Substrate

This module formalizes:

• se100.def.Substrate — Substrate

A substrate is a shared representational base providing stable reference for entities, occurrences, and institutional artifacts.

Stable reference is supplied by a referential regime consisting of individuation, co-reference, and persistence conditions.

The commitment-theory projection supports the paper's subsequent definition of substrate-layer commitment. No consistency, admissibility, neutrality, extension-stability, finiteness, enumeration, or decidability condition is built into the substrate interface.

structure SE.Substrate.SubstrateSystem (L : Logic.Language.PropositionalLanguage) (R : Referent.ReferentCarriers) : Type (max (max u (v + 1)) (w + 1))

An abstract interface for substrates over a propositional language and fixed referent carriers.

Each substrate supplies:

• its substrate-layer commitment theory; and
• the referential regime by which it provides stable reference.

Compatibility with admissible frameworks is stated separately by later framework-relative and neutrality properties.

• Carrier : Type w

  The carrier of candidate substrates.

• commitments : self.Carrier → Logic.Theory.CommitmentTheory L.carrier

  The complete substrate-layer commitment theory associated with a substrate.

• referentialRegime : self.Carrier → ReferentialRegime R

  The individuation, co-reference, and persistence conditions by which a substrate fixes and tracks its referents.