narrativeInterpret
narrativeInterpret converts an element of the forced natural numbers into its iteration count expressed as a NarrativeBeat. Researchers embedding narrative order into the Recognition framework would cite it to realize the structural claim that beat counts carry the same Peano object as the Law of Logic. The definition is a one-line wrapper applying the toNat map from ArithmeticFromLogic.
claimDefine the map sending each forced natural number $n$ (generated from the identity by iterated steps) to its iteration count $k$ by $k = $ toNat$(n)$, where the result is viewed as a narrative beat count in the natural numbers.
background
The module supplies a lightweight narrative realization whose carrier is the beat count generated by an inciting event. This formalizes the claim that narrative order carries the same forced Peano object. NarrativeBeat is defined as the type of natural numbers. LogicNat is the inductive type whose identity constructor gives the zero-cost element and whose step constructor adds one iteration, mirroring the multiplicative orbit closed under the generator.
proof idea
The definition is a one-line wrapper that applies the toNat function from ArithmeticFromLogic. toNat reads the iteration count by recursion: identity maps to 0 and step n maps to the successor of toNat n. The result is returned directly as a NarrativeBeat.
why it matters in Recognition Science
This supplies the carrier map inside narrativeRealization, which constructs a LogicRealization with NarrativeBeat as carrier and natural numbers as cost. It thereby embeds the forced arithmetic into narrative beat-count comparisons, supporting the discrete 8-tick structures of the Recognition framework. The downstream narrativeRealization uses the map to realize the structural claim that narrative order carries the same forced Peano object.
scope and limits
- Does not define any cost or comparison operation on narrative beats.
- Does not address continuous limits or continuum identifications.
- Does not prove symmetry or equivalence properties of the map.
formal statement (Lean)
33def narrativeInterpret (n : LogicNat) : NarrativeBeat :=
proof body
Definition body.
34 LogicNat.toNat n
35
36/-- Narrative realization as beat-count comparison. -/