{
  "verified_at": "2026-09-18T10:46:55.569761+00:00",
  "toolchain": "Lean (version 4.33.1, arm64-apple-darwin24.6.0, commit 819816b2e0a3bf405af45ae5c7af2491d8f5bee6, Release)",
  "source_sha256": {
    "Audit.lean": "00182ee78512cd67195146cf1298260e39eec4083223424e9770cf5a6e58a776",
    "CampingObstruction.lean": "230998b06688b2ba4e742fee61c37b36243b346b2b573d3057def78f7910781c",
    "DeliveryGame.lean": "e9024fcc8b0ece17f925ab6f8c8909adbb87b711dcf453f90fb27ce058cbc7e2",
    "DenseCounting.lean": "afe0b3eddb6d9dd40b580afb5a3db82d0e100b279e591976b449f1253e6e9733",
    "DenseZero.lean": "80ec0e9c7790bcc8d8e6960d4a0df4905947fcc8eea1f20a5fb8ac92bc3051a8",
    "ElevenVertexDense.lean": "88d54e0d578a32e18f07bec24259c6c8c60fb7620b1e2de561cd6b420c802b56",
    "ExactScoreCertificates.lean": "bdfe444b10485ed8342fc68cf13966bd70182791be3cfa0f2bdb3184a2fac8a7",
    "ExclusionCertificates.lean": "a4125681521bc9099ee25b6db86be94f4139925a26d2021bbd78f269ebb936ce",
    "Extremal.lean": "ef50058ad1ba3c9bcdb87f4332e1e030881a880c5a057eeeccc93682e3f5c1f5",
    "ExtremalExamples.lean": "b985c63a313da9c1611e8951c8de320842165c75580d33cf2f04b14b4053a113",
    "FiniteGame.lean": "2fa4f564c701cf87e0e4b96b4862e0d84875e7ab01e61fa53ca3ff33dc1bae44",
    "GuideAttachment.lean": "f4be947fd16f0225769f1521464c4c2cc7d8b0523ed86051eac8b8f3c9384c86",
    "ProtectedRouting.lean": "af7717615600f7d042f2e4f4b515c11cc67c72d272d0e8f9db35c42db8af0cb7",
    "RobustLayers.lean": "b878a6372018a5ff4aa59764d80f33a81b1b2c11f8841e43a563d375954e3d62",
    "RobustTwoMove.lean": "fb662a539af1d65808a7436a0608408a016b01a3416c68972a565525e611eea9",
    "SafeBranching.lean": "4ef3781026919c462682c9320a49c3e99709562946bfa15d108dd30c46dc7363",
    "SemanticCompleteness.lean": "b58354aa9ed82fe608ee17552ce0d2358c41564cc85bf418aa73ba47947f125e",
    "SmallDenseEnvelopes.lean": "1271ed32095e7eca909a9484530d9411d726333c187a8224ab2e04ee42462fb5",
    "StagedEnvelopes.lean": "0e751c0ff104cbde1faa99cced07a5e3c0b05ad644ca539a54d519c343c8370e",
    "TwelveVertexCertificate.lean": "24e7ac5448b04e5572f03a00c3440458fc923fba12342ca637a73abe099b7750",
    "VertexBound.lean": "1ec5f62555b41c2baea60d3557b5cb07010157655d8774963804acf4064fa731",
    "lean-toolchain": "3aac669c7a910ec2389f4e4f921b605adf6ebf2d1e0c9b9cd0be4d33f3f5db71",
    "check.py": "61e0cbc2d4a0b7c87274a1070bcfff90fb2d4e0243bf97cc5ede1ccfc5d6b61a",
    "README.md": "19fa2c925c1f7849e1a15900dc525fb5996d9be490ceb7a1609a0450e0a16c4c",
    "generate_finite_certificate.py": "b2b479cf61643336b3c461684499c2f89672bc184d678064c16d1574a0b4613e"
  },
  "modules": [
    {
      "module": "DeliveryGame",
      "seconds": 0.456,
      "exit_code": 0,
      "output": ""
    },
    {
      "module": "SafeBranching",
      "seconds": 0.317,
      "exit_code": 0,
      "output": "/Users/angel/code/math/cop-prisoner/lean/SafeBranching.lean:21:29: warning: Variable name `c` is not explicitly referenced.\n\nHint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:\n  [apply] _c\n\nNote: This linter can be disabled with `set_option linter.unusedVariables false`\n"
    },
    {
      "module": "CampingObstruction",
      "seconds": 0.305,
      "exit_code": 0,
      "output": ""
    },
    {
      "module": "TwelveVertexCertificate",
      "seconds": 6.603,
      "exit_code": 0,
      "output": "'Delivery.TwelveVertex.all_pairs_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.TwelveVertex.indirect_count' does not depend on any axioms\n"
    },
    {
      "module": "DenseCounting",
      "seconds": 0.453,
      "exit_code": 0,
      "output": "'Delivery.DenseCounting.loss_from_counts' depends on axioms: [propext, Quot.sound]\n'Delivery.DenseCounting.final_band_bound' depends on axioms: [propext, Quot.sound]\n'Delivery.DenseCounting.attaining_block_count' depends on axioms: [propext, Quot.sound]\n'Delivery.DenseCounting.complementary_blocks_two_move' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseCounting.complementary_blocks_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "ProtectedRouting",
      "seconds": 0.29,
      "exit_code": 0,
      "output": "'Delivery.ProtectedRouting.protected_witness_winning' does not depend on any axioms\n'Delivery.ProtectedRouting.protected_routing_universal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ProtectedRouting.protected_routing_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "RobustTwoMove",
      "seconds": 0.297,
      "exit_code": 0,
      "output": "'Delivery.RobustTwoMove.envelope_universal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.RobustTwoMove.envelope_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "RobustLayers",
      "seconds": 0.314,
      "exit_code": 0,
      "output": "'Delivery.RobustLayers.ranked_envelope_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.RobustLayers.safe_routing_layer' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "GuideAttachment",
      "seconds": 0.334,
      "exit_code": 0,
      "output": "'Delivery.GuideAttachment.safe_entry' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.GuideAttachment.attachment_universal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.GuideAttachment.attachment_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "StagedEnvelopes",
      "seconds": 0.321,
      "exit_code": 0,
      "output": "'Delivery.StagedEnvelopes.envelope_winning' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.StagedEnvelopes.envelope_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "ElevenVertexDense",
      "seconds": 0.806,
      "exit_code": 0,
      "output": "'Delivery.ElevenVertexDense.witnesses' depends on axioms: [propext, Quot.sound]\n'Delivery.ElevenVertexDense.all_pairs_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ElevenVertexDense.arc_count' does not depend on any axioms\n'Delivery.ElevenVertexDense.indirect_count' does not depend on any axioms\n"
    },
    {
      "module": "SmallDenseEnvelopes",
      "seconds": 23.457,
      "exit_code": 0,
      "output": "'Delivery.SmallDenseEnvelopes.masks_match_lists' depends on axioms: [propext, Quot.sound]\n'Delivery.SmallDenseEnvelopes.witnesses' depends on axioms: [propext, Quot.sound]\n'Delivery.SmallDenseEnvelopes.every_intermediate_actual_delivery' depends on axioms: [propext,\n Classical.choice,\n Quot.sound]\n'Delivery.SmallDenseEnvelopes.exact_endpoint_counts' depends on axioms: [propext]\n"
    },
    {
      "module": "FiniteGame",
      "seconds": 0.342,
      "exit_code": 0,
      "output": "'Delivery.FiniteGame.winningRegion_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.FiniteGame.losingRegion_not_winning' does not depend on any axioms\n'Delivery.FiniteGame.losingRegion_not_guaranteed' does not depend on any axioms\n"
    },
    {
      "module": "SemanticCompleteness",
      "seconds": 0.529,
      "exit_code": 0,
      "output": "'Delivery.SemanticCompleteness.winning_eventually' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.losingRegion_never_delivers' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.eventual_iff_finite' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.guaranteed_iff_eventual' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.guaranteed_iff_actual' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "Extremal",
      "seconds": 0.328,
      "exit_code": 0,
      "output": "'Delivery.Extremal.score_le_missing' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.Extremal.score_eq_zero' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.Extremal.score_eq_missing' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.Extremal.maximum_unique' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "ExactScoreCertificates",
      "seconds": 0.496,
      "exit_code": 0,
      "output": "'Delivery.ExactScoreCertificates.exact_score' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.maximum_from_classification' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.FourVertex.winning_valid' does not depend on any axioms\n'Delivery.ExactScoreCertificates.FourVertex.losing_closed' depends on axioms: [propext, Quot.sound]\n'Delivery.ExactScoreCertificates.FourVertex.score_two' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.FourVertex.mixed_outcomes' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "ExclusionCertificates",
      "seconds": 0.677,
      "exit_code": 0,
      "output": "'Delivery.ExclusionCertificates.upper_from_cover' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExclusionCertificates.graph3_complete' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExclusionCertificates.graph3_camping' depends on axioms: [propext, Quot.sound]\n'Delivery.ExclusionCertificates.three_vertex_upper' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "VertexBound",
      "seconds": 0.334,
      "exit_code": 0,
      "output": "'Delivery.VertexBound.live_source_two_neighbors' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.VertexBound.vertex_upper' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "DenseZero",
      "seconds": 0.361,
      "exit_code": 0,
      "output": "'Delivery.DenseZero.initialGraph_arcCount' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.maximum_zero' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.indirect_missing_each_row' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.arc_bound_of_indirect' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.missing_count_lower_of_indirect' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.zero_above_dense_boundary' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.zero_at_budget' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.positive_score_density_bound' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "ExtremalExamples",
      "seconds": 0.309,
      "exit_code": 0,
      "output": "'Delivery.ExtremalExamples.twelve_score' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExtremalExamples.maximum_twelve_twentyfour' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExtremalExamples.eleven_score' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    },
    {
      "module": "Audit",
      "seconds": 0.288,
      "exit_code": 0,
      "output": "'Delivery.winning_play_delivers' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.rankCertificate_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.safe_branching' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.bootstrap_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.camping_predecessor_obstruction' does not depend on any axioms\n'Delivery.undirected_no_indirect_guarantee' does not depend on any axioms\n'Delivery.TwelveVertex.certificate_valid' does not depend on any axioms\n'Delivery.TwelveVertex.all_pairs_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.TwelveVertex.indirect_count' does not depend on any axioms\n'Delivery.DenseCounting.loss_from_counts' depends on axioms: [propext, Quot.sound]\n'Delivery.DenseCounting.final_band_bound' depends on axioms: [propext, Quot.sound]\n'Delivery.DenseCounting.attaining_block_count' depends on axioms: [propext, Quot.sound]\n'Delivery.DenseCounting.complementary_blocks_two_move' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseCounting.complementary_blocks_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ProtectedRouting.protected_witness_winning' does not depend on any axioms\n'Delivery.ProtectedRouting.protected_routing_universal' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ProtectedRouting.protected_routing_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.RobustTwoMove.envelope_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.RobustLayers.ranked_envelope_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.RobustLayers.safe_routing_layer' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ElevenVertexDense.witnesses' depends on axioms: [propext, Quot.sound]\n'Delivery.ElevenVertexDense.all_pairs_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ElevenVertexDense.indirect_count' does not depend on any axioms\n'Delivery.SmallDenseEnvelopes.every_intermediate_actual_delivery' depends on axioms: [propext,\n Classical.choice,\n Quot.sound]\n'Delivery.SmallDenseEnvelopes.exact_endpoint_counts' depends on axioms: [propext]\n'Delivery.StagedEnvelopes.envelope_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.GuideAttachment.safe_entry' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.GuideAttachment.attachment_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.FiniteGame.winningRegion_actual_delivery' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.FiniteGame.losingRegion_not_winning' does not depend on any axioms\n'Delivery.FiniteGame.losingRegion_not_guaranteed' does not depend on any axioms\n'Delivery.Extremal.score_le_missing' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.Extremal.maximum_unique' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExclusionCertificates.graph3_complete' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExclusionCertificates.graph3_camping' depends on axioms: [propext, Quot.sound]\n'Delivery.ExclusionCertificates.three_vertex_upper' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.VertexBound.live_source_two_neighbors' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.VertexBound.vertex_upper' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExtremalExamples.maximum_twelve_twentyfour' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExtremalExamples.eleven_score' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.winning_eventually' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.losingRegion_never_delivers' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.eventual_iff_finite' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.SemanticCompleteness.guaranteed_iff_actual' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.exact_score' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.maximum_from_classification' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.FourVertex.winning_valid' does not depend on any axioms\n'Delivery.ExactScoreCertificates.FourVertex.losing_closed' depends on axioms: [propext, Quot.sound]\n'Delivery.ExactScoreCertificates.FourVertex.score_two' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.ExactScoreCertificates.FourVertex.mixed_outcomes' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.arc_bound_of_indirect' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.missing_count_lower_of_indirect' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.zero_above_dense_boundary' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.zero_at_budget' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.initialGraph_arcCount' depends on axioms: [propext, Classical.choice, Quot.sound]\n'Delivery.DenseZero.maximum_zero' depends on axioms: [propext, Classical.choice, Quot.sound]\n"
    }
  ],
  "all_passed": true,
  "note": "Kernel-checked proofs; the certificate generator and external solver are not proof assumptions."
}