Add independent V45 frame and ledger audit

research/independent-v45-ledger-audit/PINS.json

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+{
+  "schema_version": 1,
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "source_pr": 2979,
+  "source_head": "be191346391661f4d35fc0d1508d0a6029572576",
+  "source_package": "research/rank7-joint-endframes",
+  "source_manifest_sha256": "124bd80e6253256b716716abcde518fec172e6cd855377295875a0fc8dd96db2",
+  "scope": "Independent finite audit of the V45 frame lowering, subset controls, child-rank report and serialized owner/physical ledger."
+}

research/independent-v45-ledger-audit/README.md

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+# Independent V45 frame and ledger audit
+
+Status: scoped independent audit of PR #2979, source head
+`be191346391661f4d35fc0d1508d0a6029572576`. The worktree base is
+`20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority revision 6. This package
+does not change the selected frontier or claim a new κ.
+
+The live overlap check found PR #3823, which records the V45 triple
+intersection, and PR #3841, which records the printed V45 margin ladder and
+the five stage-one group prices. This audit keeps those finite facts as
+cross-checks. Its separate coverage is an independent implementation of frame
+application and both provider child-rank reports, all 15 endpoint subsets,
+the owner schedule/fill checks, and the complete physical invoice. It does not
+claim that the archived search-time pricing witness is independently derived.
+
+## Question and method
+
+For PR #2979's V45 group, do the four shared rank-seven end frames fit the
+recorded gates, does a one-helper control lose under the stated local pricing
+model, and do the resulting child-rank and physical totals reconcile through
+both provider words?
+
+`verify.py` is a Python standard-library-only implementation. It hashes every
+file in the pinned #2979 source package, rebuilds the F2 frame walk from the
+compressed parent/final words, applies the declared frame edits, and checks the
+rank histogram and width inventory. It independently reconstructs source
+windows and checks each serialized owner role for chronology, same-call family
+collisions, bin capacity and overlapping offsets. It imports no code from the
+source package and does not run that package's registered verifier or owner
+engine.
+
+Run:
+
+```sh
+python3 -B research/independent-v45-ledger-audit/verify.py
+```
+
+Expected status: `PASS_INDEPENDENT_V45_FRAME_COST_AND_PHYSICAL_LEDGER`.
+
+## Findings
+
+The shared space is
+`W = <256,128,64,35,16,11,5> = E_7 ∩ E_42 ∩ E_45`. It has rank 7 because
+`7 xor 42 = 45`, so the three normals impose two independent conditions. Each
+of helpers 249, 251, 265 and 267 has an eight-dimensional parent end frame
+containing W. The four endpoints become W, and 29 of the 139 recorded gate
+frame edits touch this group. Recomputed parent and complete stage-one reports
+agree with both provider word records. The gate/operator/scalar entries and
+cleanup arrays stay fixed during stage one. Five semantic controls reject a
+wrong W, a missing partner refit, a changed gate signature, a duplicate helper
+role and an over-capacity role.
+
+The independently recounted stage-one profile is `{1:2430, 2:722, 3:236,
+4:102, 5:18, 8:8}`. Its exact weighted delta is `-46,150,994` units; with 22
+freed width units at break-even `2,091,300`, the complete stage-one margin is
+`+142,394`. The five source group prices sum exactly to this independently
+recounted total.
+
+The pinned V45 group price is `-8,388,172`, with margin `+22,972`. Holding
+the complete stage-one gate edits fixed, independently toggling its four
+endpoint frames changes the child-profile cost by `-8,466,684`, exactly four
+times the rank-one tariff `2,116,671`. The difference implies a shared
+partner-refit charge of `+78,512` in the source price decomposition. The audit
+rebuilds all 15 nonempty endpoint-subset profiles in the complete stage-one
+word; the single-helper control is a direct profile variant, but its group
+margin uses that source-derived shared refit charge. The subset formula is
+then
+
+```text
+margin(k) = k * (2,116,671 - 2,091,300) - 78,512
+          = k * 25,371 - 78,512
+```
+
+It gives margins `-53,141`, `-27,770`, `-2,399` and `+22,972` for one through
+four lowered endpoints. The audit checks the profile variants and all 15
+rows against the pinned source table. An attempted V45-only gate refit on the
+parent is not a valid independent decomposition: its frame walk becomes
+nonmonotone at register 169. The archive does not include the frame-search
+optimizer, so this audit does not independently derive the V45 group price or
+establish that the chosen refit is globally optimal.
+
+The final child-rank ledger independently agrees for both providers
+(`gauge44` and `extra`):
+
+| Rank | Per-provider local children | Full 666-call profile, including idle children |
+|---:|---:|---:|
+| 1 | 2,445 | 1,645,680 |
+| 2 | 706 | 470,196 |
+| 3 | 232 | 159,468 |
+| 4 | 108 | 71,928 |
+| 5 | 18 | 13,716 |
+| 8 | 8 | 5,328 |
+| 48 | 0 | 28,190 |
+
+The final width inventory for each provider is `{4:26, 5:2, 6:16, 7:52,
+8:99, 9:213}`. Relative to the PR2942 parent, the complete local-profile cost
+delta is `-56,726,747`, rank mass falls by 27, and the recorded total margin
+reconciles to `+261,647`.
+
+The serialized owner ledger has 666 calls and 271,728 helper roles, with 416
+calls dispatched to `extra` and 250 to `gauge44`. The independent schedule and
+family check finds 54,200 distinct assigned family IDs within the 66,304
+reserved live-family stock (`74 * 896`). The full physical invoice is:
+
+```text
+66,304 live-family stock
++   408 helpers
++     8 centres
++    91 private cleanup buffers
++     2 guards (residual in the pinned owner invoice)
+= 66,813 physical families
+```
+
+The two provider records have the same independently rebuilt profile and
+width inventory. The source-selected bit/complex bounds, the numerical cap
+root and the outer release are not recalculated here.
+
+## Open next questions
+
+Can the V45 group price and single-helper control be rederived without the
+search-time group price row while preserving a valid monotone frame walk?
+First find a valid decomposition of the V45 edits from the complete 139-edit
+stage-one word, then compare its child-profile costs with the source table.
+The straightforward isolated V45 gate-edit subset fails monotonicity at
+register 169, and the archive does not include the optimizer witness.
+
+## Scope limits
+
+The archived group-price table is search-time evidence from a frame solver
+that is not present in the package. The audit does not independently derive
+the V45 group price or the `78,512` shared refit charge. It confirms the
+complete stage-one profile, constructs valid endpoint-subset profiles under
+the complete gate refit, and checks their listed margins against the pinned
+price table. An isolated gate-edit decomposition is nonmonotone, and optimizer
+completeness remains open.
+
+This is not a fresh two-sided algebra replay, native-provider replay, outer
+proof, supplier admission or multiplication theorem. Do not treat the finite
+frame and ledger result as a new κ.
+
+Credit and predecessor attribution remain with Marius-Paul Dumitrean/PR #2979,
+Mason Hale/PR #2917, Jeremy Kothe/PR #2957, PR #2942 and their cited source
+lineage. This scoped audit was prepared with model assistance; no independent
+human or formal-kernel review is claimed.