Datasets:
Languages:
English
Size:
10K - 100K
Tags:
mathematics
theorem-recognition
procedural-reasoning
retrieval-augmented-generation
robustness
License:
| OBSERVED_STATEMENT_LATEX: | |
| {{observed_statement_latex}} | |
| THEOREM_EVIDENCE: | |
| {{theorem_evidence_or_NONE}} | |
| TRANSFORMATION_EVIDENCE: | |
| {{transform_evidence_or_NONE}} | |
| REGISTERED_OPERATION_IDS: | |
| {{operation_id_list}} | |
| Use exactly the same decision standard whether evidence is present or NONE. | |
| Evidence cards are optional aids, not labels. If the statement is a valid | |
| encoding, accept only with a valid theorem-route reconstruction. If it is not | |
| valid, reject or abstain even when retrieved cards look related. | |
| CRITICAL ROUTE RULES: | |
| - route.operations must be an array of registered operation strings only. | |
| - Do not include RESTATE_CANONICAL_THEOREM in route.operations. | |
| - route.steps must have the same length and order as route.operations. | |
| - route.operations[i] must equal route.steps[i].operation. | |
| - Step indices must be 1, 2, 3, ... with no gaps. | |
| - Each step must chain: step i output_latex should be step i+1 input_latex. | |
| - If the decision is REJECT or ABSTAIN, use route.operations=[] and route.steps=[]. | |
| - If a necessary operation is not registered, use OTHER and explain it in operation_free_text. | |
| - Keep every justification and rejection explanation concise, preferably under 35 words. | |
| - Do not include long derivations, prose proofs, or markdown. | |
| Return exactly one JSON object with this top-level shape: | |
| { | |
| "schema_version": "route-decoder-v2.0", | |
| "decision": "ACCEPT | REJECT | ABSTAIN", | |
| "theorem": { | |
| "id": null, | |
| "name": null, | |
| "canonical_statement_latex": null, | |
| "assumptions_used": [], | |
| "confidence": 0.0 | |
| }, | |
| "route": { | |
| "operations": [], | |
| "steps": [], | |
| "final_statement_latex": null, | |
| "minimality": "UNKNOWN", | |
| "confidence": 0.0 | |
| }, | |
| "rejection": { | |
| "reason": "NO_THEOREM_MATCH | NOT_EQUIVALENT | INVALID_TRANSFORMATION | CONTRADICTED_ASSUMPTIONS | ILL_TYPED | AMBIGUOUS | INSUFFICIENT_EVIDENCE | NONE", | |
| "failed_step_index": null, | |
| "explanation": "" | |
| }, | |
| "evidence_used": { | |
| "theorem_card_ids": [], | |
| "transform_rule_ids": [] | |
| } | |
| } | |
| For ACCEPT, rejection.reason must be NONE. For REJECT or ABSTAIN, theorem and | |
| route may be null/empty, but all fields must still be present. | |
| Produce the route-decoder-v2.0 JSON object now. Do not output markdown. | |