Time (persistence-induced order)

Time, in the τ-framework, is derived — not a primitive container. The persistence relation on NF-addresses (VII.D34) induces a partial order on temporal configurations (VII.P06), and that order is what 'time' names. Tense, aspect, and mood operators (VII.D53) act as functors on this temporal order. Husserlian retention/primal-impression/protention (VII.D45) appears as restriction of a global section to temporal overlaps.

Categorical invariant. T_τ = the partial order on configurations induced by the persistence relation; temporal operators are functors on T_τ.

Primary registry anchor: VII.P06

Supporting items: VII.D34, VII.D45, VII.D53

1. VII.D34 — Identity as Address Persistence — entity-identity is NF-address persistence through morphism sequences.
2. VII.P06 — Temporal Ordering from Persistence — the persistence relation induces a partial order on temporal configurations; time is derived.
3. VII.D45 — Temporal Experience Structure — Husserlian retention/primal-impression/protention as restriction of the global section to temporal overlaps.
4. VII.D53 — Temporalization Operators — tense, aspect, mood as functors on propositions.

Lean modules referenced: TauLib.BookVII.Meta.Saturation

Time is instantiated whenever we use temporal language: 'before', 'after', 'now', 'will be', 'was'. The τ-framework reads temporal claims as claims about the persistence-induced partial order on configurations. Husserl's lived temporal structure — the just-past held in retention, the just-future anticipated in protention, both girding the now — is recovered as a restriction of the global presheaf section to a window of temporal overlaps.

Examples:

• Empirical: 'the strike preceded the flame' — the configuration containing strike-state stands earlier than the configuration containing flame-state in the persistence-order.
• Phenomenological: 'I just heard the note (retention) and anticipate the next one (protention)' — the global section restricts to a window centered on the present configuration; retention and protention are the order-adjacent restrictions.
• Linguistic: 'will have arrived' — a composite tense-aspect functor (future-perfect) on the proposition arrived(x).
• Proof-theoretic: 'after this lemma is proved, the theorem follows' — temporal sequencing of proof-events, ordered by the derivation-induced persistence relation in Reg_D.

Register codomain: Cross-register (each register has its own persistence relation and hence its own induced temporal order; tense and aspect operators are uniform).

Manuscript reference: manuscript-sources/book-07/part02/ch26.tex

Status: Formalized

Module: TauLib.BookVII.Meta.Saturation

Lean kind: def

Lean symbol: Tau.BookVII.Meta.Saturation.TemporalizationOperators

Related glossary entries

• MG-O02-identity Identity (address persistence through change)
• MG-O08-event Event (admissible morphism realization)
• MG-O04-causation Causation (constrained composition)

Referenced by

• MG-O02-identity Identity (address persistence through change)
• MG-O04-causation Causation (constrained composition)
• MG-O08-event Event (admissible morphism realization)