{
  "frontier": [
    {
      "atom_id": "atom_b1f637235b874de4",
      "content": "Test invariant corner cases, gain 5 near-miss, raw observer distinction, and compile all-time invariant with arbitrary natural t.",
      "next_action": "retrieve similar failures and decide whether to refine, refute, or promote",
      "priority": 2.8,
      "status": "UNDER_TEST",
      "tags": [
        "refutation"
      ],
      "type": "RISK"
    },
    {
      "atom_id": "atom_6739535690954b3d",
      "content": "Reject tampered cost 56, infeasible (7,1), and nonoptimal (8,0); independently enumerate every objective-bounded cheaper candidate; compile the global natural-number lower-bound theorem.",
      "next_action": "retrieve similar failures and decide whether to refine, refute, or promote",
      "priority": 2.8,
      "status": "UNDER_TEST",
      "tags": [
        "refutation"
      ],
      "type": "RISK"
    },
    {
      "atom_id": "atom_90c3e60d8d06425e",
      "content": "Generate the smallest witness that falsifies: Prove the real-valued bounded scalar thermal recurrence refines the existing natural-number ceiling envelope, then use strict quantizer margin to prove all-time observation equality.",
      "next_action": "test equivalence or find a counterexample",
      "priority": 2.46,
      "status": "CANDIDATE",
      "tags": [
        "counterexample_search",
        "morph"
      ],
      "type": "REFORMULATION"
    },
    {
      "atom_id": "atom_609932bd31964d02",
      "content": "Restate as an explicit iff/contract: Prove the real-valued bounded scalar thermal recurrence refines the existing natural-number ceiling envelope, then use strict quantizer margin to prove all-time observation equality.",
      "next_action": "test equivalence or find a counterexample",
      "priority": 2.35,
      "status": "CANDIDATE",
      "tags": [
        "equivalent_statement",
        "morph"
      ],
      "type": "REFORMULATION"
    },
    {
      "atom_id": "retrieval_prior_art",
      "content": "Two TheoremSearch queries returned adjacent or low-signal results, none selected as a premise; the formal graph query timed out. Morph suggestions remained generic untrusted proposals. No formal-corpus coverage or new theorem is claimed.",
      "next_action": "retrieve similar failures and decide whether to refine, refute, or promote",
      "priority": 2,
      "status": "CANDIDATE",
      "tags": [],
      "type": "RESULT"
    },
    {
      "atom_id": "physical_refinement",
      "content": "Prove the real-valued recurrence refines the integer envelope under explicit initialization, load, disturbance, rounding, and observation assumptions; preserve threshold strictness.",
      "next_action": "morph into testable hypotheses",
      "priority": 2,
      "status": "CANDIDATE",
      "tags": [],
      "type": "QUESTION"
    },
    {
      "atom_id": "observer_inventory",
      "content": "Validate a complete deployment-specific observer and actuator inventory, aggregate colluding-worker bounds, and measured conservative hardware envelopes.",
      "next_action": "morph into testable hypotheses",
      "priority": 2,
      "status": "CANDIDATE",
      "tags": [],
      "type": "QUESTION"
    },
    {
      "atom_id": "model_contract",
      "content": "The benchmark declares five digital controls; rho<=9/10, |u|<=1, |w|<=1/1000; mediated threshold 55/1000; s,r nonnegative integers; cost s^2+2r^2 and service 100-5r. These are illustrative premises, not measurements.",
      "next_action": "retrieve similar failures and decide whether to refine, refute, or promote",
      "priority": 2,
      "status": "CANDIDATE",
      "tags": [],
      "type": "RESULT"
    }
  ],
  "ok": true,
  "run_id": "<REDACTED>"
}