IndisputableMonolith.Foundation.UniversalForcing.Strict.Invariance
The module establishes that every strict realization derives forced arithmetic canonically equivalent to LogicNat. Researchers tracing the universal forcing chain cite this to confirm the natural numbers object remains fixed across realizations. The structure imports the categorical hook and states the equivalence directly from the NNO surface.
claimEvery strict realization's derived forced arithmetic is canonically equivalent to the natural numbers object $LogicNat$.
background
This module belongs to the strict invariance section of the universal forcing foundation. It imports the Categorical module, whose doc states: 'Strict categorical/Lawvere-style realization hook. The carrier is the canonical LogicNat NNO surface from CategoricalLogicRealization.' The setting fixes the natural numbers object in the strict pass so that arithmetic emerges invariantly from the forcing.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This invariance secures the canonical arithmetic for the downstream Music module, which develops domain-rich musical realizations over positive frequency ratios using equality-cost comparisons on ratios. It closes the strict categorical path in the universal forcing chain.
scope and limits
- Does not address non-strict realizations or refinements to full Mathlib NNO API.
- Does not incorporate psychoacoustic dissonance costs beyond equality on ratios.
- Does not connect to phi-ladder mass formulas or eight-tick octave structure.