IndisputableMonolith.Foundation.UniversalForcing.MusicRealization
This module formalizes musical realization as interval-step comparison to embed forced arithmetic into musical structures. Researchers modeling narrative or beat-based systems under universal forcing would cite it for the equivalence to natural-number arithmetic. The module supplies definitions for interval steps and cost functions plus lemmas for their self-consistency and symmetry.
claimMusical realization is the map sending interval steps to forced arithmetic objects, with cost function $C$ obeying $C(x,x)=0$ and $C(x,y)=C(y,x)$, together with the equivalence music_arith_equiv_nat that identifies the realization with the Peano object generated by the universal forcing theorem.
background
The module sits inside the universal forcing framework. The upstream result states that every Law-of-Logic realization carries canonically equivalent forced arithmetic. It introduces MusicalIntervalStep as the discrete unit of comparison and defines musicCost together with its self and symmetry lemmas to enforce consistency with the Recognition Composition Law.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the musical carrier that NarrativeRealization imports to realize narrative order as the beat count generated by an inciting event. It thereby extends the universal forcing theorem to show that both musical intervals and narrative sequences carry the same forced Peano object.
scope and limits
- Does not model acoustic wave propagation.
- Does not address perceptual pitch discrimination.
- Does not claim equivalence outside the forcing arithmetic.
- Does not generate numerical predictions for real music.