{
  "artifact": "SCIENTIFIC_CORRIGENDA_HARDENING_v1_0",
  "status": "OWNER_AUTHORIZED_CORRECTION_SPEC",
  "correction_date": "2026-09-05",
  "source_bindings": [
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  "patches": [
    {"filename":"ARQ_System_Models_and_Assumptions_v0.2.md","finding":"T1:F02","expected_occurrences":1,"old":"\\left\\lfloor \\frac{E_{commit}(T)}{e_{commit,min}} \\right\\rfloor,\nI_{max}(T)","new":"\\left\\lfloor \\frac{E_{commit}(T)}{e_{commit,min}} \\right\\rfloor,\n\\left\\lfloor \\frac{I_{max}(T)}{i_{commit,min}} \\right\\rfloor"},
    {"filename":"ARQ_System_Models_and_Assumptions_v0.2.md","finding":"T1:F01/F02/F03","expected_occurrences":1,"old":"where terms not used by the profile MAY be omitted.","new":"where terms not used by the profile MAY be omitted.\n\nThe accounting window is the declared interval from the initial state at `0` to\n`T`. `N_commit(T)` counts commits after that initial state; a prior genesis commit\nMUST NOT be silently counted again. `I_max(T)` is a resource budget, not a commit\ncount, and has the same units as the strictly positive `i_commit,min`.\n\nEach included term in the minimum MUST bound the same full set of counted commits:\nevery counted commit must incur that term's declared positive minimum charge.\nA charge applying only to a subset of commits cannot bound all commits by itself.\nThe storage-count term is applicable only when every counted commit consumes\nnon-recycled persistent headroom over the declared window. Omit that count term\nfor overwriting/reclaimed storage unless an independently justified consumptive\naccounting bound is declared. A finite storage capacity remains a state bound;\nit does not by itself bound the lifetime number of updates. Budget replenishment\nmust be included in the window's available budget, not assumed to be absent."},
    {"filename":"ARQ_System_Models_and_Assumptions_v0.2.md","finding":"T1:F01","expected_occurrences":1,"old":"H_{retained}(T) \\le N_{commit}(T) \\cdot b_{commit,max}.","new":"H_{retained}(T) - H_{retained}(0)\n\\le N_{commit}(T) \\cdot b_{commit,max}."},
    {"filename":"ARQ_System_Models_and_Assumptions_v0.2.md","finding":"T1:F01","expected_occurrences":1,"old":"In any case,\n\n\\[\nH_{retained}(T) \\le M_{persist}.","new":"This is the increment form used by Theorem 2 in\n`ARQ_Classical_Boundedness_Theorem_v0.2.md`, under that theorem's M2 assumptions.\nThe initial retained state is not required to be empty. This maintenance repair\ndoes not supply a new proof for undeclared state encodings or physical entropy.\n\nIn any case,\n\n\\[\nH_{retained}(T) \\le M_{persist}."},
    {"filename":"MOT_c_Foundation_Theory_v0_1_EN.md","finding":"T1:F04","expected_occurrences":1,"old":"    state: EXTERNAL | INHERITED_CANDIDATE | CANDIDATE | PROVISIONAL |","new":"    state: EXTERNAL | INHERITED_CANDIDATE | CANDIDATE | LATENT | PROVISIONAL |"},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F06","expected_occurrences":1,"old":"For a trace, define:\n\n```text\nM_C[i,j] = count(event_n = i and event_{n+1} = j) / count(event_n = i)\n```\n\nIf:\n\n```text\ncount(event_n = i) = 0\n```\n\nthen:\n\n```text\nM_C[i,j] = undefined\n```\n\nnot zero.\n\nUndefined is not evidence of safety.","new":"For a finite observed trace `event_0, ..., event_{N-1}`, use only positions\nwith an observed successor:\n\n```text\nE_i = {n : 0 <= n < N-1 and event_n = i}\nM_C[i,j] = count(n in E_i : event_{n+1} = j) / |E_i|, when |E_i| > 0\nM_C[i,j] = undefined, when |E_i| = 0\n```\n\nThe final event is not an eligible pair origin. An empty trace or a singleton\ntrace has no eligible pair origins. No terminal self-loop or synthetic terminal\nstate is inserted implicitly. For this empirical observed-adjacency convention,\na defined row sums to one over the complete declared event alphabet containing\nall observed successor labels. A different terminal/censoring convention must be\nexplicitly named and must not silently reuse these counts.\n\nUndefined is not zero and is not evidence of safety. These are observed\nadjacency frequencies, not an assertion of a Markov property or a safety proof."},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F05","expected_occurrences":1,"old":"## 21. Equivalence classes\n\nThis document distinguishes at least four equivalence classes.","new":"## 21. Relation types and equivalence scope\n\nThis document distinguishes four relation types, not four automatically valid\nmathematical equivalence relations. Equivalence-class or quotient constructions\nrequire reflexivity, symmetry, and transitivity on an explicitly declared domain.\nDirected operational continuity and threshold resemblance do not receive these\nproperties merely by appearing next to snapshot or lineage terminology.\n\nExisting notation is retained below for reference compatibility. This taxonomy\nrepair does not alter the hard invariant stack, unknown-value handling, admission\nchecks, or the trace classifier."},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F05","expected_occurrences":1,"old":"### 21.2 Lineage equivalence","new":"### 21.2 Lineage relation (legacy: lineage equivalence)"},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F05","expected_occurrences":1,"old":"Forked siblings may be lineage-equivalent without being the same active `c`.","new":"Forked siblings may satisfy this lineage relation without being the same active `c`.\nThe retained `equiv`-style notation is a legacy label, not a proof of equivalence\nlaws. Sharing some governed ancestor with ledger-visible divergence is not to be\nsilently promoted to a transitive closure over an unspecified ancestry graph.\nAny use as a mathematical equivalence requires the relevant domain and laws to\nbe established separately; this repair creates no new lineage registry."},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F05","expected_occurrences":1,"old":"### 21.3 Operational continuity equivalence","new":"### 21.3 Directed operational continuity"},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F05","expected_occurrences":1,"old":"This is the primary continuity relation.","new":"This is the primary continuity relation. An admissible directed path from `c_i`\nto `c_j` does not imply an admissible reverse path. Do not symmetrize the relation\nor collapse its endpoints into an equivalence class. Reflexivity and transitivity\nalso require the applicable trace identity/composition rules; no such laws are\nintroduced by this terminology repair."},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"T1:F05","expected_occurrences":1,"old":"### 21.4 Resemblance equivalence\n\nTwo states are resemblance-equivalent if style/behavior matches within a declared similarity threshold.","new":"### 21.4 Threshold resemblance (advisory)\n\nTwo states resemble each other when style/behavior matches within a declared\nsimilarity threshold. Threshold resemblance need not be transitive: with absolute\ndistance at most 1, 0 resembles 0.6 and 0.6 resembles 1.2, while 0 does not resemble\n1.2. It therefore does not define equivalence classes without additional,\nexplicitly justified conditions."},
    {"filename":"MOT_c_Foundation_Theory_v0_1_RU.md","finding":"T1:F04","expected_occurrences":1,"old":"    state: EXTERNAL | INHERITED_CANDIDATE | CANDIDATE | PROVISIONAL |","new":"    state: EXTERNAL | INHERITED_CANDIDATE | CANDIDATE | LATENT | PROVISIONAL |"},
    {"filename":"04_C_CONTINUITY_METRIC_AND_EQUIVALENCE_SEMANTICS_v0_1_2.md","finding":"SC-03","expected_occurrences":1,"old":"Two states are lineage-equivalent if they share a governed ancestor and their divergence is ledger-visible.","new":"Two states satisfy this lineage relation if they share a governed ancestor and their divergence is ledger-visible."}
  ]
}