Question, result, and source discipline

The question is whether a finite incidence register and its prescribed schedule already constitute a continuum physical evolution. The answer proved here is narrower and more precise: the displayed finite data do not determine such an evolution. Additional realizations can agree on those data and disagree on their time calibration, interpolation, or limiting dynamics.

The motivating records are Cheung's VIII-A, VIII-B, and VIII-C, version 3, together with VII-J, En05-A, and Landmark I CheungVIIIA,CheungVIIIB,CheungVIIIC, CheungVIIJ,CheungEn05A,CheungI. Their reported conclusions concern different interfaces: matching, packet selection, guarded commands, complete finite channels, and measurement records. Shared vocabulary does not identify those interfaces.

XIX-A named the incidence object

and separated it from a matter-defined relational lapse XIXA. XIX-B treated a different question: the direct first-coordinate comparison of VI's unswitched prescription with XVI-D's prepared candidate XIXB. Neither result is a premise below. The elementary separation tests needed here are proved again.

kinds of conclusion. We distinguish:

1. a mathematical non-determination: explicit constructions agree on named finite data and disagree on an additional target;

2. a release boundary: this manuscript supplies no construction of a named continuum or quantum object.

The second is not promoted to a theorem that every possible future construction is impossible.

records are not premises. Every proof uses definitions, equations, or finite-dimensional arguments printed here. The unpublished records provide motivation, versions, and comparison locators. We do not reconstruct their complete geometric certificates, source laws, or implementations. Where the full defining data are unavailable, the claim is an explicit interface theorem, not an authentication of the predecessor.

finite implementation is not the entire analytic family. A constructor with a continuous deficit argument need not have a finite image. A finite implementation installs only finitely many packets and parameter values, or uses a separately declared promise to select among them. We do not call an entire continuous constructor a finite set.

carrier is supplied. The conical metric used below is background data. No new or matter-derived metric is constructed. In particular, “fixed cone” means fixed during the incidence command. A separate source-replacement command may select another installed packet; that is not a simultaneous incidence–deficit evolution.