2.8 What counts as success?

Novelty and validity are necessary but too weak. A random new axiom can be novel, and an isolated theorem can be valid. A persistent theory should be assessed along several dimensions:

1. coherence: the extension has a well-defined internal semantics;

2. conservativity: established results are preserved where claimed;

3. explanatory reach: several prior anomalies receive a common account;

4. generativity: the theory produces new questions, constructions, or predictions;

5. transfer: its concepts remain useful beyond the originating example;

6. persistence: other agents can reuse and extend it; and

7. nontriviality: the gain is not explained by paraphrase, memorization, or a disguised restatement.

Formal proof can certify only some of these properties. Simulation yields simulator-relative evidence, not truth about the physical world. Corpus-based evaluation supports empirical claims only to the extent licensed by its sources and identification assumptions. Visual assurance can demonstrate structural control and counterfactual grounding without establishing that a learned representation corresponds to a human concept; open-ended artistic extension has no unique target image and requires reuse, irreducibility, persistence, and independent critical value. The five admission regimes are valuable precisely because their weaknesses differ.