap/integer-mult-bounds/pull/2979)
+is `be191346391661f4d35fc0d1508d0a6029572576`; scientific base is
+`836b19bfa309ceafbc8ee32a15e8c4b10dde7e11`, priority revision 6.
+All nine live inputs match that original PR's bytes and are bound by Git blob
+and SHA256 in `SOURCES.json`. No predecessor Python code is imported or run.
+The original author and all inherited source notices retain their attribution.
+
+```sh
+python3.12 scripts/research_package.py --package research/rank7-joint-frame-audit
+# Direct deterministic JSON, without Git or a network connection:
+python3.12 -B research/rank7-joint-frame-audit/verify.py
+```
+
+`RESULT.json` records both providers, every subset, each isolated symbolic
+invoice, chronological-event hashes and 18 deliberate rejections. Controls
+cover stale invoices, a wrong rank-seven space, an omitted gate edit, widened
+ends, singular warps, missing cleanup, wrong private names, stale preimages and
+extra edits. Five unittest methods also test explicit subspaces, charged
+climbs, warp maps, normal/optimized command equality, a Git-free export and
+corrupted-source rejection. All acceptance checks survive Python `-O`.
+
+The scope is exact finite frame accounting and cleanup syntax. The scalar
+free-operator maps, symplectic/Clifford phases, arbitrary-dirty-input and
+private-zero return, owner embedding, full storage, prefix/precision/tape,
+outer release and all-size/compiler implications remain unverified here.
+The selected bit/complex caps and selected frontier are unchanged. No new
+proof-assistant, native build or complete cold replay was run.
+
+## Implementation limits
+
+The frame oracle expands at most 512 points from nine generators, with a
+4,096-entry cache. Words have 704 slots, at most 480 warps and 10,000 gates
+per section. Input authentication precedes decoding, capped at 2 MB raw and
+8 MB decoded per file. All loops traverse these finite domains, five groups
+or 16 subsets; no recursion is used. Functions are below 60 physical lines.
+
+Python's managed allocations are a rule-3 deviation from fixed allocation.
+The bounds above limit live collections; the cache stores immutable sets.
+Rule 9's callback deviation is confined to the nine local rejection actions;
+all targets are visible in `controls`. The standard-library cache decorator
+only memoizes `span`; it does not generate or evaluate code. Replacing either
+mechanism is warranted only if these finite limits or the checker API change.
+Diagnostics use `ruff check --select E4,E7,E9,F,B,I`, `ruff format --check` and
+Python development-mode warnings as errors. No shared CI settings change.
+
+## Open next questions
+
+Can the independently checked final frame paths and #2987 owner geometry be
+joined to one independently checked native residual/phase and physical invoice?
+This decides whether the local benefit survives its actual consumer. Start
+with one lowered V45 helper's native frame-transition recipe, bind it to this
+ledger's chronological events, and check both orientations and its private
+buffer endpoint. The missing native/phase, physical storage and precision
+bindings block supplier admission; another surrogate-price calculation does
+not close them. The full #2979 release remains a separate, larger audit.
+
+## Credit
+
+Marius-Paul Dumitrean/#2979 and #2942 supplied the joint construction and
+literal words. Jeremy Kothe supplied the frame/cleanup lineage and #2957
+rewrites; Mason Hale/#2917 and Jeremy Diviney/#2908 supplied the paired
+extraction chain. This complements ToikY/#2932's older frame ledger and
+Ross Richardson's #2960/#2974/#2987 algebra, invoice and packing audits.
+Retain Yiyang Lu, Dugongue, Tekalign, icekylinx and the original geometry,
+native, owner and compiler contributors' credit. New check by Nick Petalas,
+Apache-2.0. No independent human or formal-kernel review is claimed.