Theorem: Finite incidence does not determine continuum evolution

Retain the finite incidence interface of Section sec:interface, its full-column-rank matching checks on the accessible inputs to which uniqueness is applied, its complete acceptance predicates, finite token table, exact guards, and frozen-packet incidence rule.

Then:

1. The declared controller has a unique output for every command word, including its rejection convention. Accepted matching outputs are unique within the fixed presentation. Matching acceptance does not select a matter source law.

2. A classical record does not generally determine a residual source functional. A supplied finite token does not constitute an exact expectation-acquisition instrument on an unrestricted preparation class.

3. The incidence parameter, finite reading code, normal deformation component, and matter-defined relational lapse are not interchangeable prescriptions. Incidence keeps its installed packet fixed; source replacement is a separate operation.

4. For every complete finite channel realization with all control and guard inputs represented in its dependency graph, scheduled ancestors bound Heisenberg support and operational influence. Snapshot determinacy, channel factorization, and adjoint support containment are equivalent on the declared full-state tensor interface. Physical containment requires a separately certified causal embedding.

5. Those finite data and finite support certificates do not determine a continuum evolution or an invariant physical speed. In particular, a common finite channel can have different refinement limits, as in Proposition prop:two-limits; finite graph samples can have different intermediate rates, as in Proposition prop:interpolation.

The theorem is a finite-interface and non-determination result. It is not a universal obstruction to a continuum realization supplied with additional hypotheses.

Proof. Lemma lem:matching and Proposition prop:composition prove (i). The affine equation takes its right-hand side as declared input; it does not define its matter dependence.

Propositions prop:residual, prop:token, and prop:affine prove the stated record and acquisition separations in (ii).

Lemma lem:normal, Proposition prop:lapse, and the command grammar prove (iii). The explicit schedule-defined scalar in Section sec:clock explains why the assertion is non-interchangeability, not exclusion of every special equality.

Proposition prop:comparison, Lemma lem:onelayer, and Propositions prop:schedule, prop:physical, and prop:approx prove (iv), with their exact hypotheses.

For (v), Proposition prop:two-limits gives two complete local refinement families with one common finite channel and different limits. Proposition prop:interpolation gives different rates at identical finite samples. Equation (eq:retiming) and the externally calibrated metric envelope give further rate dependence. None includes a physical frame action or matter–geometry equation. These explicit failures of determination establish the claimed separations without assuming a predecessor obstruction.