Model specification: Approximation obligations A1–A6

A later operational approximation theorem must discharge:

1. Finite protocols and quantum transmission. Construct protocols for one declared nonempty target set and supply the compatible access enlargement of Specification spec:realization. Prove transmission of the unknown message with an untouched reference. Do not substitute preservation of the reference marginal for identity transport. Theorem thm:geometry-not-transport is a standing transmission-capability test.

2. Anchored endpoint and complete-channel control. Provide actual source and receiver maps, complete comparison channels, residual and record conventions, and estimates of the form (eq:certificate). State whether the claim is logical-output comparison or a full retained-interface comparison. Use an event-aware topology when arrival events move.

3. Resource upper ledger. Give explicit resource functions under Definition def:ledger, including every operative communication and auxiliary resource. Prove the error scaling needed for (eq:certificate-convergence). No predecessor asymptotic count is transferred without its realizing-model correspondence.

4. Model-dependent locality lower bounds. State the elementary step bounds, execution rules, and cost model under which lower bounds are claimed. Theorems thm:depth and Proposition prop:site-lower apply only under their stated premises. A spatial ceiling does not prove availability of every null direction, nor does a depth bound automatically bound memory.

5. Arrival and calibration. Construct the declared output availability, arrival window or distribution, and calibrated record interface. Account for failed and late attempts without normalized postselection. Frame, scale, units, and clock correspondence must retain the status described in Proposition prop:calibration.

6. Carrier compatibility and failure tests. Retain Theorem thm:anchored-obstruction and the tests of Section sec:tests. If the operational carrier or allowed compositions are enlarged, prove their compatibility with the extracted representation. State separately any exact null-attainment or continuum evolution claim.