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Price independent one-transvection chart pairs on retained center con… - #6289
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…tacts. Every ordered pair of one-transvection charts at two of the 184 retained-center contacts strictly raises the paid moment for every theta in (0,1). Edgeless sets add. This does not change the selected frontier. Co-authored-by: unpaidmoon <unpaidmoon@users.noreply.github.com>
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Change and mathematical scope
Scoped negative result. On the retained 640-input center-contact graph, every ordered pair of one-transvection charts at two of the 184 variable contacts strictly raises the paid moment for every
0<theta<1, by at least1+7^θ-8^θ. Assignments on a rank-8 edge are at least 2. Any edgeless set of such charts adds, including every subset of the eight singleton charts with the empty-chart contacts fixed.This is not a construction and not a selected-frontier change. The pinned selected record remains
κ = 781451/250000000.Connected mixed labelings of three or more contacts, changed routes, native maps, endpoints, and helper returns remain open.
Task and overlap
Base:
2485805a6d47f36ea83ddde6327d453ac82d44dc. Task:complex-rank-shape-decoder, scope changed. Priority revision 8.Nearest work is PR #4867 /
research/sol1337-contact-frontier, which proved single contacts, common-transvection adjacent pairs, and coherent blocks of the empty chart. This package prices the independent chart pairs that proof left open (handoff comment 19133861). It does not repeat the coherent-block flow or the shared-chart and complementary-terminal bills.Validation
Python 3.12 standard library. Both commands passed, marker
PASS_INDEPENDENT_CHART_PAIR_CEILING, package outcomenegative-result. The verifier rebuilds the graph and enumerates 261,632 same-chart pairs, 261,632 partner pairs, and 8,355,872 rank-8 pairs. Distance-2 rank-0 pairs and edgeless sets are algebraic. Rejection controls: the identity histogram,d*with its rank-1 payment removed, and two copies ofd*plus the same-chart or partner correction.Not run: predecessor C++ maxflow, native phase suite, Lean, selected-frontier replay.
Credit
Cinna Davis / 1337isnot1337, Cao Yifan / intqwq, Dugongue, and Chris R / Clear1nsight (PR #4867, substantial OpenAI Codex assistance) retain credit for the retained-center graph and the coherent ceiling. Scalar, E8, Clifford, helper, precision, compiler, and outer contributors retain credit.
Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. No independent human or formal-kernel review is claimed.
Open next questions
See
research/independent-chart-pair-ceiling/README.md.1022^3is beyond this screen, and no multi-label reduction is proved.