[Dugongue]

Construct odd pairwise-coprime tensor axes using gcd selection, with an optional guaranteed-composite square construction, in the existing guard-safe bands. Supply a sufficient eventual polynomial-time Word RAM setup theorem using Iwaniec's Jacobsthal bound, exact Good–Thomas input/output conventions, and O(N + D) native CRT address streams. The complete pinned production-axis method is exercised through a host semantic adapter.

No new κ is claimed. This is a partial result from a search for a substantial native Word RAM gain: it changes grid setup, but does not reduce the dominant multiplication recurrence. It does not establish production-common conditions, numerical resampling, a faster complete transform, native supplier admission or integer recovery. In particular, faster already-subleading setup is not an exponent improvement. The imported analytic constant is not made numerically effective. The code is a bounded-word reference model, not an emitted instruction trace.

Evidence: normal and optimized Python 3.12 replays; six ordinary grids, four composite grids, six source-bound band fixtures, 2,200 permutation entries in each direction, 1,600 phase checks, 48 sparse convolutions, 225 exact modular DFT outputs, and ten invalid-input/contract controls. A deliberately wrong output permutation produces 645 failures. Source and guard mutation checks reject drift. Registered package metadata/pins and scientific replay pass, as does committed-byte preflight. Git-free export replay is included in the release validation. No independent Linux, Lean-kernel or human review is claimed. Full source-history preflight could not run because the local Git checkout is shallow; it is not reported as passed. The source pins themselves were validated against stored Git objects.

Reproduce from the repository root:

python3 -I -B research/native-coprime-grid/verify.py
python3 -I -O -B research/native-coprime-grid/verify.py
python3 -B scripts/research_package.py --package research/native-coprime-grid

Frozen canonical main: 5e0052c, priority revision 7; rechecked unchanged before release. The task card is explicitly marked changed for the donor's solo Word RAM assignment. Overlap review covered 200 recently updated PR records, targeted searches, relevant source notes and later prime-band PR bodies, not every historical diff. The README distinguishes #5554's scoped controller ceiling, #5561's additional endpoint assumptions, the complex-only #4629 headline, and the coupled-consumer gaps in #4694/#4698. Their scientific suites were not rerun.

Credit ToikY #4029 for the band and source-bound checking method; Jose Manuel #3935 for TensorPlan; Tekalign #4024 for prior CRT streams; unpaidmoon #4142; Nick Petalas #5149/#5152 for the later cutoff and product-envelope work; Cinna Davis, Chafik Boukhalfa, Josie Elliston, and the source08/Douglas Colkitt/Harvey–van der Hoeven lineage. Classical gcd, CRT, Good–Thomas and Iwaniec mathematics are not claimed as inventions. Mathlib's coprimality and Chinese-remainder sources were inspected as precedents, not rebuilt as evidence. Full notices and exact public source hashes are included. Prepared for Dugongue with substantial OpenAI Codex assistance by one solo worker.

Open next questions identify the missing composite-axis numerical caller and a genuinely cheaper dominant native transform. Only the isolated research/native-coprime-grid package is added; no selected-frontier changes.

Final related-PR refresh: #5562 (head 7eeb6fb) supplies the programmable native-stage compiler and explicitly leaves global closure unpaid. #5563 (head 33d1426) supplies paid central-Q endpoint decoders but reports that both completed bills fail the moment test. Their latest bodies were read; their complete scientific replays were not rerun. This package supplies neither a cheaper endpoint decoder nor a claimed repair of that failed bill. Both remain credited predecessor work, rather than evidence of a new profitable native supplier.