Certify coordinated and independent-pair centre-contact cost ceilings (no new κ)

research/sol1337-global-centre-cut/.gitattributes

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+# Preserve authenticated predecessor bytes, including their CRLF line endings.
+vendor/dynamic_neighbors.cpp -text
+vendor/neighbors.hpp -text

research/sol1337-global-centre-cut/BUDGET.md

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+# Research decision and optimistic bill
+
+The assigned changed premise was coordinated retagging across different original
+chart groups of the actual retained640 centre contact graph. PR4867 had closed
+single, adjacent coherent pair and arbitrary-subset/single-original-group moves;
+it had not permitted all 184 choices simultaneously across original groups.
+The prospective scope and fixed invoice were sent to the parent before the sweep.
+A public claim was not posted before the sweep finished; this file is retained
+local decision evidence, not a retrospective public claim.
+
+The paid-only optimistic test keeps `{1:2201,2:412,3:510,4:127,5:40,8:8}` and
+all helper targets `{4:28,7:7,8:47,9:326}` until actual edge repricing. It retains
+all 640 original boundary charts, every native map and scalar operation, and
+zero independent centre reward. Only 184 actual contact charts are variable.
+Each chooses old or T_a(old), with one common declared ambient nonzero axis a.
+There are 262143 such axes; the nine-chart common intersection is zero.
+
+The potentially problematic eight rank-eight edges are all singleton leaves,
+so conditional leaf elimination exactly reduces every tariff to a cut on 176
+empty-chart contacts. A 4096-axis benchmark found only 145 distinct rank-energy
+configurations and finished 1450 cuts in 0.15s. This justified all nine integer
+prefix tariffs in the complete domain: the final 419 configurations and 4190
+cuts finish in a few seconds. No search seeds, random restarts or unbounded
+expansion were used.
+
+Result: every prefix optimum is zero, hence no strict paid-moment improvement
+for any 0<theta<1. Stop at this decision. No physical supplier construction is
+warranted by this grammar. Native phase/word implementation, all 640 arbitrary
+primal/raw-dual checks, source-bound owned caller, compiler/precision and outer
+funding remain additional obligations, unrun here. There is no positive invoice
+to justify launching them. The frozen inputs and selected result are unchanged.
+
+A precisely declared independent/mixed-axis grammar or changed source operation
+or caller demand could change the decision. Another common-axis subset or seed
+cannot; the complete family is already covered. Do not manufacture a peripheral
+PR from this negative extension; root review decides whether to archive or leave
+it as compact decision evidence.

research/sol1337-global-centre-cut/LICENSE

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research/sol1337-global-centre-cut/NOTICE.md

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+Apache-2.0. New graph binding, complete changed-center screens, cut certificates
+and written paid-moment argument prepared for Chris R with substantial OpenAI
+Codex assistance. Retained exact-byte source files in vendor/ come from Cinna
+Davis #4694/#4690 and Dugongue #4841; original headers and assistance disclosures
+are preserved. The native payload is Cao Yifan #4610's frozen round-three word.
+Retain all original #4470, native Gaussian/Clifford, helper, scalar, precision,
+compiler and outer contributor attribution. No predecessor scientific admission
+or independent human proof review is asserted by this package.

research/sol1337-global-centre-cut/PAIRS-ADDENDUM.md

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+# Independent distance-one neighbours on any adjacent internal pair
+
+This additive result preserves every original common-axis scientific file.
+The source-bound pair proof is [pairs/PROOF.md](pairs/PROOF.md), produced by
+the separately assigned shared-producer agent. All eight producer scientific
+and handoff files are retained byte-for-byte, authenticated in pairs/ORIGIN.json.
+The copied original source receipt records their hashes and the exact freshly
+regenerated graph. The new wrapper adapts execution paths only: the original
+producer Python writes its outputs in scratch, and tracked receipts stay fixed.
+
+The combined result covers a second grammar: choose any one of the 264 actual
+internal edges and independently replace both endpoint charts by arbitrary
+nontrivial distance-one Lagrangian neighbours. This grammar does not require
+that their axes agree. All 640 owners/endpoints, native maps and scalar
+operations, 408 helper targets and every incident paid transition remain fixed;
+there is zero independent centre reward.
+
+For the 256 rank-zero edges, each original chart has 511 hyperplanes and two
+neighbours per hyperplane. Identical new charts are inherited from PR4867's
+coherent-pair result. The original exact single/coherent-pair receipts are
+source-pinned and their complete concave-prefix class bounds are replayed here;
+their old neighbourhood searches are not rerun or claimed as new.
+
+The new direct C++ screen covers all 261,632 assignments to opposite neighbours
+above the same hyperplane: 1,831,424 exact incident-edge rank calculations yield
+44 complete histogram classes. An independent Python implementation imports no
+predecessor rank engine and combines complete single-endpoint bills with the
+shared-edge correction. It exactly reproduces every class and multiplicity.
+All classes dominate `3H1 + H7 - H8` in the nine integer-prefix tariffs, so
+paid loss is at least `3 + 7^theta - 8^theta >= 2` for `0<=theta<=1`.
+
+For different hyperplanes, the new charts have distance two. The inherited
+single-contact loss and a simple shared-edge census give
+
+```
+Delta >= 2*(1+7^theta-8^theta) - 2 + 2^theta
+      >= 2 - 2^theta > 0                      (0<=theta<1).
+```
+
+The eight rank-eight edges have degree-four endpoints and no parallel shared
+edge. At each endpoint, at least two external edges originally have rank zero;
+the remaining external edge has rank at most two. Both changed endpoints
+therefore cost at least two jointly outside the shared edge, whose rank remains
+at least six. Even granting independent best cases for all these obligations,
+
+```
+Delta >= 2 + 6^theta - 8^theta >= 2 - 2^theta > 0
+                                                  (0<=theta<1).
+```
+
+Their full nominal 8,355,872 independent-neighbour assignments were **not
+scanned**: this complete optimistic bill stops the route analytically. The
+actual eight edge inventories are regenerated and compared exactly against
+pairs/RANK8-CENSUS.json. The written proof supplies the metric/concavity
+implications; the finite screen and census provide their source-specific data.
+Thus every nontrivial independent-neighbour move on any one actual adjacent
+internal pair strictly loses for `0<=theta<1`. No strict endpoint claim at
+theta=1, changed word/target, larger independent block or new kappa is supplied.
+
+Direct replay, requiring Python3 and C++20 g++:
+
+```
+python3 -I -W error -B research/sol1337-global-centre-cut/verify_pairs.py
+python3 -I -O -W error -B research/sol1337-global-centre-cut/verify_pairs.py
+```
+
+Expected output is `PASS_INDEPENDENT_ADJACENT_PAIRS opposite_cases=261632
+profiles=44 rank0_edges=256 rank8_edges=8 graph_controls=3`. The wrapper also
+checks the actual C++ entry point rejects a negative paid sign, nonidentity
+shared map and an inconsistent simple-edge domain. The original Python's
+same/opposite-neighbour and unsupported rank-inventory controls remain active.
+
+Credit PR4867's Cinna Davis/Cao Yifan/David Ganz lineage, the separate producer
+agent's exact screen and analytic extension, and Nick Petalas PR4864's general
+tuple/cycle geometry. Source attribution and substantial OpenAI Codex assistance
+are retained. No predecessor scientific source or original common-axis result
+was edited. Primary research toward higher kappa proceeds through a different
+changed-operation/complete-invoice gate; no further graph search is proposed.