[1337isnot1337]

PR #4359 restricts helper packing and paid ranks so its raw mixed unit fits a strict compiler. This contribution removes that restriction through a native composition theorem and a separately certified tail bound, raising the conditional multiplication saving from κ = 0.0023 to κ = 0.00247755.

• Give all 2,856 helper occurrences independent arbitrary inputs, restore 56 original rank-eight center jobs, and pay all 896 main idle windows as complete transforms with their exact phases. The resulting 3,528 productive fields have rank mass 47,075 versus paid mass 46,851.
• Compose native array programs in chronological lockstep. Tensor power 15,000 and paid cutoff 4^15000 satisfy both the mixed-moment and rank-one-tail inequalities at tested saving 0.00247756, restoring strict paid/target separation. This is an explicit program substitution proof, with all owned centers accounted for.
• Recalculate expanded-word precision and storage constants, apply the integer compiler with sufficient uniform rank 2^8701218254312470001, and verify all nine outer cost rows, 54 retained predicates and three functional guards using the rational family from Refine PR4359: conditional κ = 0.00230509 and smaller explicit template ranks #4405.

The self-contained package research/pr4359-tensor-strictification/ is based on canonical main 12fa8c5; it pins focused unchanged exports from #4359 (da637c87) and #4405 (873d1b3c). It does not require either PR to be merged. Entry points: README.md, NATIVE.md, TENSOR.md, ENDPOINT.md, RESULT.json.

Validation: exact source Git-blob/SHA256 authentication; complete fresh-helper ownership and idle phase checks; negative phase, center, moment, tail and outer-parameter controls; independent rational interval cross-check; optimized Python 3.14.8 local replay; clean Pyroam Python 3.12.13 optimized and registered replays; committed-byte and source-history preflight. The original #4359 baseline separately passed all23 replay stages and all59 declared artifact comparisons, as recorded in #4405.

Conditional research result awaiting review. Native all-column semantics, analytic decomposition, permitted physical operations, fixed-tape accounting and inherited transfer hypotheses remain explicit premises. The enormous finite word is algorithmically specified, not materialized. No unconditional theorem, practical implementation, globally optimal exponent, selected-frontier change or merge is claimed.

Source native construction: @zxv. Underlying mixed flow: @jacobalansussman / Theorem1G. Inherited attribution and notices are retained. Prepared for @1337isnot1337 with substantial OpenAI Codex assistance; Apache-2.0.