IsGloballyMinimal
plain-language theorem explainer
Definition marking a DefectBoundedSubLedger L as globally minimal when its defect equals zero or is at most one. Researchers translating the Hodge conjecture into Recognition Science cite this to isolate proper J-cost critical points within fixed Z-charge classes. The condition is a direct disjunction on the defect value.
Claim. A sub-ledger $L$ is globally minimal if its defect satisfies $defect(L)=0$ or $defect(L)≤1$.
background
The module recasts classical Hodge theory in Recognition Science terms: harmonic forms become J-cost critical sub-ledgers that minimize cost inside each cohomology class labeled by Z-charge. The defect functional is defined as $J(x)$ in the Law of Existence and vanishes at unity. Upstream results supply the active edge count $A=1$ from IntegrationGap and the DefectBoundedSubLedger type from the HodgeConjecture module.
proof idea
This is a definition that directly equates global minimality to the disjunction on defect. It supplies the predicate used by the downstream theorem globally_minimal_gives_cycle.
why it matters
The definition feeds the theorem globally_minimal_gives_cycle that extracts a JCostMinimalCycle from any such L. It supplies the non-trivial criticality condition for the RS Hodge harmonic forms, consistent with J-uniqueness (T5) and the phi fixed point (T6) in the forcing chain.
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