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Module detectability

dsfb_rf

Module detectability 

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Rich deterministic detectability taxonomy (DSFB-Lattice §IV–V).

DetectabilityClass / SemanticStatus / DetectionStrengthBand hierarchy with post-crossing persistence tracking and the deterministic τ_upper = δ₀/(α−κ) detection latency bound. Provides a full operator-advisory output for VITA 49.2 context packets and SIGINT operator dashboards. Rich deterministic detectability taxonomy for DSFB-RF.

§Theoretical Basis

A key contribution of the DSFB framework is the derivation of a deterministic upper bound on detection latency (DSFB-Lattice §V, DSFB-Semiotics-Calculus §III). Unlike Pd/Pfa quantities — which require calibrated probabilistic models and are sensitive to signal model mis-match — the DSFB detectability bound is purely algebraic:

τ_upper = δ₀ / (α − κ)   provided α > κ

where:

  • δ₀ = initial residual offset from the nominal
  • α = divergence rate (from the Lyapunov exponent λ or slew rate)
  • κ = noise-floor rate (minimum observable drift, derived from σ₀)

The bound asserts: if a structural change is occurring at rate α, the grammar layer will detect it within τ_upper sample periods.

§Interpretation taxonomy (DSFB-Lattice)

Beyond the raw bound, the lattice framework defines a full hierarchy of semantic interpretation classes, making operator-facing output actionable rather than merely numeric:

InterpretationClassMeaning
StructuralDetectedEnvelope crossing confirmed with margin; clear fault
StressDetectedCrossing detected with low post-crossing margin; degradation likely
EarlyLowMarginCrossingCrossing detected early but barely; watch state
NotDetectedNo crossing; nominal operation

The SemanticStatus refines this further with temporal persistence qualities, and DetectionStrengthBand provides a coarse ordinal for dashboard display.

§Post-crossing persistence

For SIGINT / EW applications, it is important to know not just when a crossing occurs but how long the trajectory remains outside the envelope. Long post-crossing persistence indicates a persistent structural fault (e.g., hardware failure, sustained jamming) rather than a transient spike. This module tracks:

  • post_crossing_duration: number of samples outside envelope since first crossing
  • post_crossing_fraction: fraction of recent W samples spent outside envelope
  • peak_margin_after_crossing: maximum normalised excess (‖r‖ − ρ) / ρ since crossing

§Design

  • no_std, no_alloc, zero unsafe
  • O(1) per update() call (circular buffer for fraction tracking)
  • All types Clone + Copy for zero-cost passing through audit chain

Structs§

DetectabilityBound
Deterministic detectability upper bound τ_upper.
DetectabilitySummary
Full detectability summary for one observation window.
DetectabilityThresholds
Thresholds governing the detectability taxonomy.
DetectabilityTracker
Running detectability tracker with O(1) per-sample update.

Enums§

DetectabilityClass
Coarse detection interpretation class.
DetectionStrengthBand
Operator-facing coarse strength band (for dashboard colour coding).
SemanticStatus
Fine-grained semantic status combining class and temporal context.