[aliromman]

This enabling proof and exact checker give a width-uniform operator-norm bound for the complete physical transfer-table endpoint. A positive-definite virtual metric, full block contraction and two boundary inequalities imply squared error at most a*b*c**f at width f. With 0<=c<=1 this is uniformly at most a*b*c. There is no factor from the exponentially growing payload dimension. The complete kappa calculation is unchanged.

Proof and scope, exact checks, source pins, registered replay. Base: canonical main 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Contribution head: d2502d83b1b615b02ca3753b8567bd31afe71dd8.

The table and boundaries are fixed across widths and include all independent inputs and required returns. The checker accepts rational real matrices and verifies every cross-input block with exact PSD tests. The written argument also holds over the complex field. This is a sufficient certificate; failure does not prove instability or rule out another representation or metric.

CPython 3.12.14 registered normal and optimized checks pass: nine certificates, 54 literal complete endpoint matrices, 125 independent principal-minor comparisons and ten rejection controls. Examples include an attaining parity projector, noncommuting transfers with a nonidentity metric, and the predecessor slow-phase residual. The checker rejects coherent sums that pass a separate-column bound. Both modes print PASS_TRANSFER_METRIC_ERROR_BOUND; the launcher prints PASS_REGISTERED_RESEARCH_PACKAGE.

python3.12 -B scripts/research_package.py --package research/transfer-metric-error-bound

Python 3.12 and the standard library suffice. Committed-byte checks pass. No actual native consumer, physical synthesis, precision policy, recovery proof, selected cold replay, Lean or Docker run is supplied. No independent human or proof-kernel acceptance is claimed. Hosted status is unconfirmed at publication.

Credit @zxv for PR #5441, its exact physical-table contract and approximation handoff, and its retained automata, matrix-product, native and phase lineage. Classical weighted norms, Schur complements and contractive composition retain their credit. This is a certificate in that concrete endpoint contract, separate from Perron weights for recursive costs. The scoped claim reserves no caller implementation.

Next: extract one complete physical consumer residual, obtain a rational metric, and check that its certified operator error fits an independently justified recovery budget. Those source and precision bindings remain open.

Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.