ForcedInvariant
plain-language theorem explainer
A forced invariant is a triple: a reality claim, a witness that it lies in the forcing closure of a given primitive, and a proof that the claim holds on every admissible realization. Layer universes (cost/J, phi, alpha, hbar, gravity) register their forced claims as instances of this structure. Pure structure definition; no proof body.
Claim. For a primitive $P$ and a claim universe $U$, a forced invariant consists of a reality claim $C$ on the realizations of $U$ such that $C$ belongs to the forcing closure of $P$ in $U$, and $C$ holds in every realization admissible under $U$'s admissibility class.
background
Maximal forcing classifies every claim in a closure target as forced, independent, or selected. Selected is temporary: it must be promoted to forced by a stronger admissibility condition or demoted to independent by a countermodel.
A claim universe packages a type of realizations, an admissibility class on that type, and a set of reality claims. The forcing closure of a primitive $P$ relative to $U$ is the set of claims in scope for maximal closure from $P$; membership is written InClosure. A claim is forced on an admissible class when it holds in every admissible realization.
The structure simply bundles those three pieces: the claim, the closure witness, and the forcedness proof.
proof idea
Definition only: a structure with three fields (claim, in-closure proof, forcedness proof). No tactics or lemmas. Instantiation is by supplying a concrete RealityClaim, an InClosure membership proof, and a Forced universal quantification over admissible realizations.
why it matters
This is the Phase-2 forced-register type. Downstream layer universes populate it: isJForcedInvariant (J-cost uniqueness, T5), isPhiForcedInvariant (phi fixed point, T6), alphaForcedInvariant (fine-structure window), hbarForcedInvariant (action quantum), and gravForcedInvariant (Einstein coupling). Each entry is rooted at the Law-of-Logic primitive and carries a real forcedness proof, so the corresponding universe can be marked fully classified. Without this packaging, forced claims would not share a uniform register type across the RS constant ladder.
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