Event (admissible morphism realization)
An event, in the τ-framework, is the realization of an admissible morphism in the coherence kernel — the application of a morphism f from one configuration to another, indexed by the persistence-induced temporal order. Events are not basic particulars and not mere derived 'changes in state'; they are the morphism-realizations themselves, with source-configuration, target-configuration, and admissibility witness.
τ-Definition
An event, in the τ-framework, is the realization of an admissible morphism in the coherence kernel — the application of a morphism f from one configuration to another, indexed by the persistence-induced temporal order. Events are not basic particulars and not mere derived 'changes in state'; they are the morphism-realizations themselves, with source-configuration, target-configuration, and admissibility witness.
Categorical invariant. e is event ⟺ e = (f, σ, τ) where f ∈ AdmMor(K_τ), σ = src(f), τ = tgt(f), and the realization is indexed by the persistence-temporal order.
Primary registry anchor:
VII.D32
τ-Derivation Chain
-
VII.D34— Identity as Address Persistence — configurations are NF-address sets that morphisms act on. -
VII.P06— Temporal ordering from persistence — events are temporally ordered by the persistence-induced partial order. -
VII.D32— Causation as Constrained Composition — events compose causally via admissible factorization. -
VII.D45— Temporal Experience Structure — Husserlian retention/protention applies to event-streams as restrictions of the global section.
Lean modules referenced:
TauLib.BookVII.Meta.Registers
Phenomenological Correlate
An event is instantiated whenever something happens: a match strikes, a verdict is delivered, a proof step is taken, a promise is made. The temporal verbs of natural language ('struck', 'delivered', 'proved', 'promised') name event-realizations. The τ-framework gives them the same structure regardless of register: an admissible morphism applied between two configurations, witnessed by its admissibility certificate.
Examples:
- Empirical: 'the match struck' — an admissible Reg_E morphism from configuration σ (match-untouched) to τ (match-ignited).
- Normative: 'the verdict was delivered' — an admissible Reg_P morphism from σ (case-pending) to τ (case-decided), witnessed by the procedural admissibility certificate.
- Proof-theoretic: 'the inference step was taken' — an admissible Reg_D morphism realizing one application of an inference rule.
- Commitment-theoretic: 'the promise was made' — an admissible Reg_C morphism from σ (no-commitment) to τ (commitment-in-force).
Register codomain: Cross-register (events are register-relative: each register has its own admissible morphisms, but the event-structure is uniform).
Manuscript reference: manuscript-sources/book-07/part02/ch24.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookVII.Meta.Registers
Lean kind: def
Lean symbol: Tau.BookVII.Meta.Registers.CausationAsConstrainedComposition