IndisputableMonolith.Foundation.MaximalForcing.Primitive
Defines the primitive vocabulary of maximal forcing: reality claims, forced versus independent status, and selection principles that pick among admissible options. Downstream modules import this layer rather than inventing their own base types. The two constructors of the primitive are kept intentionally distinct so equivalence can be proved later, not assumed. Pure definitional scaffolding; no theorems live here.
claimIntroduce a primitive type $\mathsf{Primitive}$ with two distinct constructors, together with the derived notions of a reality claim, forced status, independence, a selection principle, and the selected outcome of such a principle. Equivalence of the two constructors is deferred.
background
Maximal forcing is the Recognition Science discipline that refuses free parameters: every claim about physical reality is either forced by the current admissible laws or shown independent by countermodel. This module is the bottom of that stack. It only imports Mathlib and exports named types and predicates used everywhere above it.
The doc-comment states the design rule explicitly: the two constructors of the primitive are kept distinct so later modules can prove their equivalence rather than silently identify them. Sibling names in the module sketch the intended ontology: a reality claim, forced versus independent status relative to an admissible class, a selection principle that chooses among still-open options, and the selected outcome of that principle.
The local setting is pure foundation. No J-cost, phi-ladder, or eight-tick structure appears yet; those enter only after admissible realization classes are defined and tightened.
proof idea
This is a definition module, no proofs. It declares the primitive inductive (or structure) type and the companion predicates and types (reality claim, forced, independent, selection principle, selected) that later forcing modules quantify over. Argument structure is deferred to importers.
why it matters in Recognition Science
Feeds the admissible-realization layer directly: AdmissibleRealization imports this module as its base vocabulary. That downstream module states the maximal-forcing rule of engagement: if a claim is not forced on the current admissible class, either tighten admissibility by a deeper law or prove independence by countermodel. Without a shared primitive, those moves would not type-check against a common claim language.
In the broader Recognition forcing chain (T0–T8), this file is infrastructure rather than a numbered forcing step. It does not itself force $J$, $\varphi$, the eight-tick octave, or $D=3$; it only supplies the claim/forced/independent grammar those later arguments speak. Keeping the two primitive constructors non-identified is the open hinge later equivalence proofs must close.
scope and limits
- Does not prove equivalence of the two primitive constructors.
- Does not define admissible realization classes or tightening laws.
- Does not force any physical constant, dimension, or cost functional.
- Does not contain theorems; only type and predicate scaffolding.
- Does not establish independence via countermodels.