[Dugongue]

Transfer the latest funded PR #4610 provider to native Word RAM at kappa 0.0030217758, improving #4635's native value by exactly 4 times 10^-10. This matches the current #4610 headline: no changed paid profile, new raw crossing or new global multiplication record is claimed.

The exact source-bound check reconstructs 64,404 paid calls and 10,928 productive fields, funds q_C = 1057621533/350000000000 at N = 2^38569300000000000 with absorption margin 6611668/5, and checks all nine native rows and five additional rejecting controls. The inherited all-fiber, phase, whole-job, compiler, conditioning, analytic and recovery premises remain explicit.

A separate universal reciprocal-Newton proof removes unit-cost DIV with O(log w) native operations and constant-limb temporaries. Strict row margins absorb the logarithm, preserving O(n/(log n)^0.0030217758). Both logical shifts are explicit primitives; this is not Lax13 with a division-derived right shift retained. No TM simulator, TM multiplier or unbounded-word multiplication is used.

The package also supplies proved dirty-column lane and dirty-arena constructions, paid tensor normalization and a precision-safe boundary theorem. Their nonbinding effects are stated separately. Search coverage: 43 queries, 10 primary publications and 8 pinned Lean files across 4 repositories; no exhaustive worldwide novelty claim.

Validation: direct optimized and registered standard-library Python 3.12 replays, metadata/pin checks and committed-byte checks pass. Checks include independent Newton invariants, 195,102 lane cases, 20,593 relocation correspondences, 65,520 tensor entries, 168 boundary cases and corruption rejection after clean-baseline acceptance. No fresh Lean kernel, physical phase, Linux run, practical complete multiplier or independent human acceptance is claimed.

Credit Cao Yifan / intqwq (#4610), Cinna Davis and the #4470 lineage, Dugongue (#4630/#4635/#4703), Dillon, zxv, Jacob Alan Sussman, Ryanson Jonathan, Vlado Vojdanovski, Chafik Boukhalfa, Tim Trudgian, Jeremy Kothe, eumemic, icekylinx, Harvey and van der Hoeven, Lax/Problem 1.8 and public formalization contributors, primary literature authors and retained source owners. #4641's attribution is preserved; unresolved #4694/#4698 chart embedding is not used. Full proof-specific sources/notices are included. Prepared for Dugongue with substantial OpenAI Codex assistance: one lead and three workers.

Main refreshed at b58ad9e; selected frontier and canonical DAG/Lean tree unchanged. Broad final PR/discussion refresh was rate-limited; frozen inputs and coverage are documented. Remaining work: a changed admitted provider, independent universal composition audit and practical native implementation.