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.