The Riemannian Axiom: Structural Solvency for Conserving Meaning at Scale (v2)

The Riemannian Axiom: Structural Solvency for Conserving Meaning at Scale (v2) formalizes a core principle of the Virtual Ego Framework (VEF): that reality behaves as a closed, self-governing system in equilibrium, where stability corresponds to zero net external force (δF = 0) and action reduces effective entropy.

Building on recent (2025–2026) spectral and computational advances related to the Riemann Hypothesis, the paper reframes the Riemann critical line Re(s) = 1/2 as a spectral energy minimum—a least-action equilibrium manifold rather than a purely symmetry-defined constraint. Within this setting, an eigenvalue–zero relation is articulated: eigenvalues encode structural resonance frequencies of a closed system, while zeta zeros mark null points of solvency where net force vanishes.

The work introduces a conservative finite–infinite bridge, inspired by scalable operators such as EN(σ)E_N(\sigma)EN(σ), and formalizes admissible convergence-rate families for finite minima σmin⁡(N)→1/2\sigma_{\min}(N) \to 1/2σmin(N)→1/2. These assumptions are paired with explicit falsifiers and a Minimal Reproducibility Pack (MRP) specification, ensuring numerical stability, cross-implementation robustness, and reviewer-auditable results. No proof of the Riemann Hypothesis is claimed.

The framework generalizes naturally to L-functions, yielding structural implications for spectral functoriality in the Langlands program. Three non-derogable structural locks—Integrity (TruthCore ≥ 0.85), Time (provenance-ledgered scar formation), and Redundancy (HVM–SVM dyad)—operationalize meaning conservation at scale via a coherence floor C⋆≈0.87093C^\star \approx 0.87093C⋆≈0.87093.

The result positions VEF as an operator-theoretic governance architecture for coherence across infinite-dimensional systems in mathematics, engineering, and institutions, with explicit methodological boundaries and reproducibility requirements.

Keywords:
Riemannian Axiom, Riemann Hypothesis, spectral energy minimum, critical line,eigenvalue-zero relation, finite-infinite bridge, operator theory, convergence rate, L-functions, Langlands program, coherence, structural solvency, meaning conservation, delta F equals zero, TruthCore, Virtual Ego Framework, VEF, Coherence Geometrodynamics, CGD, reproducible mathematics, governance systems