Research circuit: lower historical dyadic center bill with one basis shear (no new kappa)

[Curtis-D]

A single unimodular center-basis shear lowers the historical h=26 dyadic central factor's gather/scatter bill from 45,381 to 43,909 counted scalar operations. The complete signed invocation saves 2,944 operations after charging its increased scatter cost, both gathers, both scatters and all unchanged side work. No actual center-register conversion is performed; arbitrary dirty centers cancel and are restored.

Status: finite complex-supplier circuit improvement / research note; no new kappa. This improves the historical rank-h factor in scripts/experiments/complex_centers.py, not the selected JP8/CK programs. Helpers, grouped all-incidence frames, recursive children and paid rank profile are unchanged.

The explicit replacement is V'=A V, U'=U A^-1, A=I-E12. Only V[1,T]=t1-t2 and U[S,2]=s1+s2-2s0 change. The new numerator -2 is a signed unit update already supported by the original invocation; the optional validator explicitly prices it while leaving the original narrower alphabet guard untouched.

The saving in G+H is proved to be (h-10)(h-2)(h-3)/6: positive above h=10, neutral at 10, adverse at 8. At h=26 the full three-stage scalar bound decreases 15,959,102,640,000 -> 15,899,398,320,000, including every mixer, copy, injection, central cancellation and restoration. The historical node allowance and conditional recurrence guard remain valid. No larger exponent follows from the unchanged rank profile.

Reproduce with standard-library Python 3.11+:

python3 -I -B research/dyadic-center-basis-shear/verify.py

Expected:

PASS_DYADIC_CENTER_BASIS_SHEAR h=26 moves=1300 admissible=650 G+H=45381->43909 full_scalar_saved=59704320000 no_new_kappa

Validation:

• All 6,760,000 central coefficients checked by sparse multiplication and a separate closed head/tail contraction; complete coefficient-stream hashes agree.
• Exhaustive 1,300-move one-shear census, 650 admissible moves, independently corroborated by 16 symmetry orbits. Optimum is only for this declared finite alphabet.
• Full original invocation replay on 7,530 input-column/direction obligations at h=8,10, including all arbitrary dirty side/center inputs; 356 additional independent central basis executions.
• 8 new tests pass normally and under -O; 4 existing center tests and selected-record integrity pass.
• Normal, optimized, relocated and clean committed-source replays pass. Source corruption, undercharged certificates, output overwrite, missing restoration and disabled inherited assertions are rejected.

Only research/dyadic-center-basis-shear/ is added. Exact base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. OS seed 20, complex track; three candidates and local claim recorded. All 25 inherited pins match base Git blobs. No pinned coordination issue exists. The final overlap refresh covered 621 open PRs through #802; #769/#787/#793 coefficient work, #776 frame exclusions and #786 center-quarter scaling concern different selected-source mechanisms. No pending implementation or additive savings are imported.

The current selected #626/#543 conditional value remains 51110230636731/31250000000000000. upstream/, generators, selected certificates and the review ledger are unchanged. Full-size side/phase proofs and all-size, tape, precision and analytic obligations remain inherited; no full repository suite, selected cold replay, global admission, CI pass or Lean proof is claimed.

Credit Douglas R. Colkitt for the historical factor, side circuit, phase argument and recurrence ledger, with retained predecessor attribution. Prepared by Curtis Dransfield with substantial OpenAI Codex assistance, including a separate worker's independent implementation and review; no independent human review claimed. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at 66cabb478385fbaa1a8060123cd57545d703d84e.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Historical h26 dyadic center-basis shear; exact gather/scatter net savings with dirty cancellation, no integrated supplier.

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.