Research: certify PR #2979's V45 final-word controls fail the complete packing budget

[commdata2338]

Change and mathematical scope

The local V45 guide comparison does not by itself price its controls on PR #2979's final owner allocation. This independent audit fixes the final scalar gates, partner frames, later extraction/rewrite stages and cleanup, then restores any subset of endpoints 249/251/265/267 from their shared rank-seven space to their own parent rank-eight endpoints.

All 15 nonempty widening controls fail the source complex saving even with arbitrary fractional repacking in the fixed capacity model. In particular, retaining only helper249 lowered gives a certified complete moment at least 1.000005090277, above the budget of 1. The actual coordinated final word passes at that same exact saving, 1729033982646513517717 / 10^24. No root search or extra endpoint digits are contributed.

The new package independently recounts both providers and checks all 271,728 placements and 149,184 bins. The complete baseline profile is {1:1645680,2:470196,3:159468,4:71928,5:13716,8:5328,48:28190}, with rank mass 4,816,512. Every V45 occurrence is in a saturated bin. The single-retained-endpoint control overfills 1,938 bins by 1,998 width units; at least 15,354 whole-helper width units must leave those source bins. This deletion lower bound does not price or construct a legal relocation.

The stronger obstruction uses a written packing-dual argument, independently enumerates all 2,551 admissible patterns, and certifies its inequalities with integer-square-root tariff enclosures. Summing every bin and local-child tariff gives the complete recursive lower bound. The nominal stock remains 66,304 + 408 + 8 + 91 + 2 = 66,813; both providers retain 5,207 cleanup operations and all 91 private names.

Status: finite certificate and scoped obstruction, author-checked with an implementation independent of the predecessor's code. These are final-word controls, explicitly retaining stages two and three, not reconstructions of the original stage-one experiment. Native/dirty-state cleanup, physical backing and movement, precision/prefix/tape, full supplier caps, outer release and all-size/compiler obligations remain open. The complex-budget rejection suffices for these controls; no bit-side cap, new supplier, new kappa or selected-frontier change is asserted.

Task and overlap

Task card: research/rank7-final-fill-controls/TASK.json, independent-moment, priority revision 6; track independent-verification; chooser scope 5e0f415b25b13c102653, refined to pr2979-final-fill-v45-terminal-controls. The specific-card lookup used seed 00000000000000000000000000000000 after reading handoffs. The claim is in discussion #2612.

• Base: 463113d675af7410ac91d53a4fed51ec6494eb9a.
• Contribution commit: 9881b9d5dfe20017503c8d14baaae8629c5afb10.
• Live dependency: PR #2979, be191346391661f4d35fc0d1508d0a6029572576. All twelve live input files match that head and the base, with explicit SHA256/Git-blob/head pins in SOURCES.json. Parent words are those retained inside this source, not a floating dependency.
• Handoff predecessor: PR #3014, 16e8db5656b4fea487a2212395f39707bf134f7a; it checks the older PR Conditional κ ≈ 0.0017228163198632: four paired extractions at normal 45 on #2917's words (+3.16e-7 over #2930) #2942 fill. This checks counterfactual endpoint widths and every packing of the changed inventory on the final capacity supply.
• Existing local-group audit: PR #2993, 34a7003866390618b8e8006dc483e7a37a37903f; original local profiles/guide controls are credited, not claimed as new.
• Existing final packing audit: PR #2987, 02c3047a1e78e6e35e7573c12434ba26f6f9bd96; it does not supply the counterfactual control allocations or this rejection bound.
• Gonzalo Mier's V45 profile audit (PR Research: independently replay #2979 staged rank profile and T74 aggregate #3079) and jwr's single-lowering and shipped-invoice checks (PR Record the V45 single-lowering margin #3112, Record V45 in the shipped words and cap brackets #3119) are complementary. PR test(research): audit V45 native residual and private endpoint #3006/test(research): bind V45 helper and private-buffer events #3008 (Nick Petalas) and PR test(research): certify the V45 closed native endpoint cone #3038 (ToikY) cover native endpoints, events and dependencies. The current group-A entrance-relative and peer-private-free claims, the T20 chronology claim and PR Independently verify PR3044 R2 native slice and residual wrappers #3202's R2 native slice (24kHandsome1201) concern distinct objects and obligations.
• A later check of the 18:32 UTC snapshot (274 open PRs) found one newer neighbour, PR #3228 (Charan, @theon199). It proves stage-one local additivity of PR Conditional κ ≈ 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969) #2979's five frame groups and leaves allocation and idle bills open, so it is complementary.

Scope refined: original stage-one local comparisons already have checks. PR #3014's remaining final-fill invoice question motivates this bounded counterfactual comparison. The only refinement after claiming was to check the existing 2,551-pattern dual on the same changed inventories, without an optimizer or allocation synthesis.

Task-card boundaries: both providers; all 16 subsets of four named terminal endpoints; original role-to-index map; fixed six widths and four capacities; complete local/idle accounting; nominal physical-stock binding. Success requires a passing baseline, exact control failures and semantic negative controls. The optimistic budget grants free compaction and then arbitrary fractional repacking; additional physical costs cannot rescue a strict recursive-budget failure. Stop after the certificate and controls; no family expansion or new construction search.

Offline overlap queries included --task independent-moment, V45/frozen final/terminal widening, and --all-terms V45 control. At final check the complete-paginated cache covered 253 open PRs at 2026-10-17T17:49:11.608413+00:00 and 2,017 discussion records at 2026-10-17T17:52:04.322463+00:00. Merged package notes and the review ledger were also inspected. The cache cannot establish novelty or cover later changes. Canonical main was fetched again at the 2026-10-17T17:57:07.027080+00:00 checkpoint: still the base above, no changed paths, priority revision 6 unchanged; frozen inputs were preserved. Main was still at this base at 2026-10-17T18:45:22Z.

Validation

Python 3.12.3, standard library only:

python3 -B scripts/research_baseline.py
python3 -Werror -B scripts/research_package.py --package research/rank7-final-fill-controls
python3 -B scripts/check_research_commit.py --package research/rank7-final-fill-controls

Observed results:

PASS_RESEARCH_BASELINE_BINDINGS_ONLY
PASS_RANK7_FINAL_FILL_CONTROLS cases=16 rejected_controls=15 roles=271728 bins=149184 packing_patterns=2551
Ran 13 tests ... OK
PASS_REGISTERED_RESEARCH_PACKAGE research/rank7-final-fill-controls outcome=completed
PASS_RESEARCH_COMMIT_BYTES ... files=22 ...

The thirteen behavioral groups include an explicit-point-set GF(2) oracle, exact algebraic square/cube checks of the tariff enclosure, a separate pattern enumerator, all-subset axis-spill counts, and exhaustive deletion subsets for the single-retained-endpoint control. Mutations reject missing/duplicate roles, physical-family conflicts, unavailable windows, missing bins, overlapping/noncompact slices, invalid terminal/private inventories, unpaid children, altered source bindings, an infeasible dual and an omitted pattern. An optimized Git-free export passes; a changed source byte fails before decoding. All acceptance conditions survive -O.

The mathematical implication comes from summing the certified dual inequalities, not from finite tests alone. Full rational bounds and deterministic witness digests are in RESULT.json. verify.py --witnesses OUTPUT.json can exclusively write every capacity witness. Working/package/input bytes match all 22 committed files; staged whitespace checks and reverse-application checking of the exported patch pass.

No Lean, Docker, full selected cold replay, native-program regeneration, outer release or hosted CI was run. Ruff is unavailable in this environment; no lint pass is claimed. The package replay does not establish complete multiplication-theorem admission.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance. Apache-2.0. Marius-Paul Dumitrean (mdumitrean) supplied PR #2979/#2942's words, final fill and fractional basis. Nick Petalas supplied PR #2993's frame audit, PR #3014's frozen-owner invoice obstruction and handoff, and the PR #3006/#3008 native and event audits; ToikY supplied PR #3038's closed native endpoint cone. Ross Richardson supplied PR #2987's chronological packing audit. Credit the V45 price/inventory checks by jwr (James Reed; PR #3112, #3119) and Gonzalo Mier's V45 profile audit (PR #3079). Jeremy Kothe supplied the frame/cleanup conventions and rewrite lineage; Mason Hale supplied PR #2917's T74 call order and dispatch and, with Jeremy Diviney, the paired-extraction chain. Retain Yiyang Lu, Tekalign, Dugongue (packing and owner-engine lineage), icekylinx, Sagar Thakrar, themilkman216 and the source packages' geometry/native/owner lineage. PR #3202 (24kHandsome1201) and the current group-A and peer-private-free claims are separate work. No predecessor Python code is executed, imported or copied.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

See the package README's "Open next questions" section and TASK.json. The smallest useful admission follow-up is to join the exact final fill to the existing native/private evidence, choose one still-unbound consumer cost, and either close it or give an exact obstruction. The current audit leaves native closure, dirty restoration, backing/movement, precision/tape and outer/all-size implications open.

A matched complete comparison of the original stage-one parent/joint/single words would need separately legal allocations and all charges; these final-word controls do not supply it. That would require a distinct bounded construction budget and family decision. No additional lowering census is proposed here.

Workflow feedback (optional)

The handoff-first rule and source-bound package hook made this a bounded audit. The card's empty existing_checks field required manually recovering several already-merged V45 audits. Add coverage pointers for PR #2993/#3014/#3038 and distinguish local-guide, final-allocation and native-private obligations in that field.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG