[Dugongue]

The earlier native Word RAM result #4630 gives κ = 0.0030201655. This source-bound sufficient assembly lifts Cao Yifan's stronger #4610 profile to κ = 0.0030217754, an exact increase of 0.0000016099, on w = Θ(log n) Word RAM with bounded-word MUL/DIV. The construction uses neither a TM simulator nor a TM multiplier. It does not discover another paid profile or raw root and does not change the selected frontier.

NATIVE-LIFT.md proves every κ < min(q_C, 3/32) from an actual canonical native provider satisfying the explicit endpoint, phase, restoration, whole-job, compiler and precision contracts. NATIVE-PROVIDER-4610.md closes the pinned round-three profile at q_C = 0.0030217755 using a funded critical majorant and fixed N = 2^(10^12), encoded rather than materialized. All nine native rows have strict rational margins. The analytic/fine-padding and all-fiber algebraic source proofs remain explicit inherited premises; finite checks do not establish their universal correctness or independent acceptance.

The package also proves the sufficient arbitrary-frame bridge rank formula dim U + dim V − 2 dim(U ∩ V), including constructive monomial adapters and absolute phase, and a simultaneous partial-map transporter lemma. These enlarge the valid native search interface; no additional numerical gain is attributed to them. Bounded commuting, quotient-repair and generalized-frame discovery runs found no further admitted profile.

Validation: exact emitted-word/controller reconstruction, 64,404 paid calls and 10,928 independent fields; critical-root/mirror/majorant and finite absorption with logarithmic margin 164; both orientations on 632 formal columns through two interpreters; 72 invertible native maps, all 180 actual warp classes and fresh absolute-phase lowering; all native parameter guards and rejecting controls; 36 signed complex record products; all 23 subspaces and 285 ordered frame pairs in dimensions 1–3. The stdlib-only Python 3.12 registered replay and standalone Git-free export pass, including an optimized parent with assertion-enabled isolated children and four source/inventory drift controls. No new Lean, complete practical multiplier, usable cutoff, unconditional theorem or independent human acceptance is claimed. Source snapshots retain their notices. VALIDATION.json outside the browser payload records the optional full-history guard limitation of this shallow checkout; committed bytes, immediate base parent and frozen source pins were verified.

Main refreshed at fbc9ea0. Recent PR bodies #4555–#4630 were read by the team, with later #4631 and #4633 source deltas inspected; no exhaustive comment/history audit is claimed. The quotient submissions' unresolved endpoint/admission contracts are not used to assert a larger value. The selected maintainer-reviewed κ remains unchanged. The canonical DAG/Lean tree is preserved.

Credit Cao Yifan (#4610), Cinna Davis and #4470's joint-helper/controller contributors, Dugongue's #4630/#4554 native work, Jacob Alan Sussman, zxv, Ryanson Jonathan, Dillon (#4532/#4535), Vlado Vojdanovski (#1673), the #1758 gauge-free authors, Chafik Boukhalfa (#1786) and Tim Trudgian, Jeremy Kothe, eumemic, icekylinx, Harvey and van der Hoeven, and all retained source owners. Full proof-specific attribution and source hashes are in the package. Prepared for Dugongue with substantial OpenAI Codex assistance: one lead and three research/review agents.

Remaining useful work: independently review the retained all-fiber compiler and analytic composition; build a practical complete native caller; use the new frame primitives to find a favorable fully replayed invoice. The open numerical endpoint and practical implementation are not hidden behind an unknown oracle.

Final publication checkpoint: #4633 advanced to b390d64 while this frozen package was being staged. The new commit increases the BIT quotient dimension and its supplier headline, but the latest exact-head proofs still explicitly leave changed main charts and outer admission unresolved. The complex quotient is unchanged. This source-only delta was inspected; it changes neither our pinned #4610 input nor the sufficient native result. FRONTIER-DELTA.json in the local release records exact source hashes and lines.