honestPhaseAdmissibilityBridge_iff_chargeZeroBridge
plain-language theorem explainer
The theorem proves logical equivalence between the global honest-phase admissibility bridge and the direct charge-zero bridge for all zeta phase family data. Analysts working on the analytic route to the Riemann hypothesis in Recognition Science would cite this to link admissibility directly to the zero-free criterion. The proof is a term-mode construction that pairs the two directional implications already established as sibling declarations in the same module.
Claim. The structure requiring that every zeta phase family datum is honest-phase admissible is logically equivalent to the structure requiring that every such datum has sensor charge equal to zero.
background
The Honest Phase Admissibility module develops Route C, which narrows the analytic Riemann hypothesis target to honest zeta-derived phase data. HonestPhaseAdmissibilityBridge is the structure asserting that for all ZetaPhaseFamilyData zfd the datum satisfies the HonestPhaseAdmissible predicate. This is compared to HonestPhaseChargeZeroBridge from AnalyticTrace, which asserts that the sensor charge of every zfd equals zero and thereby discharges the charge-zero field of ZeroFreeCriterion.
proof idea
The proof is a one-line term that constructs the biconditional by supplying the pair of implications chargeZeroBridge_of_admissibilityBridge and admissibilityBridge_of_chargeZeroBridge. These directional maps are the sibling declarations that convert between the two bridge structures.
why it matters
The equivalence supplies the missing link that lets the honest-phase admissibility predicate discharge the charge-zero requirement inside AnalyticTrace.ZeroFreeCriterion. It thereby advances the analytic route to the Riemann hypothesis within the Recognition Science framework, where the eight-tick phase structure and integration gap supply the underlying phase data. The result touches the open question of whether the full zero-free criterion can be established from honest phase data alone.
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