routeC_completion_boundary
Route C completion boundary shows that the witnessed honest-phase admissibility bridge forces every witnessed defect sensor to carry zero charge and is equivalent to that zero-charge condition. Number theorists deriving the Riemann hypothesis from the Recognition Composition Law cite this as the final witnessed core link before Euler ledger transport. The proof is a one-line term that directly pairs the implication lemma with the equivalence lemma.
claimLet $B$ be the witnessed honest-phase admissibility bridge. Then $B$ implies that every witnessed defect sensor has charge zero, and $B$ holds if and only if every witnessed defect sensor has charge zero.
background
A witnessed defect sensor records a complex point rho inside the critical strip, an integer charge, and a meromorphic-order witness that the charge arises from the reciprocal zeta function. The witnessed honest-phase admissibility bridge is the carrier structure asserting that every honest phase-family datum from such a sensor is admissible under the Euler carrier with finite recognition budget. The module performs final assembly of the Riemann hypothesis from the Recognition Composition Law, with BoundaryTransportCert as the remaining nontrivial datum that transports annular collapse to the T1-bounded Euler ledger boundary.
proof idea
The proof is a term-mode one-liner that supplies the pair consisting of the direct implication from the admissibility bridge to the zero-charge condition together with the already-proved equivalence between the bridge and the zero-charge statement.
why it matters in Recognition Science
This declaration completes the Route C boundary in the derivation of the Riemann hypothesis from the Recognition Composition Law. It packages the implication that honest-phase admissibility forces the witnessed zero-free region together with the equivalence that the bridge is precisely that zero-free region. The result closes the witnessed core inside NumberTheory.RH_From_RCL before any transport to the Euler ledger boundary.
scope and limits
- Does not prove the Riemann hypothesis without the admissibility bridge assumption.
- Does not extend to defect sensors lacking explicit meromorphic order witnesses.
- Does not address the non-witnessed form of the Riemann hypothesis.
- Does not connect directly to the physical transport certificate.
formal statement (Lean)
37theorem routeC_completion_boundary :
38 (WitnessedHonestPhaseAdmissibilityBridge →
39 ∀ sensor : WitnessedDefectSensor, sensor.charge ≠ 0 → False) ∧
40 (WitnessedHonestPhaseAdmissibilityBridge ↔
41 (∀ sensor : WitnessedDefectSensor, sensor.charge = 0)) := by
proof body
Term-mode proof.
42 exact ⟨direct_rh_from_witnessedAdmissibilityBridge,
43 witnessedHonestPhaseAdmissibilityBridge_iff_rh⟩
44
45end NumberTheory
46end IndisputableMonolith