{
  "schema_version": "1.3.0",
  "slug": "when-does-a-boundary-event-fall-into-two-adjacent-windows-or-neither",
  "title": "When does a boundary event fall into two adjacent windows or neither?",
  "date_of_record": "2026 November 1",
  "scope": "Applies to time or value windows aggregated independently and then summed, where each window decides boundary membership on its own. Excludes systems with a single global assignment step.",
  "projections": {
    "unified_markdown_uri": "https://corpusfetch.com/c/when-does-a-boundary-event-fall-into-two-adjacent-windows-or-neither.md",
    "method_python_slice_uri": "https://corpusfetch.com/c/when-does-a-boundary-event-fall-into-two-adjacent-windows-or-neither.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/when-does-a-boundary-event-fall-into-two-adjacent-windows-or-neither.warrant.json"
  },
  "token_profile": {
    "full_markdown_tokens": 823,
    "python_slice_tokens": 101,
    "warrant_slice_tokens": 220
  },
  "remnant_summary": {
    "core_distinction": "**Predicate.** Adjacent windows partition the timeline if and only if their intervals are half-open and the convention is identical on both sides: window i is [start_i, end_i) and window i+1 is [end_i, end_{i+1}). An event at exactly end_i belongs to exactly one window by construction. If either side uses a closed boundary, an event at the seam belongs to tw...",
    "what_was_observed": "**Signature.** Sum-of-windows differing from whole-range total by exactly the events at window boundaries. The delta is proportional to the number of windows times the boundary event rate. Drilling into a single window shows no error. **Trace.** Producer emits at timestamp t=60. Window 0 covers [0,60] closed, window 1 covers [60,120] closed. The event at 60 appears in both. Sum over windows = total + boundary events....",
    "condition_of_validity": "Window sums are exact only while at least one holds: 1. **Half-open everywhere.** Every window is [start, end), enforced at the assignment step rather than by convention. 2. **Single assigner.** One component assigns events to windows, and windows aggregate what they are given rather than filtering independently. 3. **Boundary audit.** The sum over windows i...",
    "decision_boundary": "- All windows half-open: exact partition. - Mixed inclusive and exclusive: double count or gap at every seam. - Closed windows with events that never land exactly on a boundary: works in practice, breaks when the event rate or resolution changes so that collisions become common. - Single assigner with any convention: exact, because assignment happens once.",
    "operational_effect": "The defect is a convention mismatch between components that never negotiate, so it appears when a new aggregator is added rather than when existing ones change. Remediation is to assign once and aggregate the assignment, or to enforce half-open at the shared boundary. The trap is to add an epsilon to one side. That converts a clean double count into an unpre..."
  },
  "matched_failure_symptoms": [
    "DOMAIN:EPISTEMIC_PROVENANCE_AND_FEDERATION_ROUTING"
  ],
  "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": "96f81fa3c3a230c8e071708c0b80774765d1dd118a9c3ebac91ded5bfefacf41",
    "verified_classes": [
      "BoundaryAssignmentError",
      "WindowGate"
    ],
    "verified_functions": [
      "dispatch_window_convention",
      "verify"
    ],
    "verified_functions_count": 2,
    "defensive_guards_count": 2,
    "raised_exceptions": [
      "BoundaryAssignmentError"
    ],
    "sample_fail_closed_invariants": [
      "closed-closed window double counts its end boundary",
      "open-open window drops its end boundary"
    ],
    "stdlib_dependencies": [
      "dataclasses"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}