IsPersistent
IsPersistent declares a recognition event persistent exactly when its J-cost vanishes. Researchers constructing observer structures from coherent recognition cite this predicate to enforce an invariant reference frame. The declaration is a direct abbreviation of the zero-cost condition on the event state.
claimA recognition event $ref$ is persistent if its J-cost satisfies $cost(ref) = 0$.
background
RecognitionEvent is the structure consisting of a positive real state together with a positivity witness. Its cost is the J-cost of that state, known to be nonnegative. The ObserverForcing module shows that coherent recognition of multiple events requires a reference frame whose cost is invariant under arbitrary comparisons; the module documentation states that any non-zero cost shifts with context, so only the global J-cost minimum can serve as a fixed frame.
proof idea
The definition is a direct abbreviation equating the predicate to the zero-cost condition on the supplied RecognitionEvent.
why it matters in Recognition Science
IsPersistent supplies the predicate that equips a CoherentRecognition with a fixed reference inside the Observer structure. It is invoked in the observer_forcing_certificate that assembles the six facts forcing an observer from nontrivial recognition, and in cooper_pairing_yields_persistent and identity_persistent. It realizes the module's step 4: persistence demands zero J-cost, achieved at the identity tick or by Cooper pairing.
scope and limits
- Does not assert existence of any persistent event.
- Does not identify which states achieve zero J-cost.
- Does not address behavior under recognition composition.
- Does not connect to spatial dimensions or physical constants.
formal statement (Lean)
90def IsPersistent (ref : RecognitionEvent) : Prop := ref.cost = 0
proof body
Definition body.
91
92/-- The identity event is persistent. -/