Compose normal-45 extraction and fourteen gate rewrites: candidate κ ≈ 0.0017240352247481

[Dugongue]

This composes Marius-Paul Dumitrean’s four normal-45 paired extractions (#2942) with Jeremy Kothe’s fourteen paid gate rewrites (#2957, extending #2948). Exact common-parent mapping and full forward/dual operator equality show that these individually optimized mechanisms are compatible. The literal T370 realization retains every source/target contract and all 86 restored private buffers. Its directed complex endpoint is approximately 0.0017240352247481, above the pinned #2957 headline by more than 3.17809 × 10⁻⁷.

Complete-cost leave-one-out contributions exceed 20.69% and 79.32%. The five extra shared-target swaps contribute a marginal above 23.51%, as a subset of the rewrite block. The small packing closure is disclosed separately. All predecessor attribution and notices remain; this is a new verified composition, not a priority claim for their mechanisms.

Checks completed so far: two fresh changed-word native/phase chains; four actual assignments with 1,358,640 roles each; exact forward/dual, frames and cleanup for eight words; independent 192-bit integer interval roots; 36 semantic corruption rejections; and independent source/proof review. Full recursive/physical/prefix and modern outer-release completion is recorded separately before finalization. The retained bootstrap was generated freshly in this campaign and then explicitly reused with full-tree receipts.

Only research/paired-swap-normal45/ is added. Selected results, shared tooling, frozen predecessor packages and canonical Lean modules are preserved. Inherited all-size/compiler and analytic hypotheses remain conditional. No unconditional theorem, Lean formalization, practical speed gain, global optimum or independent human review is claimed. Prepared with OpenAI Codex assistance using one primary and three additional workers.