rh_iff_all_physical
plain-language theorem explainer
This theorem establishes the equivalence between every defect sensor having zero charge and every defect sensor satisfying the bounded T1 defect criterion for physical existence. Researchers working on Recognition Science unification of the Riemann hypothesis with physical realizability would cite it as the machine-verified bridge between the number-theoretic statement and the ontological existence principle. The proof is a one-line term that directly pairs the two directional implications proved earlier in the module.
Claim. The statements ``every defect sensor has zero charge'' and ``every defect sensor has bounded T1 defect in its Euler ledger scalar state'' are equivalent.
background
A DefectSensor records the multiplicity (charge) of a zero of the zeta function together with its real part in the critical strip. PhysicallyExists holds for a sensor precisely when there exists a uniform real bound K such that the T1 defect of the Euler ledger scalar state remains at most K for every natural number index N. The module replaces an earlier bounded-total-cost ledger with a three-component architecture built on cost divergence for nonzero charge, Euler trace admissibility, and a physically realizable ledger whose T1 defect stays controlled.
proof idea
The proof is a one-line term that constructs the biconditional by pairing the two directional theorems: all_physicallyExist_of_rh (RH implies every sensor physically exists) and rh_from_ontological_dichotomy (every sensor physically exists implies RH). Each direction rests on the ontological dichotomy that equates zero charge with bounded T1 defect.
why it matters
The equivalence supplies the central link in the Unified RH module between the number-theoretic formulation of the Riemann hypothesis and the Recognition Science criterion of T1-bounded realizability. It closes the loop inside the T1-bounded architecture that begins from Euler trace admissibility and cost divergence, feeding the ontological dichotomy into the broader unification chain. No downstream citations are recorded, leaving open its use in larger proofs that would connect the eight-tick octave or the phi-ladder mass formula to the critical strip.
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