HonestPhaseAdmissible
HonestPhaseAdmissible asserts that zeta phase family data counts as admissible precisely when the annular J-cost of its realized defect sampled family stays bounded under arbitrary mesh refinement. Analysts working on the analytic Riemann hypothesis route via honest phases would cite this predicate to obtain the zero-charge conclusion. The structure is a direct one-field wrapper that imports the bounded-cost property without additional steps.
claimLet $zfd$ be zeta phase family data. Then $zfd$ is honest-phase admissible when there exists a real $K$ such that for every natural number $N$ the annular cost of the mesh-$N$ realization of the sampled family derived from $zfd$ satisfies annular cost at most $K$.
background
Route C narrows the analytic approach to the Riemann hypothesis to honest zeta-derived phase data. The module supplies the admissibility predicate for that data and shows its equivalence to the charge-zero condition required by the zero-free criterion in AnalyticTrace. Zeta phase family data packages the phase information extracted from the meromorphic continuation on the circle, together with the associated sensor and sampled family. The imported predicate RealizedDefectAnnularCostBounded states that the annular J-cost of a realized sampled family remains bounded independently of mesh refinement, replacing an earlier over-strong quantification over arbitrary meshes.
proof idea
The declaration is a structure definition with a single field. That field directly requires the realized defect annular cost to be bounded on the sampled family obtained from the phase family data. No lemmas are applied and no tactics are used; the structure simply names the imported bounded-cost property.
why it matters in Recognition Science
This predicate supplies the central link in Route C. It is invoked to prove that admissible honest phase data has zero charge and to build the global admissibility bridge together with its witnessed counterpart. The witnessed bridge in turn yields the witnessed RH core. In the Recognition framework the predicate connects the eight-tick phase structure and the finite recognition budget to the charge-zero requirement of the analytic trace zero-free criterion.
scope and limits
- Does not prove existence of any honest phase data satisfying the predicate.
- Does not apply to phase families outside the honest zeta class.
- Does not supply an explicit numerical value for the bound K.
- Does not address the full Riemann hypothesis, only the charge-zero implication.
formal statement (Lean)
18structure HonestPhaseAdmissible (zfd : ZetaPhaseFamilyData) : Prop where
19 finiteRecognitionBudget :
20 RealizedDefectAnnularCostBounded (zfd.phaseFamily.toSampledFamily)
21
22/-- Admissible honest phase data has zero charge. -/