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Scoped obstruction: sharp P112 endpoint dimension and complete linear-lift cost - #1417
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100-PR batch review at Merged to Reviewed scope: Sharp dimension18 obstruction for nondegenerate P112 plane labels, linear-lift tensor rigidity and complete fixed-boundary moment no-improvement proof. Exact graph/edge/stream premises pass; nonlinear labels, cross-edge children and changed controller boundaries remain outside scope. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
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The proposed second unpaid endpoint direction must change more than the rank budget. This package proves that every nondegenerate two-plane representation of the selected P112 graph needs dimension at least 18, with equality attained by the tensor representation. It also proves an all-size cost obstruction for arbitrary coupled linear endpoint lifts of the retained supplier and controller.
Review files: Proof and scope · Evidence · Source pins and credit.
The cost theorem permits arbitrary native factorizations of each retained role-stream edge, rank-zero adapters, and arbitrarily many extra coordinates with slanted or nonmonotone frames. It derives the tensor form from 80 independent graph-edge constraints and then uses exact Fourier rank and live-stream accounting. If M(p) is the full reference moment, every such padded lift satisfies M_lift(p) >= lambda M(p) + 1-lambda. Thus the optimal complex moment exponent cannot increase. An exact rational cap also excludes the next selected kappa grid point, 0.001672660197076919. No new kappa is claimed.
The sharp dimension theorem covers nonlinear plane assignments. The cost theorem does not cover new scalar words, new controllers, or joint children across separate arrays or frozen edges. Nonlinear dimension 18 assignments with a different complete word remain open. PR #791's warning that arbitrary rank-two projector penalties need not double is respected: rank scaling is used only after linear-lift rigidity and exact frame-distance checks.
The source-bound verifier checks the selected canonical/program/archive bytes, all 3,494 local native edges in each orientation, all 7,526 idle children, the 144-call owner chronology, the full 510,662-child histogram, rational moment bounds, five rejected mutations and small exact lemma controls. The written proofs establish the universal statements; finite checks are not presented as a formal proof or cold supplier replay.
Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Selected source head: 0fc329d0bec93ca7cd288eaea1295172e8789810. Only research/p112-linear-endpoint-lifts/ is added. The selected frontier and upstream/ are unchanged.
Reproduce with Python 3.12 and its standard library:
Expected: PASS_REGISTERED_RESEARCH_PACKAGE research/p112-linear-endpoint-lifts outcome=negative-result.
Registered CPython 3.12.13 replay, optimized CPython 3.14.7 replay, source-pin rejection, report equality, metadata validation and whitespace checks pass. No hosted CI or complete compiler/ancestry replay is claimed. The inherited all-size/compiler, exact-frame, owner-chart, precision/tape, analytic-transfer and bit H1--H5 assumptions remain unchanged.
Credit: the retained @icekylinx and Colkitt geometry and frame notes; Rohan Arun (@rohanarun)'s PR #1094 and the Kothe/Arun/Hao Yan (@FanPUYen) construction lineage; @DreamingOfClouds' PR #717; Douglas Colkitt (@Mister-Meeseeks)'s PR #1240; Curtis Dransfield (@Curtis-D)'s PR #791; Sagar Thakrar (@thakrarsagar)'s existing emitted-ledger audit PR #1262; Gareth Davidson (@bitplane)'s idle-axis counterexample PR #1387; and the prior PR #1120 scoped geometry work. The ledger recount is supporting evidence, not a new ledger claim. Prepared for Ali Romman (@aliromman) with substantial OpenAI Codex assistance in research, proof, implementation, verification and writing. A separate Codex coordinator checked graph premises and reviewed the proof; independent human review is not claimed. New material is Apache-2.0.
Coordinator publication check: main advanced to cd91ac8e2652bfee6bf09da3b8724253bcf78f5f through a historical PR reconciliation. The selected certificate and all ten proof-source inputs are unchanged. The coordinator read the mathematical proof, separately checked its graph premises, and reproduced the decisive verifier and registered Python 3.12 package command before publication.