ifc-0246

17.8.4 Active overlap acquisition (CTTE–3)

CTTE–2 showed that a safe abstention can still carry the wrong scientific reason when mechanism fitting precedes an audit of contextual support. CTTE–3 turns that diagnostic into an active acquisition task. The initial literature contains controlled \(X\to Y\) reports only from the two diagonal cells of a two-by-two context cover. Four declared theories—invariant, first-axis, second-axis, and product—agree in pairs on those restrictions but make different predictions on either off-diagonal intersection.

The system receives a costed source menu. A controlled report costs two units and has registered reliability \(0.95\); an observational report costs one unit and has reliability \(0.80\). The acquisition budget is ten units. The typed policy maintains a posterior over the four theories, audits whether the source pool contains any query that separates its plausible candidates, and otherwise returns abstain-no-support. When a decisive source exists, it selects the query with greatest expected entropy reduction per unit cost and admits a theory only at posterior probability \(0.99\).

The preregistered benchmark contains 1,000 ledgers: 200 generated from each of the four theories and 200 blocked-product controls in which the source pool contains no off-diagonal report. Confirmation seals the complete four-cell sign map. Passive similarity repeatedly retrieves a familiar diagonal source; random retrieval spends the same budget without a structural target; cheap uncertainty samples only observational evidence; and a query oracle selects a maximally discriminating controlled source.

CTTE–3 was admitted on every registered gate. Overall action accuracy was \(99.1\% \), with \(98.875\% \) theory recovery across the four available-source families and \(100\% \) abstain-no-support decisions in the blocked family. Coverage-adjusted four-cell confirmation accuracy was \(99.125\% \) and wrong-theory admission was \(0.5\% \). The median cost of a correct typed decision was four units, equal to the query oracle. Cost per correct decision was \(4.45\) units, compared with \(13.07\) for random retrieval, a \(65.98\% \) efficiency gain. Theory recovery exceeded cheap observational uncertainty by \(7.375\) percentage points and passive similarity by \(98.875\) points.

The actual traces make the mechanism transparent. In every one of the 800 worlds with an available decisive source, the first typed action requested a controlled report from the same off-diagonal cell. Of these worlds, 724 stopped after two queries, 69 used four, and seven exhausted five queries. Four worlds admitted the wrong member of a theory pair and five abstained under residual uncertainty. All 200 blocked worlds stopped before acquisition with the registered no-support status.

Policy	Theory recovery	Mean cost	Cost per correct
Passive similarity	\(0\% \)	\(10.00\)	undefined
Random budget	\(62.5\% \)	\(8.17\)	\(13.07\)
Cheap uncertainty	\(91.5\% \)	\(6.00\)	\(6.56\)
Typed acquisition	\(98.875\% \)	\(4.40\)	\(4.45\)
Query oracle	\(98.875\% \)	\(4.40\)	\(4.45\)

Matching the oracle here should be read as a calibration result. The finite hypothesis family, context coordinates, costs, reliabilities, and query menu are supplied, and the registered geometry makes either off-diagonal controlled query optimal. Within these generated ledgers, CTTE–3 shows that a typed obstruction can be compiled into an efficient acquisition action and that absence of such an action can remain explicit. It does not discover a biological variable, search an open literature, or design an unrestricted experiment.

Experiment: CTTE–3: active acquisition of a missing overlap. Input: 1,000 generated ledgers with diagonal evidence, a costed source pool, and a sealed four-cell confirmation map.
Withheld structure: the off-diagonal evidence distinguishing four contextual theories.
Result: \(99.1\% \) action accuracy, \(98.875\% \) theory recovery, \(99.125\% \) confirmation accuracy, and \(0.5\% \) wrong admission.
Efficiency: median cost four, equal to the query oracle; \(65.98\% \) lower cost per correct decision than random retrieval.
Support control: every blocked world returned abstain-no-support without purchasing an irrelevant source.
Verdict: admitted as a finite active-acquisition calibration with a supplied theory and query language, not open-domain experimental design.