ifc-0308
19.15 The withheld-generator experiment
A decisive calibration uses a controlled visual grammar in which the missing operation is known. Let \(S\) contain registered generators for color, shape, texture, layering, ordinary perspective, and composition. Construct an expanded theory
with one additional operation. A useful initial choice is simultaneous multi-viewpoint projection: the same object may expose geometrically incompatible viewpoints inside one coherent composition. The renderer and held-out corpus use \(c^\star \), while the learner initially receives only \(S\).
The experiment then asks five separate questions.
Detection: does a nonzero quotient residual distinguish examples using \(c^\star \) from noise and unfamiliar compositions expressible inside \(S\)?
Localization: does the residual identify the viewpoint and composition interface rather than an irrelevant color or texture component?
Recovery: does the proposed generator agree with \(c^\star \) up to the registered observational and presentation equivalence?
Closure: does adjoining the proposal remove the residual on held-out examples without damaging old-theory cases?
Productivity: does the admitted operation generate coherent new works across unseen objects, palettes, layouts, and renderers?
The withheld operation gives ground truth without making exact syntax the only success criterion. A different presentation may be equivalent if it generates the same models, transports the old theory conservatively, and passes the same counterfactual probes.
Experiment: DILATE-TE–0: Withheld Visual Generator. Epistemic status. Proposed benchmark; no result is reported.
Frozen reference. A visual sketch \(S\), its renderer, old-theory corpus, observer family, probe family, and presentation equivalence.
Withheld structure. One typed generator \(c^\star \) and its defining relations in \(S^\star \).
Positive worlds. Works generated using \(c^\star \) in subjects and compositions disjoint from proposal examples.
Negative controls. Noise, transient optimizer spikes, unfamiliar but expressible compositions, corrupted observers, and unrestricted capacity additions.
Primary endpoints. Detection, localization, equivalent recovery, residual closure, conservativity, productivity, and false extension.
Claim boundary. Recovery of one registered missing operation is a calibration of transformational theory extension, not unrestricted invention of an art-historical movement.