pith. machine review for the scientific record. sign in
module module moderate

IndisputableMonolith.Foundation.UniversalForcing.MetaphysicalRealization

show as:
view Lean formalization →

The MetaphysicalRealization module defines a metaphysical ground as the structural principle that assigns every Law-of-Logic realization its forced arithmetic while guaranteeing canonical identity across all such realizations. It extends the imported BiologyRealization, where generation count serves as carrier and reproduction as generator. Researchers working on the Recognition Science forcing chain would cite this module to secure uniqueness of arithmetic objects. The module consists of definitions and a uniqueness statement with no proofs.

claimA metaphysical ground is a structural principle $G$ such that for every Law-of-Logic realization $R$, $G(R)$ yields the forced arithmetic object with the property that $G(R) = G(R')$ canonically for all realizations $R, R'$.

background

This module sits inside the Universal Forcing section of the Foundation layer and imports BiologyRealization. The upstream module supplies a lightweight biological carrier whose objects are generation counts and whose generator is the reproductive step. The metaphysical ground is introduced as the principle that maps each realization of the Law of Logic to its forced arithmetic while enforcing that all such arithmetic objects coincide. Sibling declarations include MetaphysicalGround, universalGround, and the uniqueness lemma metaphysical_ground_unique.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the metaphysical-ground definitions that feed directly into the AxiomAudit module, which assembles the reproducible theorem surface for the entire Universal Forcing Lean program. It closes the step that guarantees canonical arithmetic objects for every Law-of-Logic realization, linking the biological carrier to the broader forcing chain.

scope and limits

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (4)