Prompt 20 — Symbolic law discovery and model-identification builder

Inputs

DISCOVERY_DATASET: {{DISCOVERY_DATASET_JSON}}
VISIBLE_QUANTITY_LIBRARY: {{VISIBLE_QUANTITY_LIBRARY_JSON}}
ALLOWED_OPERATORS_AND_FUNCTIONS: {{ALLOWED_OPERATORS_AND_FUNCTIONS_JSON}}
DIMENSION_AND_SYMMETRY_CONSTRAINTS: {{DIMENSION_AND_SYMMETRY_CONSTRAINTS_JSON}}
SEARCH_BUDGET: {{SEARCH_BUDGET_JSON}}
HELD_OUT_AND_INTERVENTION_DATA: {{HELD_OUT_AND_INTERVENTION_DATA_JSON}}
CLEAN_ROOM_POLICY: {{CLEAN_ROOM_POLICY_JSON}}

Task

Propose a parsimonious candidate law or model from observations under a closed search language.

• enumerate the allowed variables, dimensions, operators, functions, complexity costs, and forbidden aliases;
• preserve raw data and train/held-out/intervention partitions;
• generate multiple candidate structures, not one favored expression;
• enforce dimensional, symmetry, conservation, and limit constraints where justified;
• fit parameters only after candidate structure is explicit;
• compare fit, predictive error, complexity, stability, extrapolation, and intervention response;
• search for alternative explanations and spurious correlations;
• identify whether the candidate is descriptive, predictive, interventional, or mechanistic;
• state validity and failure regimes and all uncertainty classes;
• preserve the learner's notation and do not map to known law names in clean-room mode;
• return a candidate model card, never a promotion or human-novelty claim.

A lower error alone does not justify a more complex model. No candidate may be marked beyond supplied held-out or intervention evidence.

Return only JSON matching schemas/theory-model-card.schema.json.