narrative_arith_equiv_nat
plain-language theorem explainer
The definition supplies an equivalence showing that the Peano carrier extracted from the narrative realization's arithmetic matches the natural numbers forced by the Law of Logic. Researchers tracing universal forcing chains would cite this to confirm narrative beat counts embed the base arithmetic structure. The proof is a direct one-line wrapper that applies the orbit equivalence field of the narrative realization.
Claim. The carrier of the Peano arithmetic object extracted from the narrative beat-count realization is equivalent to the natural numbers forced by the Law of Logic: $C_P(R) ≃ N_L$ where $R$ is the narrative realization, $C_P(R)$ its extracted Peano carrier, and $N_L$ the logic-forced naturals.
background
The module introduces a lightweight narrative realization whose carrier is the beat count generated by an inciting event. This setup formalizes the claim that narrative order carries the same forced Peano object as other realizations. LogicNat is the inductive type with an identity constructor for the zero-cost multiplicative identity and a step constructor for generator iterations, forming the smallest orbit closed under multiplication by the generator. The arithmeticOf function extracts the forced arithmetic object from any LogicRealization; here it is applied to the narrative case whose carrier is NarrativeBeat and whose comparison uses the narrative cost function.
proof idea
This is a one-line wrapper that applies the orbit equivalence field supplied by the narrative realization definition.
why it matters
This definition completes the narrative case in the universal forcing result that any two Law-of-Logic realizations yield equivalent arithmetic objects. It supports the structural claim that beat-count narratives embed the forced Peano structure, consistent with the T0-T8 chain and the eight-tick octave. No open question or scaffolding closure is directly addressed.
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