Arithmetic Non-Realizability of Off-Line Blaschke Factors in the Riemann Zeta Function: Constraint Metric Tensor and the Bound Λ ≤ 0.081

We study constraints on hypothetical zeros of the Riemann zeta function lying off the
critical line Re(s) = 1/2 , using only the partial-fraction structure of ζ′/ζ, the Levinson lower
bound N0(T) ≥ cT log T, the Ingham zero-density estimate, Titchmarsh bounds, and the
Hadamard factorization of ξ. The framework is organized into three layers.
Layer A (rigorous). We establish, as theorems, an Apollonius disc confinement of vanishing radius, a self-consistency upper bound h0 ≤ Ln/(2√Cn), measure collapse, monotone decrease of an auxiliary functional, antisymmetry of ξ′/ξ, the Hadamard curvature identity, a Blaschke inner-function characterization with explicit obstruction remark, a concavity equivalence chain on the critical line, and the unconditional bound Λ ≤ 0.081 on the de Bruijn-Newman constant via the two-zero collision-time argument combined with the critical-strip constraint h0 < 1/2 , improving on the Platt-Trudgian bound Λ ≤ 0.2 by a factor of 2.5.
Layer B (numerical observations). A 5 × 5 Gram tensor Gij of five independent prime-side weight classes is introduced; the structural inequality E(T)/B(T) → ∞ between constraint energy and Poisson capacity is rigorous, while observations of universal collision-time ratio η = 0.456 ± 0.002, square-root Speiser scaling, and Cn ∈ [1.002, 2.306] across all
1999 tested gaps are supported by computations at 25-digit precision with 2000 zeros.
Layer C (conjectural). We formulate Arithmetic Non-Realizability: nontrivial off-line Blaschke factors of ξ lie outside the Euler-realizability set Rζ . This reformulates the obstruction at the prime side, motivated by Theorem 12.1 which shows that analytical methods on the critical line cannot distinguish Φoff ≡ 1 from Φoff ̸≡ 1.