ifc-0209

15.13.2 The admitted artifact

15.13.2 The admitted artifact

Selecting “POMDP” from a supplied menu is family selection, not yet persistent theory construction. The stronger target is a reusable package

\[ \mathcal T^{+} = (F^{+},\xi ^{+},O^{+},\mathsf{Ctrl}^{+},\sim _{F^{+}},\eta ), \]

containing a behavior functor, a realized coalgebra, observation and control interfaces, a declared behavioral equivalence, and a transport map from the old theory. When \(\eta \) is claimed to be a natural transformation, its naturality and its action on coalgebras belong to the certificate; a typed syntax translation alone is not enough. Its admission contract has six parts:

  1. a declared embedding or translation preserves the old models and observations on the subdomain where the old theory remains valid;

  2. the proposed extension explains the localized residual on fresh data;

  3. behaviorally equivalent hidden presentations receive the same score;

  4. downstream prediction or control improves under a matched budget;

  5. unsupported extensions are rejected or retained as unresolved; and

  6. the new constructor transfers to later environments without rebuilding the entire learner.

The fourth condition prevents coalgebraic elegance from substituting for a learning result. The third prevents recovery of a privileged state syntax from being mistaken for discovery. The fifth is essential because passive trajectories may leave several behavior functors observationally equivalent.

No experiment reported below satisfies this full six-part contract. DIAL-URL–0 through –4 isolate type recovery, finite-data uncertainty, active discrimination, expression synthesis, and a withheld comparison law. An admit label inside a rung is a trial-level verdict under that frozen contract; the experiment-level endpoint audit remains separate. In particular, URL–4 did not pass all of its preregistered endpoint families. None of the rungs demonstrates downstream control improvement or persistent transfer of a newly invented constructor to later environments; the package \(\mathcal T^{+}\) remains the grand-challenge target.