Copied centers and reversed corners for conditional κ = 3.850771033e-5 > 2^-15

[rohanarun]

Under the retained analytic and fixed finite-alphabet multitape hypotheses,

T(n) = O(n (log n)^(1 − κ)), with κ = 3850771033/10^14 = 3.850771033 × 10⁻⁵ > 2⁻¹⁵.

This composes icekylinx's copied-center schedule (#36, 11817cc) with James Chang's reversed boundary family (#34, 7fecbe3) at dimensions (23,25) and the attributed RaD balanced assembly. It improves #36's reported κ by 0.132122792%; this compares conditional exponent savings, not measured runtime.

Change and proof

The data profile becomes 9 singletons + [21,17,481], replacing 11 singletons + [21,15,481]. Every copied-center transform and all 4,073,300 paid rank-one endpoint corrections remain. Original producer choices, role volume, total rank and maximum child are preserved. The new rank-one cleanup complements are included in the same common-basis argument.

The exact bit saving is 962729831/25000000000000. The unchanged #36 complex saving is 717/10^7. The semantic envelope explicitly retains the scalar gate charge G; C1=1 and product row degree 2000. All 47 strict constraints and seven margins pass, with a positive final absorption gap.

Checked before filing

• All 25 controlled permutation completions, both restriction trees, actual local/auxiliary contractions, all 47 rank cuts, and three exact rational pivot witnesses.
• Complete physical accounting and an independent class-by-class reconstruction; the old profile fails at the new saving by a rigorous lower moment bound.
• Copied-center schedules in both orientations on arbitrary dirty inputs, including phase-copy directions and paid endpoint correction; scoped independent agent reviews are included.
• 12 focused tests pass, including corrupted source/rank-cut controls, rank-preserving child-list corruption, old precision envelope, invalid rows, and next-grid lower exclusion.
• The focused patch reconstructs 19 files byte-for-byte from pinned Copied retained centers and two-stage assembly for conditional kappa = 3.84569e-5 #36.

Full rerun passed: make verify completed successfully on research commit cb86e50e9a07685068874d8e4174b2e6c209b95c: 182 tests, fresh selected h28/d19 complex producer, inherited h25/h23/h57 scalar and positive-label checks, historical complex h28 reconstruction, and all 18 historical patch checks. The new 12 focused tests pass as well. The validation receipt records completion and log SHA-256 020a0bb269ff326b34056e893484eb408ce0c06c3cae9ced920f64ba1f491f2e. Only an inherited JSON key-order difference was generated; exact parsed equality was verified and the pinned historical file restored. The validation follow-up changes documentation and the receipt, not the scientific sources. The refreshed focused patch reconstructs 20 files. Ready for review; no formal verification or external expert acceptance is claimed.

Start with the proof and reproduction guide. Run make copied-reversed-check, make copied-reversed-producer, and make verify. The inherited analytic, tape, routing, recovery, constructive setup and eventual-threshold hypotheses remain explicit.

Attribution

Rohan Arun, with substantial OpenAI Codex assistance, supplies this composition and checks. Credit icekylinx (#36 copied centers/complex graph and earlier producers), James Chang (#34 reversed family), RaD/hipotures (balanced routing/semantic/bulk transfer), Dominik Scholz (#33), Rohan Arun/Codex (#31), Zhihao Chen (#29/#21/#23), Aurel Prosz/Paureel, Swapnil Jain, eumemic, Douglas Colkitt, OpenAI, Harvey–van der Hoeven and all retained source notices. The inherited techniques are not claimed as new here. Apache-2.0; original licenses and AI-assistance disclosures remain.