IndisputableMonolith.Foundation.UniversalForcing.Strict.Invariance
This module asserts that every strict realization's derived forced arithmetic is canonically equivalent to LogicNat. Researchers tracing the universal forcing chain would cite it to confirm arithmetic uniqueness across strict realizations. It imports the categorical hook and prepares the invariance layer for the music realization. The module contains no local proofs and relies on the upstream categorical definition.
claimFor every strict realization $R$, the derived forced arithmetic satisfies $A_R$ canonically equivalent to the natural numbers object LogicNat.
background
The module sits inside Foundation.UniversalForcing.Strict and imports the Categorical module. That upstream module supplies the Lawvere-style realization hook whose carrier is the canonical LogicNat NNO surface from CategoricalLogicRealization. The local theoretical setting is the invariance of forced arithmetic under strict realizations, with the DOC_COMMENT stating the canonical equivalence claim directly.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the Music module, which develops domain-rich musical realizations over positive frequency ratios using equality-cost on ratios. It supplies the invariance step that guarantees every strict realization reduces to the same LogicNat arithmetic, closing the strict pass of the universal forcing chain before richer psychoacoustic refinements are added.
scope and limits
- Does not treat non-strict realizations.
- Does not refine the NNO surface to full Mathlib category theory.
- Does not introduce explicit arithmetic derivations or computations.
- Does not address dissonance costs beyond equality.