IndisputableMonolith.Foundation.UniversalForcing.Strict.Invariance
This module asserts that every strict realization yields forced arithmetic canonically equivalent to LogicNat. Researchers extending categorical foundations to physical forcing would cite the result. The module imports the categorical realization hook and states the invariance directly from that surface.
claimFor every strict realization $R$, the derived forced arithmetic satisfies $A_R \cong \mathrm{LogicNat}$.
background
The module belongs to the Strict subcategory of UniversalForcing and imports the Categorical module. That upstream module supplies a Lawvere-style realization hook whose carrier is the canonical LogicNat NNO surface from CategoricalLogicRealization. The local setting therefore treats strict realizations as those whose arithmetic is forced onto this fixed natural-numbers object.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The invariance result feeds the Music module, which builds domain-rich musical realizations over positive frequency ratios using equality-cost comparison. It closes the strict pass of the forcing chain by guaranteeing that arithmetic remains LogicNat before richer costs are introduced.
scope and limits
- Does not treat non-strict realizations.
- Does not refine the NNO to full Mathlib category theory.
- Does not introduce explicit arithmetic operations beyond the equivalence.
- Does not address psychoacoustic costs; those appear only downstream.