direct_rh_from_honestPhaseChargeZeroBridge
Any direct honest-phase charge-zero bridge forces every witnessed defect sensor to have vanishing charge, thereby discharging the analytic core of the Riemann hypothesis. Researchers pursuing axiom-free derivations of RH from zeta phase data would cite this to complete the pure analytic route without external boundary assumptions. The proof is a one-line term wrapper that extracts a ZeroFreeCriterion from the bridge and feeds it directly into rh_from_zero_free_criterion.
claimIf a structure exists such that honest zeta phase family data implies zero charge for the associated sensor, then no witnessed defect sensor has nonzero charge.
background
The Analytic Trace module builds an axiom-free interface for the Riemann hypothesis by assembling carrier-side infrastructure from the sampled Euler package, floor-coverage theorems, and phase data. Former axioms for zero winding and charge-zero forcing have been replaced by proved results such as contour winding from holomorphy and the floor-covered iff charge-zero equivalence. HonestPhaseChargeZeroBridge is the structure that directly supplies the charge-zero conclusion: for every ZetaPhaseFamilyData the sensor charge vanishes. This discharges the ZeroFreeCriterion needed by the analytic route, as described in the module's account of the two RH paths (ontology via EulerBoundaryBridgeAssumption versus pure analytic via honest phase data). Upstream lemmas include rh_from_zero_free_criterion, which converts a satisfied ZeroFreeCriterion into the RH statement, and the extractor zeroFreeCriterion_of_honestPhaseChargeZeroBridge.
proof idea
The proof is a one-line term wrapper. It first applies zeroFreeCriterion_of_honestPhaseChargeZeroBridge to the supplied HonestPhaseChargeZeroBridge to obtain a ZeroFreeCriterion, then feeds that criterion into rh_from_zero_free_criterion.
why it matters in Recognition Science
This theorem completes the pure analytic route to the Riemann hypothesis core inside the Recognition framework by showing that any honest-phase charge-zero bridge suffices. It sits downstream of the floor-coverage and charge-zero extractor lemmas and targets the analytic RH statement that complements the ontology route in UnifiedRH. The result advances the module's goal of eliminating axioms while preserving the connection to the eight-tick phase structure and the charge-zero condition required for the analytic trace.
scope and limits
- Does not construct or prove existence of an honest-phase charge-zero bridge.
- Does not address the ontology route that relies on EulerBoundaryBridgeAssumption.
- Does not derive the full unified RH theorem.
- Does not supply numerical verification or explicit zeta phase data.
formal statement (Lean)
235theorem direct_rh_from_honestPhaseChargeZeroBridge
236 (hb : HonestPhaseChargeZeroBridge) :
237 ∀ (sensor : WitnessedDefectSensor), sensor.charge ≠ 0 → False :=
proof body
Term-mode proof.
238 rh_from_zero_free_criterion
239 (zeroFreeCriterion_of_honestPhaseChargeZeroBridge hb)
240
241/-! ### §4c. Vector C insertion point -/
242
243/-- A successful Vector C bridge is exactly a mechanism that turns honest
244zeta-derived phase data into a `ZeroCompositionWitness` for the witnessed zero.
245
246Once this structure is instantiated, the existing analytic RH route closes
247without any further changes to the `ZeroFreeCriterion` contract. -/