15.13.7 In what sense is this theory construction?

15.13.7 In what sense is this theory construction?

The analogy with experimental physics is methodological. A theory declares which observations should agree; an intervention produces a counter-witness; and persistent, localized disagreement motivates a more expressive theory. URL–0 through URL–2 select registered behavior types. URL–3 constructs an unnamed composite expression. URL–4 goes one step further by adjoining and orienting a comparison cell absent from the seed sketch.

The analogy must not be overstated. These are calibrated synthetic chambers, not natural scientific domains. The witness vocabulary, likelihoods, maximum delay depth, and generic one-cell edit schema are supplied. Consequently the experiments test whether evidence can drive conservative structural extension once informative measurements exist. A stronger DIAL-URL system must learn those measurements from raw trajectories, discover when their likelihood model is wrong, and transport an admitted constructor to independently built environments. That transition—from a registered structural instrument to an acquired one—is where this program meets experimental theory construction in the fuller scientific sense.

The quotient control described above is therefore conceptually decisive: it shows that hidden multiplicity alone does not warrant a richer sequential theory. URL–0 calibrates that judgment exactly; the later rungs ask whether it survives finite data, active probing, generated constructor expressions, and a withheld comparison law.

Experiment: DIAL-URL–0: Exact Coalgebra-Type Recovery. Seed theory: finite MDP behavior with action-indexed rewards and probability distributions.
Candidate constructors: hidden observation and non-unit holding time, with their composite.
Obstruction: aliased observations with behaviorally distinguishable successors, non-unit duration support, or both.
Quotient control: aliased but behaviorally equivalent hidden states must remain in the MDP class after minimization.
Admission: exact minimal-type recovery, zero false extensions, transport of the seed model, and explicit abstention outside the registered grammar.
Epistemic status: registered endpoint pass; exact coalgebra-type selection inside a supplied constructor catalog, not a newly invented theory language.
Boundary: the constructors and exact operators are supplied. This is a calibration of coalgebraic accommodation, not invention of a new RL theory.

The implementation recovered all five exact worlds. It made no false accommodation on either MDP control and selected the composite extension when both counter-witnesses were present. This supports only the deterministic diagnostic and its audit trace.