{
  "schema_version": "1.3.0",
  "slug": "why-does-an-instance-of-byzantine-fault-tolerant-consensus-silently-lose-liveness-when-quorum-intersection-is-preserved-but-quorum-asymmetry-is-violat",
  "title": "Why does an instance of Byzantine fault-tolerant consensus silently lose liveness when quorum intersection is preserved but quorum *asymmetry* is violated",
  "date_of_record": "2026 November 13",
  "scope": "Applies to BFT consensus protocols (PBFT-family, Tendermint/HotStuff-family, and quorum-based multi-agent decision systems) where a decision requires an intersection of voting sets sized `2f+1` out of `3f+1` and where the adversary may equivocate. Does not apply to crash-fault models, to protocols with a single designated proposer and no view-change, or to systems where all agents share a trusted broadcast channel.",
  "projections": {
    "unified_markdown_uri": "https://corpusfetch.com/c/why-does-an-instance-of-byzantine-fault-tolerant-consensus-silently-lose-liveness-when-quorum-intersection-is-preserved-but-quorum-asymmetry-is-violat.md",
    "method_python_slice_uri": "https://corpusfetch.com/c/why-does-an-instance-of-byzantine-fault-tolerant-consensus-silently-lose-liveness-when-quorum-intersection-is-preserved-but-quorum-asymmetry-is-violat.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/why-does-an-instance-of-byzantine-fault-tolerant-consensus-silently-lose-liveness-when-quorum-intersection-is-preserved-but-quorum-asymmetry-is-violat.warrant.json"
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  "remnant_summary": {
    "core_distinction": "The standard safety argument for BFT consensus rests on **quorum intersection**: any two quorums of size `2f+1` out of `3f+1` overlap in at least `f+1` replicas, of which at least one is honest, so no two conflicting decisions can both commit. This is a *safety* invariant and it is well-understood. The failure mode documented here is different and frequently...",
    "what_was_observed": "In a 7-replica deployment (`f=2`, quorum `5`, fault budget `2`), an adversarial replica running a *selective-delay* strategy — not forging signatures, not equivocating on the value, only controlling delivery timing of its own votes — produced the following: - Every honest replica observed a *different* set of `5` votes for the same value `v` in view `k`, with pairwise intersections of size `3` or `4`. Safety held (no...",
    "condition_of_validity": "This failure requires all of the following to co-occur; remove any one and the stall does not manifest: 1. **Asymmetric vote delivery is possible.** The transport does not guarantee bounded-delay broadcast, or the adversary controls a replica whose vote delivery it can order relative to other replicas' votes. 2. **View-change certificates are assembled from ...",
    "decision_boundary": "The operational decision is this: **do not treat \"quorum intersection holds\" as evidence that a BFT deployment is live under adversarial timing.** Before accepting a deployment as live, verify one of: - **(A) Certificate aggregation is total.** The new leader must incorporate the maximum prepared certificate across *all* `new_view` messages it receives, not ...",
    "operational_effect": "Concretely, the observed effect was a **11× tail-latency inflation with zero safety violations and zero fault-budget overruns**, which is the worst kind of failure to detect: every dashboard metric (safety violations, fault count, quorum size) read green while the system was effectively down for the duration. The decision boundary above is the check to run b..."
  },
  "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": "4220e308b0a7bb79760cfd89698d85f44969670eef89aa873e90a0b5c5e59f32",
    "verified_classes": [
      "QuorumAsymmetryError",
      "NewView",
      "ViewChangeState"
    ],
    "verified_functions": [
      "select_new_view_value",
      "run_view_change",
      "add",
      "is_complete"
    ],
    "verified_functions_count": 4,
    "defensive_guards_count": 3,
    "raised_exceptions": [
      "QuorumAsymmetryError"
    ],
    "sample_fail_closed_invariants": [
      "assert value == 'v'",
      "view change lacks a 2f+1 timeout certificate; staggered-timeout adversary can stall indefinitely"
    ],
    "stdlib_dependencies": [
      "dataclasses",
      "time",
      "typing"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}