RecognitionEvent
plain-language theorem explainer
RecognitionEvent defines a positive real number as the state of a recognition event. It serves as the base object in the seven-step argument that derives an observer from any nontrivial coherent recognition structure. The declaration is a bare structure with a state field and a positivity constraint, introducing no computational content.
Claim. A recognition event is a real number $s$ such that $s > 0$.
background
The ObserverForcing module shows that any nontrivial coherent recognition structure forces an observer. RecognitionEvent is defined as a positive real state whose J-cost is Cost.Jcost applied to the state, which is nonnegative from the properties of J established in LedgerFactorization. The module doc-comment lists seven steps that begin with this definition and proceed through persistent reference frames to the observer. Upstream, LedgerForcing supplies a related but distinct RecognitionEvent carrying source, target and ratio, while DAlembert.LedgerFactorization calibrates the underlying J function on positive reals.
proof idea
The declaration is a structure definition. It introduces the type with fields state : ℝ and state_pos : 0 < state. No lemmas or tactics are applied; the definition stands alone as the carrier type for the subsequent cost and persistence constructions in the same module.
why it matters
This definition launches the forcing argument in the module and supplies the events consumed by LedgerForcing's add_event, balanced_list and conservation_from_balance theorems. It feeds the master theorem nontrivial_recognition_forces_observer. The construction aligns with T5 J-uniqueness in the forcing chain, where only the identity state yields zero cost, and supports the later emergence of the eight-tick octave and D = 3.
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