[aliromman]

This proves two scoped limits for the historical actual 112-port centre query. The proof, source pins, and independent agent review give the exact models. Neither result changes the complete kappa calculation.

First, the doubled centre Gram has scalar minimal-polynomial degree at least 409 at every positive tensor size. A scalar-polynomial inverse of aI+bA, when it exists and b != 0, therefore has degree at least 408. This rules out shorter scalar-polynomial decoder identities for this operator. It does not bound general ADD circuits, matrix-valued encodings, rational expressions, or native decoder cost.

Second, the least scalar cache that contains a query and is invariant under given diagonal updates has dimension equal to the sum of the query's ranks on the joint diagonal fibers. A basis on each fiber attains this dimension. For the pinned query, the specified normal-character family needs 56 rows, while six specified coordinate characters already need all 112 source directions. This gives an exact cache-size test. It assumes a common scalar input representation and does not supply or price native access, cache preparation, storage, or restoration.

The base is cef4b52f2a59009865bf8eabde1be3f159063703. The consumed historical supplier is pinned at bce54fb3f895cbe5cd4c0eb477c3afeed100190f; its archive and contributor lineage are preserved. PR #1719 supplied the doubled port representation. PR #4720 already retained the actual query and its separate source-span theorem. PR #4750 supplied a fixed-code invariance test. The new cache theorem gives the least invariant enlargement; those predecessor results are not claimed again.

From the repository root, with Python and NumPy, use a new output path:

env OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -I -B research/centre-polynomial-cache-limits/replay.py --out /tmp/centre-polynomial-cache-replay

Expected final line:

PASS_CENTRE_POLYNOMIAL_CACHE_LIMITS

The new replay passed under Python 3.14.7 and NumPy 2.5.4. The producer and separate sparse-operator reviewer agree on all 817 moments and the nonzero 409-by-409 Hankel determinant, 2984 modulo 65537. The reviewer checks all 57,344 Bell columns. Exact rational cache checks reproduce the dimension sequences and all 512 character ranks. Duplicate-row, duplicate-column, removed-cache-row, changed-moment, and changed-interface controls passed. The review receipt includes source binding, a separate forward query reconstruction, and signed-integer overflow bounds.

The infinite-size and least-cache claims follow from written proofs, not finite samples alone. No full supplier, selected-frontier, outer-kappa, or proof-kernel check is claimed. Substantial OpenAI Codex assistance was used; the independent review is by a separate agent, not a human. The remaining native implementation and composition obligations are explicit in the proof guide.