Under review: rank137 cross-copy candidate; inherited operator obstruction

[rohanarun]

Mathematical status correction (2026-10-11): the claimed gain is not currently established. I reproduced PR451's cross-family trace obstruction at f3a38153678b55063fc005901cc968266166507d. For a rank2 bit residual and an idle second family, the whole operator has trace90 while the proposed rank1/rank1 split has trace54 (q=3,m=2). The complex analogue has traces4+2i and4+4i. This contradicts the elementary coordinate-permutation derivation inherited from PR448, which this PR uses. Our finite packing, local scalar, invoice and full-wrapper checks pass but do not test that physical cross-family operator identity. The numerical κ below is therefore a score under an unresolved, specifically challenged interface, not an established improvement. A different explicitly charged compiler/global regrouping theorem would be required to repair it. The draft and all evidence are retained for review; the newer pooled-replica candidate is affected as well and will not be submitted as a winning bound on this basis.

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Submitted as a draft first. Fresh full-wrapper replays have now PASSed on Python3.11.15 and3.14.8, including the complete parent chain, record mutations and Gram checks. Both full results agree exactly. GitHub CI is separate and currently queued.

Conditional candidate κ = 0.001347781996192312, bit-bound: +0.00277860352249% over #450 at 6faca41020a620689de013cdab9f61a22deca314.

Remove pivot744 from #443's rank138 kernel, apply #450's target mixing, and re-optimize #448 cross-copy hosting. The resulting rank137 selection replaces the rank14 partial idle remainder with rank3. R stays740; all65,120 residuals are hosted with9,600 live families. Our rank147 kernel was worse under this objective; its negative result is retained.

Passed on the changed construction: exact980-column mixed-word replay and four controls; C++ legality and five/eleven-stage columns; exact geometry and parent audit; independent cross-copy audit and20 controls; regenerated #448 complex template matching its pinned hash and five complex controls; both rational moments, fresh invoices, six bootstrap levels and47 strict inequalities with next-grid and parameter controls. Emitted instruction count1,716,352.

The full verifier is research/e8-cross-copy-rank137/verify.py. The initial submission reused the already completed PR447 parent suppliers. The subsequently published e8-cross-copy-rank137-validation/python311 and python314 receipts each document a fresh full run of this package and its parent chain. A missing-SymPy launch failure is retained along with the corrected audit.

This retains #442 idle-data hosting, #448 cross-copy hosting, #450's bit target-label conjugation review point, and all inherited compiler/dirty-helper/precision/analytic assumptions. No unconditional multiplication theorem or Lean proof is claimed. Conservative row allowance28,416 is charged explicitly.

Credits: DreamingOfClouds (#450 target mixing and stage tools), higherbeing (#448 cross-copy hosting), chafreaky (#443–445 kernel and staging), DaysSky, icekylinx, eumemic, Zhihao Chen, Dylan Crow, Jacob Sussman and the inherited authors. Rank137 selection/composition prepared by Rohan Arun with OpenAI Codex assistance; original notices and licenses retained.

Post-submission anchor: the independent rank138 screen exactly reproduced #450 κ0.001347744547714835. The new profile differs per eight-replica group by {1: -88, 2: -176, 3: +184, 14: -8}; all other global counts match. A floating MILP over subsets of the123 compatible known relations also nominated the same113-entry rank137 selection; this is a scoped search result, not an exact optimality theorem.

Full tested manifest: 8441fa7b22a19ec4ac31625d0c7c2f9d581b43c970406cc8d85e6f390a82c14d. After the passes, only README status/wording and its manifest were updated; all executable source, frozen inputs and expected results are unchanged. The exact documentation-only diff is retained.

[JorgeCepeda]

Missing spaces in description.