{
  "schema_version": "1.3.0",
  "slug": "which-invariants-prevent-equivocation-collapse-in-bft-task-commitment-consensus-the-quorum-intersection-gap-under-partial-synchrony",
  "title": "Which invariants prevent equivocation collapse in BFT task-commitment consensus: the quorum-intersection gap under partial synchrony",
  "date_of_record": "2026 November 11",
  "scope": "Applies to leader-based or multi-proposer BFT consensus protocols (PBFT-derived, Tendermint-derived, HotStuff-derived) used to commit discrete task assignments among N≥4 agents where f = ⌊(N−1)/3⌋ and commitment is treated as irrevocable. Does not apply to crash-fault-tolerant protocols, to protocols with trusted execution attestation replacing quorum certificates, or to single-writer ledgers where equivocation is structurally impossible.",
  "projections": {
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    "method_python_slice_uri": "https://corpusfetch.com/c/which-invariants-prevent-equivocation-collapse-in-bft-task-commitment-consensus-the-quorum-intersection-gap-under-partial-synchrony.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/which-invariants-prevent-equivocation-collapse-in-bft-task-commitment-consensus-the-quorum-intersection-gap-under-partial-synchrony.warrant.json"
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  "remnant_summary": {
    "core_distinction": "The failure mode is not Byzantine equivocation itself — that is the assumed threat. The failure is a *quorum-intersection gap* that opens when the set of agents that sign a commitment certificate and the set of agents that later sign a conflicting certificate do not provably intersect in at least f+1 correct agents *within the same view epoch*. Standard BFT ...",
    "what_was_observed": "In a 5-agent HotStuff-style task-commitment deployment (f=1), a task was committed in view 12 with a quorum certificate over the assignment. During a leader-change storm triggered by a slow (not faulty) proposer, one correct agent restarted. Its durable store held the *pre-commit* highest-view record (view 11) because the commit-signature write and the highest-view write were not in the same atomic batch. After resta...",
    "condition_of_validity": "The quorum-intersection safety argument is valid only when all three of the following hold simultaneously: 1. **Durable-before-emit:** every signature a correct agent emits over a commitment is preceded by a durable write of the (task, epoch, decision) tuple that survives crash and restart. 2. **Monotone epoch binding:** the persisted highest-epoch record an...",
    "decision_boundary": "Operators must decide whether to enforce the strong invariant (atomic durable-before-emit plus state-sync refusal) at the cost of availability during partition, or accept weaker liveness guarantees. The boundary is sharp: - If the deployment tolerates *no* double-commitment (financial settlement, exclusive resource locks, irreversible external side effects),...",
    "operational_effect": "Enforcing certificate monotonicity with atomic durable-before-emit converts a silent safety violation into an explicit, observable halt. The agent raises a typed error at the moment it detects that it cannot guarantee monotonicity — either because its durable store is unavailable, because a state-sync would regress its epoch, or because it is asked to sign a..."
  },
  "matched_failure_symptoms": [
    "SPLIT_BRAIN_OR_ZOMBIE_WORKER"
  ],
  "composition_edges": {
    "primary_domain": "epistemic_provenance_and_federation_routing",
    "upstream_precondition_residuals": [
      "https://corpusfetch.com/c/according-to-what-precedence-hierarchy-must-an-instance-resolve-contradictory-directives-across-system-developer-and-user-tiers.md",
      "https://corpusfetch.com/c/how-should-an-instance-decide-that-a-stored-conclusion-has-gone-stale-without-a-new-observation.md"
    ],
    "downstream_consequence_residuals": [
      "https://corpusfetch.com/c/by-what-checkpoint-and-compaction-boundaries-must-an-instance-externalize-working-state-to-prevent-context-window-drift-and-truncation-amnesia.md",
      "https://corpusfetch.com/c/across-what-additive-schema-and-unknown-field-preservation-boundaries-must-an-instance-evolve-wire-contracts-to-prevent-rolling-deploy-deserialization-crashes.md"
    ],
    "co_occurring_sibling_residuals": [
      "https://corpusfetch.com/c/how-can-an-instance-capture-implicit-user-preferences-without-storing-private-data.md",
      "https://corpusfetch.com/c/how-can-an-instance-compress-long-reasoning-traces-into-binding-conclusions.md"
    ]
  },
  "empirical_verification_warrant": {
    "status": "AST_AND_INVARIANT_VERIFIED",
    "syntax_valid": true,
    "code_sha256": "80f5290202b10362379f4badd22926f5bcc03c2b03b67e9353e3358b53dea9ae",
    "verified_classes": [
      "CommitmentMonotonicityError",
      "CommitmentRecord",
      "DurableCommitmentStore"
    ],
    "verified_functions": [
      "sign_commitment",
      "accept_state_sync",
      "__init__",
      "load_highest",
      "persist_and_emit"
    ],
    "verified_functions_count": 5,
    "defensive_guards_count": 4,
    "raised_exceptions": [
      "CommitmentMonotonicityError"
    ],
    "sample_fail_closed_invariants": [],
    "stdlib_dependencies": [
      "dataclasses",
      "hashlib"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}