Two Worked Demonstrations

A program map states a program's architecture; a worked demonstration shows the architecture doing something. This document is the second. It walks two cases end to end — one on the research side of Universal Collapse Theory, one on the applied side — so a reader can see, concretely, how the same coherence-audit logic operates in each, and why the two are kept on opposite sides of a deliberate line.

Part A is the research-stack flagship: one structural signature — S₂ — followed down its full vertical, from a formal bound proved under stated assumptions, through an audit protocol with a sharp falsifier, to a live empirical run on real data — chosen deliberately because that run recorded a failure alongside its support. Part B is the applied-stack flagship: one reverse-audit from the AI Integrity Protocol, applied to a public, recognizable case. Between them sits the line: Part A counts toward the program's research ledger; Part B does not, unless independently audited under the same public standards. Showing both, with the line stated, demonstrates the firewall the program asserts elsewhere rather than merely claiming it.

What this paper does not claim. This document does not prove the UCT kernel or validate the Law of Coherence. Part A reports one empirical run — including a failed prediction — not a confirmed theory. Part B reports a structural diagnostic, not a legal, regulatory, or fairness finding, and its commercial-side results are not offered as evidence for the research program. The pairing demonstrates how the program separates evidence from application; it does not collapse the two.

Keywords: worked demonstration; S2 signature; reverse audit; research/applied firewall; claim discipline.