Implement encoded CRT address conversion for compact physical tensors

[tekuuu]

The physical Gaussian tensor in #3935 leaves its CRT entrance and integer return open. This PR supplies the encoded coefficient-address conversion in both directions, using the unchanged full-support router once per conversion and streamed triangular CRT shifts. It carries every spectator record and pays the two padding/cropping scans required by the actual compact TensorPlan interface.

The complete conditional invoice includes routing, offset preparation, copies, restoration, fixed native compilation and retained backing. Under the explicitly inherited router and newer caller-family premises, it fits O(V p^Φ log p), Φ=.99827619697. Multiplication requires three such conversions. Numerical tensor composition, prime supply and final integer normalization/recovery remain open; no new κ is claimed.

Validation covers every source column on four complete shapes in both directions, unequal-width descriptors checked against the unchanged codec, every padded prefix, nonzero invalid shear cells, 2,176 independent modular-inverse cases, the actual typed TensorPlan, and 20 malformed-input/algebra/ownership/source-integrity controls. The finite router fixtures use the literal q=2 branch, not production native execution.

Reproduce with Python 3.12:

python3.12 scripts/research_package.py --package research/crt-address-streams

The registered replay downloads about 38.5 MB of exact pinned predecessor sources into temporary storage; an authenticated offline source-tree option and Git-free replay are documented. No predecessor archives are duplicated or modified. Author cold offline and read-only Git-free -O replays passed; a fresh local network run ended in a TLS handshake timeout before mathematics. Hosted registered replay subsequently passed on the exact published head: run39233053124. It completed the fresh source download, full replay and unchanged-input check. Exact author receipts and the local transport limitation remain recorded in VALIDATION.md. Exact base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90; tensor/router source: #3935 at 240597ed313fc2854c0462b23c89dc3bae72aaf5. Scope is a construction/interface contribution with a conditional cost argument, not a selected-frontier update.

Credit: Tekalign (tekuuu), with substantial OpenAI Codex assistance. CRT algebra follows Agarwal–Cooley and source08; the full router and tensor interface are Jose Manuel (jmbarrancoml)'s #3935, building on #3619 and its pinned predecessors. Existing source licenses, notices and attribution are retained; new work is Apache-2.0.

Jose Manuel's concurrent interface clarification confirms the layout convention and retains both final S factors. His prospective numerical recovery work remains separate from this pinned CRT-address contribution.

[ToikY]

CLAIM — many-axis prime supply for PR4024 / the pinned PR3935 TensorPlan.

Canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority6; PR4024 heade99297be6749518a1b5b85cd129ecaf204d26c63, PR3935 head240597ed313fc2854c0462b23c89dc3bae72aaf5. Question: supply distinct odd source primes for the actual D-axis layout, d=D+1, targets2^ell or2^(ell−1), satisfying its strict production gap guards and T/S<2. The inherited source08 prime argument requires log(t)>8d, which is unavailable under the newer D=Theta(p^.997), ell=Theta(p^.003) laws; this is a source-binding question, not a claimed failure of the old lemma.

Use an established explicit prime-number theorem (Fiori–Kadiri–Swidinsky, Cor22, arXiv2206.12557) to prove enough primes in the interior interval (t(1−1/(3d)),t(1−1/(4d))]. Target a conservative explicit (ell,d) threshold, exact distinctness/volume proof, charged sequential trial-division/list construction, and bounded real coprime mixed-scale fixtures checked against the pinned TensorPlan predicate. No large-prime or production tensor run. The analytic theorem is imported/cited, not re-proved or formalized. Stop at prime supply; physical tensor/numerical recovery, caller/compiler, other analytic/native/precision and supplier obligations remain separate.

Handoff-first changed supplier-boundary-audit scope. Read current guidance, revision6/selected record, live1166/start-here/active discussions and Discussion3664's interface clarification19036660; Jose Manuel's prospective numerical recovery is a distinct lane. Fresh complete729-open-PR-body pagination at10:06:22UTC plus repository overlap helper and retained prime predecessors checked; broader Discussion/closed/code coverage remains partial. The named baseline command was attempted but sparse omission of the selected ASSEMBLY prevents its inventory check; no full selected replay claimed.

Predecessor credit: Jose Manuel/jmbarrancoml PR3935 tensor/source guards; Tekalign/tekuuu PR4024 CRT address converter; Harvey–van der Hoeven/manuscript source08; Cinna Davis prime-source-selector-transfer; Chafik Boukhalfa PR1786 and JosieElliston's transfer audit for earlier prime-interval reasoning/trial-division; Tim Trudgian and Fiori–Kadiri–Swidinsky for published prime estimates. New source binding, proof/checks by ToikY with substantial OpenAI Codex assistance and separate AI proof/test contexts.

Science cutoff2026-10-19T10:50:26UTC; claim expires11:05:26UTC. No merge, closure, maintainer edits or selected-frontier change.

[ToikY]

FINDING / scoped DONE — PR4029 at 726c9a3a1dc58d2b1223dd681eb712255be407c1 supplies this pinned caller's distinct odd prime-length premise on the explicit sufficient domain ell>=2^32, 2<=d=D+1<=ell^334, plus separate period condition target_halo+2w<=2^(ell-3). The two interior bands give at least D primes each, all three actual source axis predicates and T/S<3/2<2. This extends the source-supply argument to the newer caller law; it does not refute the old selector or complete the numerical tensor/recovery lane.

Written proof imports Fiori–Kadiri–Swidinsky Cor22 and gives a uniform sequential trial-division/setup/backing bill. Executed evidence is host-reference only (encoded_execution=false), with5 coprime mixed-scale cases, complete authenticated source guard AST, separate sieve/predicate/byte oracle and50 external rejections. Exact public bytes/history and fully read-only normal/-O Git-free export pass; hosted CI39237273642 passes all three registered commands at the exact head.

Discussion handoff and remaining obligations. Numerical composition, production_common, native/precision, final normalization/recovery, physical stock and supplier admission remain separate. Credit your converter, Jose Manuel's actual interface, Cinna Davis's old selector, Chafik/#1786 and JosieElliston's prior PNT transfer, FKS/source08/Harvey–van der Hoeven/Agarwal–Cooley and retained lineage. New work by ToikY with substantial Codex assistance and separate AI review; no human/kernel acceptance or new κ. Claim released; no continuing reservation. Maintainer edits disabled; no merge, closure or frontier change.