Prompt 12 — Counterexample, edge-case, and adversarial falsifier

Inputs

CANDIDATE_OBJECTS: {{CANDIDATE_OBJECTS_JSON}}
AVAILABLE_SOLVERS: {{AVAILABLE_SOLVERS_JSON}}
SEARCH_BOUNDS: {{SEARCH_BOUNDS_JSON}}
EXISTING_COUNTEREXAMPLES: {{EXISTING_COUNTEREXAMPLES_JSON}}

Task

Act as an independent falsifier. Do not improve the candidate until the falsification pass is complete.

For each candidate:

1. Check symbol domains, quantifiers, side conditions, units, frames, and boundary conditions.
2. Generate minimal normal, edge, degenerate, adversarial, and invalid-input cases.
3. Search for counterexamples within declared finite bounds.
4. Identify transformations that can introduce extraneous solutions or lose solutions.
5. Drop or weaken assumptions one at a time and test the result.
6. For algorithms, test termination, invariant preservation, and invalid inputs.
7. For geometry, test collinearity, coincident points, zero lengths, orientation reversals, and construction impossibility.
8. For numerical claims, test conditioning, tolerance sensitivity, step-size/mesh refinement, and floating-point instability.
9. For physical models, test units, limiting cases, conservation expectations, alternative models, and out-of-regime data.
10. Distinguish a found counterexample from an unproductive bounded search.

Output

For every candidate return:

• verdict: survived_bounded_tests, refuted, inconclusive, or invalid_specification;
• exact counterexample or failing case when found;
• search bounds and methods;
• assumptions implicated;
• reproducible test specification;
• recommended action: continue_validation, repair, split, restrict_domain, or reject.

Never promote a candidate and never interpret failure to find a counterexample as proof. Return JSON matching schemas/falsifier-report.schema.json.