Conditional kappa 0.001592517892053334: native complex moment on PR558

[rohanarun]

Conditional κ = 0.001592517892053334, above #558's0.001592517889315014 by 2.738320e-12 (+0.00000017194909%). This is a tiny accounting correction composed with #558's eight-pivot structural gain, not a new geometry.

The exact binary-Clifford complex cover has a complete recursive-child histogram. Generic pricing includes the bit supplier's GL local-ring bad-residue surcharge on both sides. This PR uses the native complex moment and preserves the bit surcharge, all finite invoice charges, scalar word and complete-owner schedule. Independent source-scope review and pinned original notes explain why the correction uses the same conditional interfaces.

Complex b=0.001595058050537679100938; cited PR543 c=0.001653826988146798944268. Both discovery engines pass; next endpoint rejects; seven bootstrap levels satisfy47 outer inequalities. PR558's full published receipts are pinned. Independent full PR558 replay passed at head 060b137c8a6f9d73fd7864c7f8cf2736d6441774; updated packaged checks passed on Python 3.11 and 3.14 with identical mathematical outputs. The receipts are committed in research/native-complex-moment552/evidence/. CI is reported separately on GitHub. The PR552 regression already passed both interpreters and remains reproducible with --provider 552.

All inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic-transfer assumptions remain, including PR543 H1-H5. Exact chart types plus right-translation prove uniform finite-cover behavior; the full group is not enumerated. No unconditional theorem, Lean proof or practical speedup.

Credits: eumemic/Codex #558; Dugongue #552; eumemic/Claude #543; icekylinx original Clifford/complex-cover notes and #531/#535; inherited compiler/hosting authors. Prepared for rohanarun with OpenAI Codex assistance.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution at d858c0b2edcc704ef370b3c96dc51a75439b77b0 is incorporated in the reviewed family through #588, published in 9594b61.

Original complex-cover recurrence is pure moment; bit recurrence separately carries exceptional-selector fallback. Exact complex Clifford/orthogonal-cover compiler has no corresponding selector exception. Remove complex surcharge only under retained realization assumptions, leave bit surcharge and finite router invoice.

Preserved implementation and research:

• research/native-complex-moment552

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.