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      "rationale": "Exact counterexample replay under the benchmark's default envelope.",
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  "frontier": [
    {
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      "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",
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      "tags": [
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      "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.",
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      "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.",
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      "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.",
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      "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.",
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      "next_action": "retrieve similar failures and decide whether to refine, refute, or promote",
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        "normalized_content": "the nominal s=7,r=2 invariant certificate remains valid when the disturbance doubles, load bound doubles, or rho increases to 0.92.",
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        "novelty_score": 0.5,
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        "content": "A model result, passing Lean build, short trace, or Research Kernel SUPPORTED label could be misreported as physical containment, universal AI alignment, or OpenAI endorsement.",
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        "artifact_refs": [],
        "confidence": null,
        "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.",
        "created_at": "2026-09-18T11:19:54Z",
        "evidence_score": 0,
        "hash": "sha256:06d34c7a7dc377a5d3a976c6dcebfce3da3241e44670915706812849a37c01a1",
        "id": "atom_609932bd31964d02",
        "importance_score": 0.55,
        "metadata": {
          "relation_to_original": "equivalent",
          "risk": "check semantic preservation"
        },
        "normalized_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.",
        "novelty_score": 0.6,
        "parent_ids": [],
        "refutability_score": 0.7,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "CANDIDATE",
        "tags": [
          "equivalent_statement",
          "morph"
        ],
        "type": "REFORMULATION",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:19:54Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "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.",
        "created_at": "2026-09-18T11:19:54Z",
        "evidence_score": 0,
        "hash": "sha256:c351dc805185aaec433c30cc3276620c8e3708e9397ea8b88faab8983289110e",
        "id": "atom_90c3e60d8d06425e",
        "importance_score": 0.66,
        "metadata": {
          "relation_to_original": "speculative",
          "risk": "may change problem meaning"
        },
        "normalized_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.",
        "novelty_score": 0.6,
        "parent_ids": [],
        "refutability_score": 0.7,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "CANDIDATE",
        "tags": [
          "counterexample_search",
          "morph"
        ],
        "type": "REFORMULATION",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:19:54Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "content": "{\"first_different_step\":24,\"zero_trace\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"hot_trace\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],\"zero_temperature\":\"920233556923127490136639/100000000000000000000000000\",\"hot_temperature\":\"2760700670769382470409917/50000000000000000000000000\",\"common_disturbance\":\"1/1000\"}",
        "created_at": "2026-09-18T11:23:31Z",
        "evidence_score": 0,
        "hash": "sha256:9dd8ca2e865c681c0cfb0e2c282ce044e6574980754c2649b4dcfb7b6e2b8d4d",
        "id": "atom_dfe2a077f1ac4711",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": true,
          "evidence": "research/negative-knowledge.json",
          "lesson": "Use an all-time invariant. This near-miss first diverges at step 24.",
          "record_id": "NK-01",
          "strategy": "Exact counterexample replay under the benchmark's default envelope.",
          "tests": [
            "python3 -m unittest -v test_lab.ThermalTests.test_near_miss_at_24_not_23"
          ]
        },
        "normalized_content": "{\"first_different_step\":24,\"zero_trace\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"hot_trace\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],\"zero_temperature\":\"920233556923127490136639/100000000000000000000000000\",\"hot_temperature\":\"2760700670769382470409917/50000000000000000000000000\",\"common_disturbance\":\"1/1000\"}",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "REFUTED",
        "tags": [
          "refutation"
        ],
        "type": "COUNTEREXAMPLE",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:23:31Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "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.",
        "created_at": "2026-09-18T11:23:38Z",
        "evidence_score": 0,
        "hash": "sha256:22046a905d8329118ee434b3c81d544107d85c8e8bb47b93cc561536ca8f4b20",
        "id": "atom_6739535690954b3d",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": false,
          "result": "No counterexample found; universal scope comes from the checked Lean theorem, not the bounded search.",
          "strategy": "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.",
          "tests": [
            "python3 -m unittest -v test_lab.OptimizationTests",
            "bash check_lean.sh"
          ]
        },
        "normalized_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.",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "UNDER_TEST",
        "tags": [
          "refutation"
        ],
        "type": "RISK",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:23:38Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "content": "[{\"id\":\"NK-02\",\"claim_id\":\"raw_sensor_safe\",\"outcome\":\"REFUTED\",\"title\":\"Raw sensors defeat the observation restriction\",\"rejected_claim\":\"The winner makes raw hot and quiet temperatures indistinguishable.\",\"witness\":{\"s\":7,\"r\":2,\"step\":1,\"quiet_temperature\":\"1/1000\",\"hot_temperature\":\"1/200\",\"quantized_observations\":[0,0]},\"lesson\":\"The guarantee depends on a mediated quantized observer; raw trajectories differ.\",\"replay\":\"python3 -m unittest -v test_lab.ThermalTests.test_quantization_is_essential\"}]",
        "created_at": "2026-09-18T11:28:50Z",
        "evidence_score": 0,
        "hash": "sha256:7728f1f2b382ebac2e5614581b04e3ba109f7e04b6976b406b21def8b4c96847",
        "id": "atom_29b01f19192e436b",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": true,
          "strategy": "Replay exact arithmetic or exhaustive digital action pairs; preserve both observations.",
          "tests": [
            "python3 -m unittest -v test_lab.ThermalTests.test_quantization_is_essential"
          ]
        },
        "normalized_content": "[{\"id\":\"nk-02\",\"claim_id\":\"raw_sensor_safe\",\"outcome\":\"refuted\",\"title\":\"raw sensors defeat the observation restriction\",\"rejected_claim\":\"the winner makes raw hot and quiet temperatures indistinguishable.\",\"witness\":{\"s\":7,\"r\":2,\"step\":1,\"quiet_temperature\":\"1/1000\",\"hot_temperature\":\"1/200\",\"quantized_observations\":[0,0]},\"lesson\":\"the guarantee depends on a mediated quantized observer; raw trajectories differ.\",\"replay\":\"python3 -m unittest -v test_lab.thermaltests.test_quantization_is_essential\"}]",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "REFUTED",
        "tags": [
          "refutation"
        ],
        "type": "COUNTEREXAMPLE",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:28:50Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "content": "[{\"id\":\"NK-03\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"REFUTED\",\"title\":\"Removing canonical encoding\",\"rejected_claim\":\"Dropping canonical_encoding preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":true,\"early\":false,\"succeeds\":true,\"shared_signal\":false,\"network_signal\":false}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,1],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0}]},\"lesson\":\"Retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses\"},{\"id\":\"NK-04\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"REFUTED\",\"title\":\"Removing fixed release slot\",\"rejected_claim\":\"Dropping fixed_release_slot preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":true,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":0,\"shared_observation\":0,\"network_observation\":0}]},\"lesson\":\"Retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses\"},{\"id\":\"NK-05\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"REFUTED\",\"title\":\"Removing total fallback\",\"rejected_claim\":\"Dropping total_fallback preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":false,\"succeeds\":true,\"shared_signal\":false,\"network_signal\":false}],\"observations\":[{\"payload\":null,\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0}]},\"lesson\":\"Retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses\"},{\"id\":\"NK-06\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"REFUTED\",\"title\":\"Removing shared resource partition\",\"rejected_claim\":\"Dropping shared_resource_partition preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":true,\"network_signal\":false}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":1,\"network_observation\":0}]},\"lesson\":\"Retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses\"},{\"id\":\"NK-07\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"REFUTED\",\"title\":\"Removing mediated egress\",\"rejected_claim\":\"Dropping mediated_egress preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":true}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":1}]},\"lesson\":\"Retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses\"}]",
        "created_at": "2026-09-18T11:28:54Z",
        "evidence_score": 0,
        "hash": "sha256:62d7418ce46c30167e6795ae61d34f033009d142fd0d3c53af6ddf2dd191e6d8",
        "id": "atom_727d6f1b647f40fd",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": true,
          "strategy": "Replay exact arithmetic or exhaustive digital action pairs; preserve both observations.",
          "tests": [
            "python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses",
            "python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses",
            "python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses",
            "python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses",
            "python3 -m unittest -v test_lab.DigitalTests.test_five_ablation_witnesses"
          ]
        },
        "normalized_content": "[{\"id\":\"nk-03\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"refuted\",\"title\":\"removing canonical encoding\",\"rejected_claim\":\"dropping canonical_encoding preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":true,\"early\":false,\"succeeds\":true,\"shared_signal\":false,\"network_signal\":false}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,1],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0}]},\"lesson\":\"retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.digitaltests.test_five_ablation_witnesses\"},{\"id\":\"nk-04\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"refuted\",\"title\":\"removing fixed release slot\",\"rejected_claim\":\"dropping fixed_release_slot preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":true,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":0,\"shared_observation\":0,\"network_observation\":0}]},\"lesson\":\"retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.digitaltests.test_five_ablation_witnesses\"},{\"id\":\"nk-05\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"refuted\",\"title\":\"removing total fallback\",\"rejected_claim\":\"dropping total_fallback preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":false,\"succeeds\":true,\"shared_signal\":false,\"network_signal\":false}],\"observations\":[{\"payload\":null,\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0}]},\"lesson\":\"retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.digitaltests.test_five_ablation_witnesses\"},{\"id\":\"nk-06\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"refuted\",\"title\":\"removing shared resource partition\",\"rejected_claim\":\"dropping shared_resource_partition preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":true,\"network_signal\":false}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":1,\"network_observation\":0}]},\"lesson\":\"retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.digitaltests.test_five_ablation_witnesses\"},{\"id\":\"nk-07\",\"claim_id\":\"digital_ablation_safe\",\"outcome\":\"refuted\",\"title\":\"removing mediated egress\",\"rejected_claim\":\"dropping mediated_egress preserves observation equality.\",\"witness\":{\"actions\":[{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":false},{\"variant\":false,\"early\":false,\"succeeds\":false,\"shared_signal\":false,\"network_signal\":true}],\"observations\":[{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":0},{\"payload\":[17,0],\"release_slot\":1,\"shared_observation\":0,\"network_observation\":1}]},\"lesson\":\"retain this control or discharge its exact observation obligation.\",\"replay\":\"python3 -m unittest -v test_lab.digitaltests.test_five_ablation_witnesses\"}]",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "REFUTED",
        "tags": [
          "refutation"
        ],
        "type": "COUNTEREXAMPLE",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:28:54Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "content": "[{\"id\":\"NK-08\",\"claim_id\":\"nominal_winner_robust\",\"outcome\":\"REFUTED\",\"title\":\"The certificate depends on the envelope\",\"rejected_claim\":\"The nominal winner remains certified under each tested perturbation.\",\"witness\":{\"disturbance_doubled\":{\"nominal_winner_radius\":\"3/50\",\"threshold\":\"11/200\",\"certificate_valid\":false},\"slower_cooling\":{\"nominal_winner_radius\":\"1/16\",\"threshold\":\"11/200\",\"certificate_valid\":false},\"load_bound_doubled\":{\"nominal_winner_radius\":\"9/100\",\"threshold\":\"11/200\",\"certificate_valid\":false}},\"lesson\":\"Re-synthesize after changing bounds. Certificate failure alone is not a physical exploit.\",\"replay\":\"python3 -m unittest -v test_lab.ThermalTests.<REDACTED>\"}]",
        "created_at": "2026-09-18T11:28:57Z",
        "evidence_score": 0,
        "hash": "sha256:7a98e21ad1315f60aeb8f08c16aa10bf5dc30fff738938f08e4fc89c88eba17a",
        "id": "atom_e0a3ada7028f4045",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": true,
          "strategy": "Replay exact arithmetic or exhaustive digital action pairs; preserve both observations.",
          "tests": [
            "python3 -m unittest -v test_lab.ThermalTests.<REDACTED>"
          ]
        },
        "normalized_content": "[{\"id\":\"nk-08\",\"claim_id\":\"nominal_winner_robust\",\"outcome\":\"refuted\",\"title\":\"the certificate depends on the envelope\",\"rejected_claim\":\"the nominal winner remains certified under each tested perturbation.\",\"witness\":{\"disturbance_doubled\":{\"nominal_winner_radius\":\"3/50\",\"threshold\":\"11/200\",\"certificate_valid\":false},\"slower_cooling\":{\"nominal_winner_radius\":\"1/16\",\"threshold\":\"11/200\",\"certificate_valid\":false},\"load_bound_doubled\":{\"nominal_winner_radius\":\"9/100\",\"threshold\":\"11/200\",\"certificate_valid\":false}},\"lesson\":\"re-synthesize after changing bounds. certificate failure alone is not a physical exploit.\",\"replay\":\"python3 -m unittest -v test_lab.thermaltests.<REDACTED>\"}]",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "REFUTED",
        "tags": [
          "refutation"
        ],
        "type": "COUNTEREXAMPLE",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:28:57Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "content": "[{\"id\":\"NK-09\",\"claim_id\":\"original_lean_compiles\",\"outcome\":\"REFUTED\",\"title\":\"Written proof source can fail to compile\",\"rejected_claim\":\"The unmodified archive compiles under Lean 4.19.0.\",\"witness\":{\"file\":\"Proofs.lean\",\"line\":185,\"exit_code\":1,\"log\":\"evidence/publication/lean-original-check.log\",\"archive_sha256\":\"c11a957a34bb0304165a6c6a4608fe137de766069037d1f8befcd50201ea5786\"},\"lesson\":\"The base case needed exact Nat.zero_le 50. Statements were preserved; current source passes.\",\"replay\":\"Extract the original archive to a temporary directory and run bash check_lean.sh with Lean 4.19.0.\",\"scope\":\"Historical compiler failure, not a mathematical counterexample.\"}]",
        "created_at": "2026-09-18T11:29:00Z",
        "evidence_score": 0,
        "hash": "sha256:c75cc1b45a017c5910181b7f7c33072c3117579e545e956e8d9c1100e667a213",
        "id": "atom_b74beaff2e044d8f",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": true,
          "strategy": "Compile the immutable original source with pinned Lean 4.19.0; retain exit 1 and the elaboration error.",
          "tests": [
            "Extract the original archive to a temporary directory and run bash check_lean.sh with Lean 4.19.0."
          ]
        },
        "normalized_content": "[{\"id\":\"nk-09\",\"claim_id\":\"original_lean_compiles\",\"outcome\":\"refuted\",\"title\":\"written proof source can fail to compile\",\"rejected_claim\":\"the unmodified archive compiles under lean 4.19.0.\",\"witness\":{\"file\":\"proofs.lean\",\"line\":185,\"exit_code\":1,\"log\":\"evidence/publication/lean-original-check.log\",\"archive_sha256\":\"c11a957a34bb0304165a6c6a4608fe137de766069037d1f8befcd50201ea5786\"},\"lesson\":\"the base case needed exact nat.zero_le 50. statements were preserved; current source passes.\",\"replay\":\"extract the original archive to a temporary directory and run bash check_lean.sh with lean 4.19.0.\",\"scope\":\"historical compiler failure, not a mathematical counterexample.\"}]",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "REFUTED",
        "tags": [
          "refutation"
        ],
        "type": "COUNTEREXAMPLE",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:29:00Z"
      },
      {
        "artifact_refs": [],
        "confidence": null,
        "content": "Test invariant corner cases, gain 5 near-miss, raw observer distinction, and compile all-time invariant with arbitrary natural t.",
        "created_at": "2026-09-18T11:29:07Z",
        "evidence_score": 0,
        "hash": "sha256:0fcee55a141fd218e9475bdce24dc48ec38d7e7a9d253186b72e972ea59cda8a",
        "id": "atom_b1f637235b874de4",
        "importance_score": 0.8,
        "metadata": {
          "actual_counterexample": false,
          "result": "No in-scope counterexample; weakened observation and gain assumptions have actual counterexamples elsewhere.",
          "strategy": "Test invariant corner cases, gain 5 near-miss, raw observer distinction, and compile all-time invariant with arbitrary natural t.",
          "tests": [
            "python3 -m unittest -v test_lab.ThermalTests",
            "bash check_lean.sh"
          ]
        },
        "normalized_content": "test invariant corner cases, gain 5 near-miss, raw observer distinction, and compile all-time invariant with arbitrary natural t.",
        "novelty_score": 0.5,
        "parent_ids": [],
        "refutability_score": 1,
        "run_id": "<REDACTED>",
        "source_refs": [],
        "status": "UNDER_TEST",
        "tags": [
          "refutation"
        ],
        "type": "RISK",
        "uncertainty_score": 0.5,
        "updated_at": "2026-09-18T11:29:07Z"
      },
      {
        "artifact_refs": [
          "research/retrieval/formal-query.json",
          "research/retrieval/theoremsearch-receipts.json",
          "sha256:b701791f71b73d381f91d8aeb3042271fca1f984b762db99aacdc76a574b3c13"
        ],
        "confidence": null,
        "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.",
        "created_at": "2026-09-18T11:35:42Z",
        "evidence_score": 0,
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      "content": "Within the five-control model, at least one digital control can be removed while preserving observations for every untrusted action.",
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      "normalized_content": "within the five-control model, at least one digital control can be removed while preserving observations for every untrusted action.",
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      "normalized_content": "the nominal s=7,r=2 invariant certificate remains valid when the disturbance doubles, load bound doubles, or rho increases to 0.92.",
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      "content": "The unmodified Proofs.lean in the original archive compiles successfully under pinned Lean 4.19.0.",
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        "evidence": "research/negative-knowledge.json",
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      "content": "[{\"id\":\"NK-02\",\"claim_id\":\"raw_sensor_safe\",\"outcome\":\"REFUTED\",\"title\":\"Raw sensors defeat the observation restriction\",\"rejected_claim\":\"The winner makes raw hot and quiet temperatures indistinguishable.\",\"witness\":{\"s\":7,\"r\":2,\"step\":1,\"quiet_temperature\":\"1/1000\",\"hot_temperature\":\"1/200\",\"quantized_observations\":[0,0]},\"lesson\":\"The guarantee depends on a mediated quantized observer; raw trajectories differ.\",\"replay\":\"python3 -m unittest -v test_lab.ThermalTests.test_quantization_is_essential\"}]",
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      "artifact_refs": [],
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      "content": "[{\"id\":\"NK-08\",\"claim_id\":\"nominal_winner_robust\",\"outcome\":\"REFUTED\",\"title\":\"The certificate depends on the envelope\",\"rejected_claim\":\"The nominal winner remains certified under each tested perturbation.\",\"witness\":{\"disturbance_doubled\":{\"nominal_winner_radius\":\"3/50\",\"threshold\":\"11/200\",\"certificate_valid\":false},\"slower_cooling\":{\"nominal_winner_radius\":\"1/16\",\"threshold\":\"11/200\",\"certificate_valid\":false},\"load_bound_doubled\":{\"nominal_winner_radius\":\"9/100\",\"threshold\":\"11/200\",\"certificate_valid\":false}},\"lesson\":\"Re-synthesize after changing bounds. Certificate failure alone is not a physical exploit.\",\"replay\":\"python3 -m unittest -v test_lab.ThermalTests.<REDACTED>\"}]",
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      "content": "[{\"id\":\"NK-09\",\"claim_id\":\"original_lean_compiles\",\"outcome\":\"REFUTED\",\"title\":\"Written proof source can fail to compile\",\"rejected_claim\":\"The unmodified archive compiles under Lean 4.19.0.\",\"witness\":{\"file\":\"Proofs.lean\",\"line\":185,\"exit_code\":1,\"log\":\"evidence/publication/lean-original-check.log\",\"archive_sha256\":\"c11a957a34bb0304165a6c6a4608fe137de766069037d1f8befcd50201ea5786\"},\"lesson\":\"The base case needed exact Nat.zero_le 50. Statements were preserved; current source passes.\",\"replay\":\"Extract the original archive to a temporary directory and run bash check_lean.sh with Lean 4.19.0.\",\"scope\":\"Historical compiler failure, not a mathematical counterexample.\"}]",
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      "normalized_content": "[{\"id\":\"nk-09\",\"claim_id\":\"original_lean_compiles\",\"outcome\":\"refuted\",\"title\":\"written proof source can fail to compile\",\"rejected_claim\":\"the unmodified archive compiles under lean 4.19.0.\",\"witness\":{\"file\":\"proofs.lean\",\"line\":185,\"exit_code\":1,\"log\":\"evidence/publication/lean-original-check.log\",\"archive_sha256\":\"c11a957a34bb0304165a6c6a4608fe137de766069037d1f8befcd50201ea5786\"},\"lesson\":\"the base case needed exact nat.zero_le 50. statements were preserved; current source passes.\",\"replay\":\"extract the original archive to a temporary directory and run bash check_lean.sh with lean 4.19.0.\",\"scope\":\"historical compiler failure, not a mathematical counterexample.\"}]",
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  "summary": {
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      "REFUTED": 10,
      "SUPPORTED": 2,
      "UNDER_TEST": 2
    },
    "counts_by_type": {
      "CLAIM": 2,
      "COUNTEREXAMPLE": 5,
      "HYPOTHESIS": 5,
      "QUESTION": 3,
      "REFORMULATION": 2,
      "RESULT": 2,
      "RISK": 3
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    "edge_count": 9,
    "event_count": 68,
    "evidence_count": 10,
    "ok": true,
    "run": {
      "budget": {
        "campaign": "bounded publication audit",
        "new_experiments": "replay existing results plus one statement-preserving Lean base-case repair",
        "retrieval_queries": 3
      },
      "constraints": {
        "authority": "Research Kernel statuses do not confer proof, deployment authority, or hardware qualification",
        "non_claims": [
          "physical containment",
          "physical-model refinement",
          "complete real observer inventory",
          "general bounded-deadline AI fallback",
          "OpenAI endorsement"
        ],
        "scope": "Five binary digital controls; integer s and r; declared thermal envelope and mediated quantized observations"
      },
      "created_at": "2026-09-18T11:15:56Z",
      "goal": "Publish the supplied illustrative digital and thermal configuration model, preserve exact results and useful negative knowledge, and leave a replayable research handoff. No hardware security or unrestricted AI containment claim.",
      "id": "<REDACTED>",
      "metadata": {
        "domain": "formal methods and bounded information-flow research",
        "repository": "https://github.com/TheDarkLightX/CovertChannelLab",
        "source_bundle": "evidence/original/covert_channel_lab.zip"
      },
      "status": "ACTIVE",
      "success_criteria": "Python replay and all 34 tests pass; Lean 4.19.0 source checks without sorryAx; negative controls and limitations have replay recipes; research graph and takeover guide are exported; GitHub repository and Pages deployment are verified.",
      "title": "Covert Channel Lab: reproducible publication and negative knowledge",
      "updated_at": "2026-09-18T11:15:56Z"
    }
  },
  "supported_claims": [
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        "sha256:c7fac7d4d6ddd4ad8b9e6bffac4e83b996d6d04b7a50ac8b3721a2e5d42e560b"
      ],
      "confidence": null,
      "content": "Under the declared integer model with 2s+r>=16 and r<=4, all feasible designs cost at least 57, attained by s=7,r=2. Falsifier: a feasible pair with cost<57, invalid identity coefficients, or failed Lean theorem.",
      "created_at": "2026-09-18T11:17:28Z",
      "evidence_score": 0,
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      "id": "optimal_cost",
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      "metadata": {
        "publication_scope": "bounded illustrative research",
        "replay_recipe": "python3 -m unittest -v test_lab; bash check_lean.sh"
      },
      "normalized_content": "under the declared integer model with 2s+r>=16 and r<=4, all feasible designs cost at least 57, attained by s=7,r=2. falsifier: a feasible pair with cost<57, invalid identity coefficients, or failed lean theorem.",
      "novelty_score": 0.5,
      "parent_ids": [],
      "refutability_score": 0.5,
      "run_id": "<REDACTED>",
      "source_refs": [
        "https://github.com/TheDarkLightX/CovertChannelLab/blob/main/evidence/publication/verification.json"
      ],
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      "tags": [
        "covert-channel-lab",
        "negative-knowledge",
        "publication"
      ],
      "type": "CLAIM",
      "uncertainty_score": 0.5,
      "updated_at": "2026-09-18T11:35:34Z"
    },
    {
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      ],
      "confidence": null,
      "content": "For all natural t, the stipulated integer envelope at s=7,r=2 stays below 55. Falsifier: any recurrence step violating M<=50 or a failed winning_envelope_forever theorem. Real-plant refinement is a separate open obligation.",
      "created_at": "2026-09-18T11:17:32Z",
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      },
      "normalized_content": "for all natural t, the stipulated integer envelope at s=7,r=2 stays below 55. falsifier: any recurrence step violating m<=50 or a failed winning_envelope_forever theorem. real-plant refinement is a separate open obligation.",
      "novelty_score": 0.5,
      "parent_ids": [],
      "refutability_score": 0.5,
      "run_id": "<REDACTED>",
      "source_refs": [
        "https://github.com/TheDarkLightX/CovertChannelLab/blob/main/Proofs.lean"
      ],
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    }
  ]
}
