[Clear1nsight]

Change and mathematical scope

At fixed C=.0030217758, preserve and independently verify the exact native recursive rank-moment optimum on #4994's 18 small components/68 contacts, with the 1271-variable component fixed at source. Both orientations retain source histogram {1:2201,2:412,3:510,4:127,5:40,8:8}. The source is a minimizer; the chosen tie-rule assignment changes four labels, with no uniqueness claim.

The separate integer-cut extension fails at cut 3: minimum 5075 versus source 5080, while the same witness costs +0.077586985710037469603912620755..756 at the fixed power price. Cuts 1/2 equal source; cuts 4..8 were not run. This is a fixed-C restricted recursive-moment result, not a global/all-concave/physical/caller optimum or new κ. Equal profiles may differ in finite routing/storage/precision costs.

Task and overlap

Public head f33fa4d019916901c202ddf382010f6e3833af65, branch Clear1nsight:research/small-coupled-frame-optimum-20261023. Scientific base f259dabc7d70e0db8d6d36bfda888f008bbfecc1; task complex-rank-shape-decoder, scope explicitly changed to supporting exact restricted verification under the #4994 claim. Source #4994 ef2810fe43829960789f783e44ee6484d0368f09 retains #4971 0130b196145a43a7d305de41f49e56e8e8556378; independent arithmetic uses exact 20bb research/higher-moment-strictification/verify.py. Original requests and exact retained bytes remain bound separately in SOURCES/ORIGINS; all source heads are ancestors.

#5016 supplies neighboring numerical full-domain MILP evidence. #5024, head 390d7255f0e128be54e007962d7febb47697a7c5, supplies an all-price optimum for intact source zero-edge regions. This package permits per-contact choices in the declared small components and fixes the large component; the restrictions differ and no dominance is asserted. Pre-submission canonical main 4c0a359d88f22f05189d51f48387750b801a45d4 retains the same governing guidance and selected record. Fresh bounded all-author overlap check at 2026-10-23 07:52 UTC found no duplicate of this exact restricted question; this is not a novelty proof. No new optimization campaign was run for publication.

Validation

Python 3.12 standard library. Registered normal/optimized commands replay the unchanged independent certificate audit and author fixed-price/cut drivers into private outputs; fresh receipts match all frozen semantics except elapsed metadata and summary hashes binding that metadata. The independent checker reconstructs complete subspace domains, multiedge/unary factors and traceback; checks 8,760 bucket evaluations, all 29,790 containments per assignment and 119 rigorous signed power comparisons. Meaningful controls reject missing unary/edge factors, a nonminimal argmin and a wrong histogram; the original weaker controls remain visibly qualified.

python3 -B scripts/research_package.py --package research/small-coupled-frame-optimum --check-only
python3 -B scripts/research_package.py --package research/small-coupled-frame-optimum
python3 -B scripts/check_research_commit.py --package research/small-coupled-frame-optimum --check-source-history
python3 -I -W error -B research/small-coupled-frame-optimum/verify.py
python3 -I -O -W error -B research/small-coupled-frame-optimum/verify.py

Local normal/O replay, exact frozen-tree equality, committed-input/source-history preflight, diff check, official export/integrity, and Git-free read-only export normal/O pass. The final metadata-only task-card correction leaves all verifier/scientific/evidence bytes equal to the tested snapshot; final metadata/source-history/export checks pass. Each direct replay takes about 14 seconds here. No hosted CI claim, native phase/emitter campaign, full selected cold replay, large-component search or k4..8 is included.

Credit

Prepared by Chris R / Clear1nsight with substantial OpenAI Codex assistance. Retains 1337isnot1337's #4994 interval/realization model, Dugongue's #4971 frame-carrying swaps, Cao Yifan and native/controller/compiler predecessors, Astra's source-specific proposal and fit to Rina Dechter's bucket-elimination theorem, and the independent review/implementation credit. krzysztofwojt's #5024 and #5016 retain their distinct parallel credit. The whole frozen independent packet, author BRIEF/stopping decision, control clarification and original Apache-2.0 LICENSE/NOTICE remain byte-exact.

Open next questions

See TASK.json and README. A changed word/interface must first provide a justified fully charged source-bound bill before another search. The large component, broader schedules, native phases, uniform physical implementation and complete caller remain open; this result neither proves them impossible nor changes the selected frontier.