zeroInducedBridge_iff_rh
plain-language theorem explainer
The zero-induced proxy physicalization bridge holds precisely when the Riemann hypothesis is true. Number theorists connecting directed Euler ledgers to zeta zeros cite this equivalence to show that the remaining gap in the recognition-science physicalization thesis is exactly the classical Riemann hypothesis. The proof is a term-mode biconditional that assembles the forward implication through the RS thesis and the converse that renders the bridge vacuous under the hypothesis.
Claim. The statement that every non-trivial zero ρ of the Riemann zeta function with 1/2 < Re(ρ) < 1 induces a zeta defect sensor satisfying the proxy physicalization bridge is equivalent to the Riemann hypothesis.
background
In the Proxy Physicalization Bridge module the directed Euler ledger system has already been shown admissible and realizable for finite prime supports. The remaining step is to transport from the bounded proxy state to actual physical existence for zeta-zero sensors. ZeroInducedProxyPhysicalizationBridge is defined as the universal quantification over all non-trivial zeros ρ of ζ with real part strictly between 1/2 and 1, asserting that the corresponding zetaDefectSensor satisfies the proxy physicalization bridge. Upstream results establish that this bridge is equivalent to charge zero and to physical existence for each sensor, and that the zero-induced version is equivalent to the RS physical thesis.
proof idea
The proof is a term-mode biconditional that directly pairs the forward implication through the RS thesis with the converse that assumes the hypothesis to eliminate strip zeros. It applies the extraction of the RS physical thesis from the zero-induced bridge followed by the known implication to the Riemann hypothesis, then uses the equivalence to absence of strip zeros to show the hypothesis forces the antecedent false for any strip zero.
why it matters
This theorem closes the reduction chain in the Proxy Physicalization Bridge module by proving that the directed-ledger infrastructure isolates exactly the Riemann hypothesis as the remaining gap. It feeds the equivalence to the RS physical thesis and ultimately confirms that the recognition-science physicalization claim reduces to the classical zeta-zero location problem. In the framework it aligns with the functional equation by showing no additional hypotheses are required beyond the already-proved admissibility results.
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