RH is equivalent to cofinal original quartet half-bound windows
ProvedConnesGreen.mathlib_RH_iff_cofinal_quartet_half_windowsFor every actual critical-strip zeta zero, retain its original reflected/conjugate quartet and canonical inner Picard marker on the original completed Dirichlet carrier. Mathlib RH holds exactly when, for each such quartet and each real lower bound B, there exists a positive support radius T greater than B at which the quartet marker is at least one half of the identity. The good windows need not initially be specified at every radius: support-window antitonicity recovers all smaller positive windows. An assumed off-line quartet has a certified finite last good radius, so it forbids this cofinal condition. This sharply specifies a sufficient and necessary global arithmetic target using only the existing finite actual-zero quartets. The theorem proves neither RH nor that the half-bounds actually persist to arbitrarily large windows; a bound at a single inner or right endpoint is not the quantified condition.
import Definitions.Def_ConnesGreen_RG0_original_inner_marker import Definitions.Def_ConnesGreen_original_quartet open Complex MeasureTheory ConnesRZ ConnesRZFrontier ConnesRZQuartet ConnesGreen WeilDefect WeilDefect.ConnesNative open scoped InnerProductSpace lp ENNReal Classical ComplexOrder Topology set_option autoImplicit false set_option maxHeartbeats 3000000 noncomputable section
theorem ConnesGreen.mathlib_RH_iff_cofinal_quartet_half_windows :
RiemannHypothesis ↔ ∀ ρ : CriticalZeros, ∀ B : ℝ,
∃ T : ℝ, ∃ hT : 0 < T, B < T ∧
(1 / 2 : ℝ) • (1 : ℓ²({τ : CriticalZeros // τ ∈ quartet ρ}, ℂ) →L[ℂ]
ℓ²({τ : CriticalZeros // τ ∈ quartet ρ}, ℂ)) ≤
canonicalPicardMarker T hT (quartet ρ) := by sorry
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.