19.16 Baselines and ablations

A credible comparison must prevent visual quality from substituting for theory recovery. The corresponding ablation matrix includes:

• a CAN-style art-plus-style-ambiguity objective;

• reconstruction error without a typed quotient;

• raw bracket magnitude without projection into \(Q_{\mathrm{art}}\);

• quotient residual without Weil persistence;

• persistent residual with an unrestricted proposal network;

• sketch extension without Kan transport or conservativity;

• full DILATE with all admission criteria; and

• an oracle supplied with \(c^\star \), which gives an upper bound rather than a deployable baseline.

The central false-positive control is an image family that looks unfamiliar but is exactly expressible by long compositions of existing generators. CAN may assign high style ambiguity, and a reconstruction model may report high error, but irreducibility-aware DILATE should refuse an extension. The central false-negative control varies the surface realization of \(c^\star \) while retaining its structural action; a pixel-level detector should fail to transfer while a correct theory-level proposal should persist.

Together these baselines form \(\mathsf{Ctl}_{\mathrm{DILATE}}\). The full system may propose \(\Upsilon _{\mathrm{DILATE}}\) only when the unfamiliar family survives the quotient and Weil-persistence tests and the registered controls fail to express it inside the current paintbrush grammar. High novelty, bracket magnitude, reconstruction error, or observer response alone opens no theory-extension branch.