ifc-0247

17.8.5 Missing-presentation construction (CTTE–4)

The first four rungs progressively remove supplied documentary structure, but CTTE–3 still chooses among four completed theories. CTTE–4 withholds those domain-level mechanism names. It supplies only a generic finite-sketch grammar: add one mediating object and a factorization equation; add one contextual product and its cone; add one typed exceptional arrow; or add one memory object with update and readout arrows. The constructive target is therefore not a class label but a presentation consisting of new objects, arrows, and equations.

Each of 1,200 ledgers contains five noisy reports for each coordinate of an eight-dimensional discrepancy between a frozen theory and its sources. There are 200 closed, mediating-factor, contextual-product, exceptional-arrow, memory-state, and compound factor-plus-memory worlds. The factor and product families deliberately have the same documentary signature. No amount of additional evidence of that same type can decide which presentation is appropriate. The compound family requires two new generators and exceeds the registered one-generator budget.

The constructor first projects the source residual onto each admissible one-generator signature. If the old theory explains the reports, it returns no-change; if no single constructor explains them, it returns abstain-complexity. Otherwise it retains every minimum-fit presentation. It then compiles an external probe whose predicted response has maximum range across those candidates. For a singleton candidate, this is the operation that most strongly excites its proposed generator. For the factor/product pair, an internal clamp distinguishes a mediated response from a contextual one even though their corpus fits coincide. Five independently generated probe measurements are opened only after the question is fixed. Here “external” means external to the construction ledger: the probe is still generated by the benchmark oracle, not performed in nature.

Because the four one-generator presentations form a finite registered grammar, the exhaustive residual comparison supplies a nonrealizability gate for that grammar: the old theory is rejected only when it fails its frozen threshold, and a one-generator proposal is withheld when no registered candidate is adequate. This does not establish inadequacy relative to arbitrary scientific theories or unregistered presentations.

CTTE–4 passed all preregistered gates. It returned the correct structural action in all 1,200 worlds and recovered the exact finite presentation whenever an extension was applicable, admitted no wrong extension, preserved every frozen base prediction, and selected a maximum-disagreement probe in every queried case. It returned no-change for every closed world and abstain-complexity for every compound world. A fixed best-fit constructor reached \(83.33\% \) because it could not resolve the factor/product equivalence. Random probe selection reached \(57.58\% \): uninformative probes were rejected by the admission firewall instead of being mistaken for confirmation.

System	Structural-action accuracy	Constructs typed presentation?
Flat residual regression	\(0\% \)	no
Fixed best-fit sketch	\(83.33\% \)	yes, without a probe
Random-probe synthesis	\(57.58\% \)	yes
CTTE–4 typed synthesis	\(100\% \)	yes
Extension oracle	\(100\% \)	yes

This perfect synthetic result should be interpreted through the withheld structure. The system did not invent the constructor grammar, parse scientific prose, or prove that a presentation is the world’s unique causal explanation. It did perform a more substantive operation than theory selection: construct a minimum finite presentation, recognize when documentary fit is non-identifying, turn that obstruction into an external question, and refuse a world that lies beyond its declared expressive budget.

Experiment: CTTE–4: finite sketch extension and probe synthesis. Input: 1,200 generated residual ledgers, a frozen base sketch, and a generic four-constructor grammar with a one-generator budget.
Withheld structure: the domain-level mechanism and its finite presentation; factor and product are observationally equivalent in discovery.
Constructed artifact: one minimal set of objects, arrows, and equations, together with a maximum-disagreement external probe.
Result: \(100\% \) structural-action accuracy and exact-presentation recovery on applicable extensions, zero wrong admissions, and \(100\% \) closed and complexity-abstention controls.
Baselines: \(83.33\% \) for fit-only selection and \(57.58\% \) for random probe synthesis.
Verdict: admitted as controlled finite-presentation synthesis, not open-ended theory invention or causal identification.