Datasets:
Languages:
English
Size:
10K - 100K
Tags:
mathematics
theorem-recognition
procedural-reasoning
retrieval-augmented-generation
robustness
License:
File size: 2,214 Bytes
c98c6c0 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 | 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.
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