[artuskg]

Gives a written source-specific argument for the pinned PR390 heterogeneous physical provider and a closed ordinary exact scalar/index RAM witness. The chart/window/routing, data levels, four-pair chain, terminal corrections, owner bijection and dirty-helper argument are inherited from PR377 and retained in PR390. This addendum supplies the heterogeneous-sink treatment, constructive lowering, all-f transport and charged recurrence. It changes no circuit or selected multiplication bound.

For every fixed K and positive tensor multiplicity, the explicit word acts correctly on all actual live arrays, including correlated helpers. The optimized m73/W58899 instance gives native exact Gaussian/Walsh work O(N(log(N+2))^(1023/1024)) on powers of two. Rank-zero canonical-chart adapters are stated before the character-phase translations. The original homogeneous sink contract remains false and the separate paid rank-one repair is distinguished.

The pinned Sussman source f010392c923279e3dd59ef3aa5fedad23affc5fd already proves its all-length cyclic and convolution theorems through the P193 hillsZ_program. This provider is a second, non-Lean witness for that same premise at a stronger native exponent. The cyclic exponent 1-7474546/10^10 is neither improved nor newly established. Its supplied canonical positive root has selected order 0<D(N)<8N^3, with one charged root primitive and preparation, indexing and allocation charged.

The declared model is unit-cost exact scalar/index RAM with one fixed polynomial word/arena cap and unrestricted scalar heights. This is a mathematical program-existence/work argument, without a new Lean kernel certificate, original Family130 manuscript equivalence, root-free field algorithm, Family109 bit/precision/tape/caller-ABI closure, practical crossover or global multiplication result.

Corrections add the 240+2 local endpoint adapters; explicit rho(q,0), cut/bridge/recovery/terminal chronology; a nonchild batch lemma deriving the pass templates and fresh pointer/code preparation costs; the n=0 recurrence boundary; and precise PR377 credit. Profile, exponent, root convention and numerical constants are unchanged.

Fresh validation ran the exact supplied scalar interpreter on all 1023 live plus eight initially dirty scratch columns in both orientations, with target/helper/sink frame guards. It records 3953 frame occurrences and 3135 unique actual edges, rather than claiming a supplied phased-recipe audit. The new independent arithmetic checker verifies all twelve integer root inequalities, the strict moment and the printed pass/recurrence constants. FINITE-VALIDATION.json carries their bounded finite evidence. Those checks corroborate their finite statements; the all-size claims rest on the written proof. Unpublished AI referee replays are not included and are not offered as evidence.

The addition remains within research/pr390-heterogeneous-provider-closure/, now with fourteen files including two public finite-evidence files. Three literal inputs and the original source notice remain exact copied public bytes. Contributor programs, selected records, generators, workflows and source mirrors are unchanged. No contributor program, installation or new Lean build was run. Substantial OpenAI Codex and ChatGPT Pro assistance is disclosed; AI checks are not independent human peer review. Raw private Pro/referee outputs are excluded.

Credit Dugongue's PR390 and its retained predecessors; Jacob Sussman's frame/bank/RAM/Fourier work and P193 supplier; PR363/373/375/377/381/397 bridge lineage; PR401 normalization; PR430's conditional interface audit; and OpenAI/math exact-width, sector, CRT/chirp and uniform-transfer lineage. This is a bounded source-specific assessment, without worldwide novelty or upstream endorsement.

This exact fourteen-file correction revision was accepted as written in the existing persisted Opus 5.5 session (revision-02 archive SHA-256 fcaaf783b91e08df01378205a33e48aa8e33242f47a915ff15589c9d07f128dd), with xhigh effort requested by the CLI. This records AI review provenance; the unpublished report is not offered as mathematical evidence. Acceptance does not assert CI success or human/formal certification.