Theorem: Non-determination underlying the release boundary

On the explicit comparison domains of this note:

1. density multiplication and fixed convolution are not the same operation, and the displayed fixed density ramp fails a transition-region harmonic pure-gauge test;

2. all pure-trace evaluations do not determine an unrestricted compact smooth three-slot kernel or its functional on the displayed free solution family;

3. off-locus agreement does not select an extension, and a finite normal-order bound does not imply a finite-dimensional ambiguity;

4. scheduled channel support does not determine a physical causal embedding, metric scale, clock lapse, or continuous-time completion;

5. an asymptotic source coefficient need not survive a comparison operation, and independent localization and smoothing parameters cannot be identified by notation.

These are failures of determination by the named data. They are not universal obstructions to constructions supplied with additional comparison, normalization, dynamical, or physical hypotheses.

Proof. Propositions prop:placement and prop:ramp prove (i). Proposition prop:blind proves (ii). Proposition prop:extension proves (iii).

For (iv), Proposition prop:support isolates the additional physical embedding hypothesis. Proposition prop:channel-algebra separates channel statements from observable products. Proposition prop:conformal supplies equal causal data with different clock normalization, and Proposition prop:continuum supplies equal coarse channel data with different limits.

Lemma lem:asymptotic and the explicit two-parameter example prove (v). No predecessor theorem is used in these proofs.