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    "kind": "proposition",
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    "kind": "theorem",
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    "kind": "theorem",
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    "kind": "proposition",
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    "kind": "theorem",
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    "kind": "corollary",
    "title": "The size of partition correction memory",
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    "kind": "theorem",
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      "Komorebi.MachineTheory.Bayes.ReportingModel.preservesAll_of_reconstructs"
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    "kind": "theorem",
    "title": "Least refinement closed under prediction and correction",
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    "kind": "theorem",
    "title": "One quotient for reports, posteriors, and feedback",
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    "kind": "theorem",
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    "formalization_note": "Bounded metric response error plus total variation on the same finite world set; actual finite minimizers, capped regret, strict-gap uniqueness and risk threshold. Direct conditional-history and stored-record composition included as supporting results."
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    "kind": "theorem",
    "title": "A common artifact for fixed recipients",
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    "kind": "theorem",
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    "kind": "proposition",
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    "kind": "theorem",
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    "printed_page": "29",
    "source_lines": [
      888,
      898
    ],
    "check_group": "r:governance",
    "admission_edition": "0.1",
    "status": "KERNEL_CHECKED_BLOCK15",
    "lean_modules": [],
    "lean_endpoints": [
      "Komorebi.MachineTheory.LegalQuotient.finite_source_legal_quotient",
      "Komorebi.MachineTheory.LegalQuotient.exists_quotient_iff",
      "Komorebi.MachineTheory.LegalQuotient.representativeQuotient_factors",
      "Komorebi.MachineTheory.LegalQuotient.quotient_unique",
      "Komorebi.MachineTheory.LegalQuotient.ofEnabled_reconstruct",
      "Komorebi.MachineTheory.LegalQuotient.finite_legal_quotient_sequences",
      "Komorebi.MachineTheory.LegalQuotient.Factors.execute_map",
      "Komorebi.MachineTheory.LegalQuotient.Factors.labels_eq",
      "Komorebi.MachineTheory.LegalQuotient.Factors.lift_execution"
    ]
  },
  {
    "kind": "theorem",
    "title": "Safe continuation that retains an ending strategy",
    "label": "r:ending",
    "number": "8.3",
    "printed_page": "30",
    "source_lines": [
      918,
      927
    ],
    "check_group": "r:ending",
    "admission_edition": "0.1",
    "status": "KERNEL_CHECKED_BLOCK16_RECOVERY",
    "lean_modules": [
      "MachineTheory.FiniteFixedPoints",
      "MachineTheory.SafeEnding",
      "MachineTheory.SafeEndingPolicies",
      "MachineTheory.SafeEndingExamples"
    ],
    "lean_endpoints": [
      "Komorebi.MachineTheory.SafeEnding.ending_stabilizes",
      "Komorebi.MachineTheory.SafeEnding.running_stabilizes",
      "Komorebi.MachineTheory.SafeEnding.endRank_zero_iff",
      "Komorebi.MachineTheory.SafeEnding.rank_action",
      "Komorebi.MachineTheory.SafeEnding.ending_region_iff",
      "Komorebi.MachineTheory.SafeEnding.safe_continuation_iff",
      "Komorebi.MachineTheory.SafeEnding.source_core83",
      "Komorebi.MachineTheory.SafeEnding.command_rank_bound",
      "Komorebi.MachineTheory.SafeEnding.command_rank_arrival",
      "Komorebi.MachineTheory.SafeEnding.running_has_infinite_path",
      "Komorebi.MachineTheory.SafeEnding.ending_prefix_extends"
    ],
    "assurance_note": "Admission requires completed current-source final16/fresh16 gates and production comparison. Full-history strategies, deadlock, observable command, first-arrival safety and first-entry rank are explicit. The source hold-at-goal assumption is unnecessary for first-arrival semantics."
  }
]