test(research): certify V45's frozen-owner invoice obstruction

research/rank7-v45-frozen-owner-invoice/README.md

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+# V45 needs a changed owner assignment
+
+Lowering all four V45 endpoints on PR2942's existing owner-bin assignment
+**increases** the complete recursive moment for every positive saving parameter.
+The same holds for all 16 endpoint subsets with the V45 partner frames fixed.
+This is a scoped obstruction to retaining that assignment, not a defect in
+PR2979, which supplies a different allocation and additional word changes.
+
+The new result closes a specific gap between [PR2993][2993]'s local symbolic
+invoice and an actual idle bill. It complements [PR2987][2987]'s analysis of
+the different final pattern mix. It does not repeat the frame-only audit or
+claim a new supplier, exponent or selected-frontier change.
+
+## Exact result
+
+The reference is PR2942's literal T74 fill, retained on scientific base main
+`836b19bfa309ceafbc8ee32a15e8c4b10dde7e11`, priority revision 6.
+The changed frame record is [PR2979][2979] at
+`be191346391661f4d35fc0d1508d0a6029572576`.
+All ten live inputs have SHA256 and Git-blob pins in [SOURCES.json](SOURCES.json).
+The selected record and catalogue are historical provenance, not live inputs.
+
+Keep each role's call, owner replica, child and port fixed. Grant free
+compaction of offsets within each bin, preserving the role order. Bill one
+idle child for the complete remaining capacity, including empty bins.
+This is favorable to the changed word. It does not charge movement or prove
+that the changed native program can execute physically.
+
+Both providers independently recount the V45 local difference for `k` lowered
+endpoints, with all 61 V45 gate-frame edits retained:
+
+```text
+Delta_local(k) = (2-k) H1 + 10 H2 + 6 H3 - 10 H4.
+```
+
+`Hr` denotes one rank-r recursive child. There are 666 actual calls, 250 base
+and 416 extra. The four helpers have ordered indices 25, 27, 41 and 43 among
+the 408 live helpers. The checker derives those indices from original role
+names 249, 251, 265 and 267, rather than assuming original and compact names
+coincide.
+
+For the joint change, all 2,664 freed width units land in previously full bins:
+
+| Freed capacity per touched bin | Bins | New idle bill |
+|---:|---:|---:|
+| 1 | 2,370 | 2,370 H1 |
+| 2 | 147 | 147 H2 |
+
+The unchanged parent idle bill is
+`17316 H1 + 5861 H3 + 6215 H5 + H14 + 27291 H48`.
+All 149,184 bins, 271,728 role placements and source availability windows
+are checked, including those unaffected by the change. Adding the actual idle
+difference to 666 copies of the local difference gives
+
+```text
+Delta_complete(4) = 1038 H1 + 6807 H2 + 3996 H3 - 6660 H4.
+```
+
+This is a complete recursive-histogram difference under the fixed assignment.
+The role counts, 86 private cleanup names, eight centres and nominal source
+stock of 66,808 remain unchanged. Counting those names is not physical storage
+or cleanup-semantic admission.
+
+## Proof of the strict sign
+
+The signed rank mass is exactly zero:
+
+```text
+1038*1 + 6807*2 + 3996*3 = 6660*4 = 26640.
+```
+
+In the retained moment, a rank-r tariff is proportional to `r^(1-a)`.
+For every `a > 0` and `r < 4`, `r^(-a) > 4^(-a)`.
+Replace each positive term `n_r r^(1-a)` by
+`n_r r * 4^(-a)`. Every replacement strictly decreases the sum, and the
+rank-mass equality makes the resulting signed sum zero. The original
+complete difference is therefore strictly positive. The common normalization
+`73^(a-1)/(896*74)` preserves its sign.
+
+The checker certifies the same sign pattern and rank-mass identity separately
+for every endpoint subset, including the fixed-partner zero-endpoint control.
+For example, any singleton has complete difference
+`1264 H1 + 6694 H2 + 3996 H3 - 6660 H4`.
+No floating-point prices, approximate idle tariffs or root estimates are used.
+
+For the usual `0 < a < 1`, splitting a bin's idle remainder into several
+positive-rank children cannot lower this bill, since `x^(1-a)` is subadditive.
+Thus the obstruction also covers such splits with fixed role-to-bin placement.
+It does not cover moving roles between bins, changing the word's partner
+frames, using different endpoint paths or changing the coverage contract.
+
+PR2979's positive surrogate guide used a width tariff near `H48/48`.
+The frozen parent fill actually produces new H1/H2 children. This result
+explains why that guide cannot establish a saving on this unchanged fill.
+It neither prices nor invalidates PR2979's different final allocation.
+
+## Reproduce and evidence
+
+The checker uses only the Python standard library and executes no predecessor
+code. It writes no repository files during verification and needs no network.
+
+```sh
+python3.12 -B scripts/research_package.py --package research/rank7-v45-frozen-owner-invoice
+python3.12 -O -Werror -B research/rank7-v45-frozen-owner-invoice/verify.py
+python3.12 -Werror -B research/rank7-v45-frozen-owner-invoice/test_verify.py
+```
+
+`verify.py --emit` prints deterministic evidence. [RESULT.json](RESULT.json)
+contains the independently recounted parent invoice, both providers' frame
+profiles for every subset, complete idle and recursive histograms, touched-bin
+counts and digests of the rebound rows. The default command compares fresh
+evidence with that committed result. [TASK.json](TASK.json) records the scope
+refinement, overlap coverage and source heads. [decisions.tsv](decisions.tsv)
+records the bounded investigation.
+
+Seven behavioral test groups check genuine source geometry and reject missing
+or duplicated roles, capacity violations, unavailable source windows, unbound
+providers, noncompact source prefixes, invalid frame endpoints, omitted frame
+edits, unpaid idle children, false sign claims, duplicate JSON keys and corrupt
+source exports. A subprocess checks the real optimized CLI. All acceptance
+conditions use exceptions and remain enabled under Python `-O`.
+
+## Limits
+
+This proves a finite invoice obstruction for one frozen assignment. The
+Clifford/native semantics, arbitrary dirty-state restoration, physical movement,
+precision/tape, selected stock coefficients, full supplier and outer release,
+and all-size/compiler implications were not replayed. It does not generalize
+to PR2979's shipped final allocation or to all rank-seven mechanisms.
+
+## Open next questions
+
+The useful continuation is to join the already published changed packing and
+native event evidence to an independently checked physical invoice. Start with
+PR2987's actual final fill and [PR3008][3008]'s named helper/private-buffer event
+inventory. The remaining native dependency closure, physical ownership and
+precision costs block admission. Another unchanged-parent packing calculation
+is unnecessary. This session stops at the fixed-assignment theorem.
+
+## Credit and engineering constraints
+
+Nick Petalas. Apache-2.0. Marius-Paul Dumitrean supplied PR2942's words/fill and
+PR2979's joint mechanism. Jeremy Kothe supplied the frame/cleanup conventions;
+Mason Hale and Jeremy Diviney supplied the paired-extraction chain. Ross
+Richardson supplied the complementary packing audits. The source-window and
+family conventions retain Tekalign's owner-checker lineage. Retain Yiyang Lu,
+Dugongue, icekylinx, Sagar Thakrar, themilkman216 and the geometry/native/owner
+contributors credited by the source packages. No predecessor code is copied,
+modified or imported here. No independent human or formal-kernel review is claimed.
+
+Build the Lever determined the rerunnable integer certificate. Prove It Works
+required reading every actual role placement and idle bin. Test Behavior, Not
+Implementation determined the semantic failure controls. Unslop shaped the prose.
+
+Power of Ten inspection covers the four Python files. Loop bounds come from
+ten authenticated inputs, 704 word slots, nine binary axes, at most 10,000
+gates per section, 480 warps, 666 calls, 408 helpers, 18 idle children per
+replica, 112 ports and 16 subsets. File reads stop at 16 MiB raw and 64 MiB
+decoded; the immutable span cache has 4,096 entries. No recursion or dynamic
+code loading is used. Source authentication runs before decoding and again
+after replay. Ruff and warning-as-error execution check the new code.
+
+Rule 3 deviation: Python allocates managed objects during the bounded recount.
+The fixed domains and file/cache caps bound live state; no resident service is
+introduced. A service accepting larger inputs would need fixed-capacity storage
+and a separate allocation audit. Rules 8/9 deviation: `lru_cache`, the strict
+JSON object hook and unittest callbacks use standard-library dispatch. Their
+targets are fixed local functions; the cache is bounded and contains immutable
+sets. Boundary, optimized CLI and corruption tests exercise these paths.
+
+[2979]: https://github.com/CrocSwap/integer-mult-bounds/pull/2979
+[2987]: https://github.com/CrocSwap/integer-mult-bounds/pull/2987
+[2993]: https://github.com/CrocSwap/integer-mult-bounds/pull/2993
+[3008]: https://github.com/CrocSwap/integer-mult-bounds/pull/3008