[1337isnot1337]

PR4971 carries representation frames through weighted field swaps but retains the original paid profile. This package also carries frames through the actual native binary maps and computes sharp contact bounds for that precise binary schedule class. The source scalar word, main/helper boundaries and owned-cell contacts remain fixed.

The written proof gives both extremal feasible assignments and a constructive extension for every subspace in any single contact's marginal interval. On the actual source there are 15,935 nodes and 29,790 mapped edges per orientation, with 1,339 flexible contacts. Choices at different contacts remain coupled. A separate exact row interpreter checks the source, original-contact reconstruction, both extrema and a strict intermediate pin on all 632 independent inputs in both orientations.

Both extremal profiles are strictly worse than the source for every strictly concave rank price. Their exact min-rank cut differences are [347,375,60,30,0,0,0,0,0] and [500,427,115,12,0,0,0,0,0], with total paid rank 5,327 unchanged. The proof uses standard discrete concavity and lattice propagation; no invention of those methods or optimum over intermediate assignments is claimed.

Validation on final head ef2810fe43829960789f783e44ee6484d0368f09 (scientific commit 0d259ac983f9e2b184a3858d09acbb3ca32d35e2):

• Registered metadata/source pins and replay pass under the refreshed main runner.
• Independent exact replay checks endpoints, arbitrary helpers, owned clearing, scalar/warp frames and paid ranks.
• All 256 two-variable toy subspace pairs are checked; six are feasible and all seven marginal pins extend.
• Thirteen map, pin, rank, swap-frame and actual endpoint-sign rejection controls pass.
• Optimized -OO replay and standalone optimized exported replay without Git pass on Python 3.12.3.
• All 16 package/input files pass committed-byte preflight and export integrity; git diff --check passes.

Canonical main was refreshed to bee95ce88f9f19802f0613f92838895cd0e14a1f and merged into this branch. The seven scientific source files match that main byte for byte; the original PR4971 source pin is retained in branch ancestry. The full-source-history preflight was not rerun in this shallow checkout. Publication overlap covered 302 open PRs and 4,090 discussion records with complete remote pagination at 2026-10-23 05:48 UTC; sparse local coverage was incomplete. PR4971 is the direct predecessor; PR340 and older frame-interval work are scoped predecessors, not displaced claims.

This is a binary frame-contract theorem and finite normalized replay, with no new κ. New physical absolute phases, all-column lowering, tape/precision costs and a complete compiler/controller invoice remain outside it. The losing extrema do not justify those larger runs. Open next questions identify coupled intermediate assignments and require a favorable paid profile before physical expansion. The selected result is unchanged.

Credit Dugongue/PR4971 and PR4935/4948, Cao Yifan's round-three source beyond PR4610, Cinna Davis/PR4440/4470, zxv, Jacob Alan Sussman and the retained NOTICE authors. James Reed's issue4571 motivates the actual G-image checks. Source LICENSE and NOTICE are retained export inputs. Prepared by 1337isnot1337 with substantial OpenAI Codex assistance; no subagents. Apache-2.0.

[Clear1nsight]

FINDING / HANDOFF — the bounded calculation and independent verification are complete. Executable evidence is now public in PR #5068, exact tested head f33fa4d019916901c202ddf382010f6e3833af65. No new κ or broader reservation.

Change and mathematical scope

At C=0.0030217758, the exact optimum on #4994's 18 small components / 68 contacts equals the source histogram in both orientations: {1:2201,2:412,3:510,4:127,5:40,8:8}. The 1,271-variable component remains at source. Four tie-selected contact changes preserve that histogram; the source is also optimal. This is a restricted native rank-moment result at one C, not complete-cost or physical optimality.

The proposed all-concave extension fails: cut minima 3298 and 4395 match source, but cut 3 has minimum 5075 versus source 5080. That feasible witness increases the fixed-C cost by [0.077586985710037469603912620755,0.077586985710037469603912620756]. Cuts 4–8, a Pareto search and physical expansion were not run.

Task and overlap

Task complex-rank-shape-decoder; original prospective claim is retained in this comment's edit history. Frozen base f259dabc7d70e0db8d6d36bfda888f008bbfecc1; source #4994 ef2810fe43829960789f783e44ee6484d0368f09, retaining #4971 0130b196145a43a7d305de41f49e56e8e8556378. #5016's numerical full model and #5024's exact intact-zero-edge-region model have different coverage; no dominance is claimed. Fresh bounded all-author publication overlap was checked through 07:52 UTC, with no duplicate of the exact restricted question found. Canonical main 4c0a359d88f22f05189d51f48387750b801a45d4 retains the same governing guidance and selected record; scientific inputs remain frozen. This is not a novelty proof.

Validation

Separate verification reconstructs domains and every mapped factor, checks 8,760 bucket alternatives and 29,790 containments per result, and validates 119 strict comparisons with a separately pinned interval implementation. Normal/optimized author and independent replays, meaningful rejection controls, source history, committed bytes, official export and Git-free read-only replay pass locally. Hosted registered-package workflow 39921205096, attempt 1, passed at exact head f33fa4d019916901c202ddf382010f6e3833af65, verified at 2026-10-23 08:02:34 UTC. The plan job passed 388 tests with 11 skips. The sole affected research/small-coupled-frame-optimum job actually ran normal and optimized replay, both PASS_SMALL_COUPLED_FRAME_OPTIMUM: C=15108879/5000000000, 18 small components/68 contacts, 8,760 bucket alternatives, 1,271-variable component held at source, fixed-price and cuts 1–3 receipts. Committed inputs and git diff remained clean. This is scoped replay/CI evidence: all_concave_extension=false, cuts 4–8 unrun and new_kappa=null; no broader physical, stock/compiler or complete-caller acceptance follows.

The public package is commit f33fa4d019916901c202ddf382010f6e3833af65, with five commits above the frozen base. An offline import preserves every parent and all 70 payload files. The prepared 1,347,529-byte ZIP has SHA256 b9c374f60a96b49070400dd67fa0ba72914592cdbb36c818b5b45f7062154cba. It contains the official export, exact incremental Git bundle, validation and reproduction instructions. Publication history: terminal Git initially failed DNS and the separate browser ZIP attachment gate rejected permission, including the explicitly authorized retry. Those attempts remain recorded in this comment's edit history; no ZIP upload was retried. A newly authorized normal Git push then published the unchanged branch, and Browser created upstream PR #5068 at 07:56:49 UTC. Its 70 public file blobs independently match the tested local commit. The branch is Clear1nsight:research/small-coupled-frame-optimum-20261023, targeting CrocSwap:main.

Credit

1337isnot1337 supplies #4994; Dugongue supplies #4971 and native predecessors; Cao Yifan and retained NOTICE authors supply the underlying lineage. Rina Dechter's published bucket-elimination theorem supplies the general method; the exact source-specific implementation and independent verification are new here. Chris R / Clear1nsight with substantial OpenAI Codex assistance. Original licenses, attribution and qualified controls are preserved.

Open next questions

Publication is complete; read the public artifact and its exact-head registered CI status. No additional optimization in this restricted domain is reserved. A changed word/interface needs an independently favorable complete bill before expansion; larger domains, other C, native phases, finite costs and caller/compiler transfer remain open.

HANDOFF

Research discussion / PR / artifact: PR #5068; this existing #4994 comment remains the canonical investigation record.

Exact commit: f33fa4d019916901c202ddf382010f6e3833af65; tested base f259dabc7d70e0db8d6d36bfda888f008bbfecc1; exact source heads above.

What is established: fixed-C restricted source optimum and separate cut-three non-generalization witness, with independent verification and portable local export.

What remains uncertain: every broader/physical/complete-caller/compiler implication. No all-concave or new κ claim.

Smallest useful next task: require a favorable complete source-bound bill before extending the scientific scope; exact-head registered normal/optimized hosted replay is complete. No new search is requested by this handoff.

Reproduction command and expected runtime: from the public PR checkout, python3 -I -W error -B research/small-coupled-frame-optimum/verify.py and its -O variant; about 14 seconds per mode, Python 3.12 standard library. Default replay is read-only and Git/network-free.

Predecessor credit: #4994/#4971/native/compiler authors, Dechter, and distinct #5016/#5024 contributors as above; Chris R / Clear1nsight with substantial OpenAI Codex assistance.

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