[Dugongue]

Close the actual whole-K/E negative terminal Q0^(-1) P D to its full independent Gaussian rank using one rank-2 query, replacing the previous two rank-1 repair queries. The decoder uses the characteristic translation fixed by each columnwise native normalizer; explicit XOR-coordinate permutations prove the child normalization and full-rank output with exact phase. The proof includes all positive lift widths, ordinary P inverse, reciprocal orientations, owned-storage cleanup and field-volume precision guards.

The package also constructs a faithful ambient-18 whole-K/E primitive from the degenerate binary product-cube support, retaining actual native child ranks 8,9,8,9 and rebuilding its physical modal code. Companion results give rank-selective autonomy for the eight-mode provider, a complete 632-input full-rank promotion, scalar subspace-gauge defect tariffs, and a sector-multiplexed query-sharing algorithm with a strict full-map example.

No higher complete multiplication kappa is established. The full-rank repair improves its concave moment by v(2 - 2^t), but the complete supplied invoice remains unprofitable; the older rank-dropping repair also retains a better isolated concave moment. No saving from a hypothetical sector-sharing instance is charged to the selected provider. Changed ambient dimensions always use their changed output ranks.

Adds five mathematical Markdown documents containing 31 numbered results with informal proofs. No numerical experiments, solvers, web searches or Lean checks were used. The source comparison uses locally retained canonical commit 5e0052c, without claiming a fresh upstream or literature novelty audit. No selected-frontier change is proposed.

Credit Dillon Amburgey PR5402; Chris R/Clear1nsight PR5407 and PR5413; Ali Romman PR5377, PR5383 and PR5439; Cinna Davis PR4694/PR4698 and the controller lineage; THU New Media Research Center PR5464; Cao Yifan; DaysSky; Nick Petalas; Ryanson Jonathan; Dugongue; Jacob Alan Sussman; zxv; Harvey and van der Hoeven; and the retained native, Clifford, scalar, compiler and analytic sources. The individual notes identify the relevant predecessor documents and distinguish classical tools from their concrete provider applications. Substantial OpenAI Codex assistance from four workers.

Suggested review: decoder.md D1-D3 and D6-D7, whole-k.md K1-K6, current-provider.md Theorems 1 and 8-9, and typed-provider.md T3 and T6-T7. Only research/characteristic-gaussian-provider is added.