[
  {
    "query": "Audit the Sage calculation supporting Claim C7.",
    "should_trigger": true
  },
  {
    "query": "Run the finite-field experiment and state exactly what it proves.",
    "should_trigger": true
  },
  {
    "query": "Run this exact checker with reproducible input and result hashes plus memory and CPU caps.",
    "should_trigger": true
  },
  {
    "query": "Check whether the paper states its recurrence over integers.",
    "should_trigger": false
  },
  {
    "query": "Explain what a Gr\u00f6bner basis is.",
    "should_trigger": false
  },
  {
    "query": "Refactor this unrelated CLI.",
    "should_trigger": false
  }
]