Resolution of the Cosmological Constant Problem via Spectral Thermodynamic Invariance

This paper presents a mathematically and physically consistent resolution of the Cosmological Constant Problem (CCP) using a Spectral Thermodynamic Framework derived from bounded-geometry field theory and operator reflection positivity.

Within this construction, the cosmological constant emerges as a renormalization-invariant spectral quantity determined by a canonical Fejér–Hardy evaluator and Seeley–DeWitt coefficients, requiring no fine-tuning or anthropic assumptions. The framework establishes:

• A regulator-independent selection of the physical constant Λₚₕᵧₛ from a unique spectral slope.

• Order-0 bridge operators preserving Osterwalder–Schrader (OS) positivity and enabling Wightman reconstruction.

• A sharp, state-universal Quantum Null Energy Condition (QNEC) with rigidity and a Lyapunov-type stability bound preventing secular drift.

• A renormalization-group (RG) Ward identity that stabilizes Λ across all scales.

• Empirical falsifiability through precise predictions: ρΛ¹ᐟ⁴ ≈ 2.2–2.3 meV and w₀ = −1, wₐ = 0 (any |w₀+1| ≳ 10⁻³ falsifies).

This resolution meets all modern theoretical and observational criteria for the Cosmological Constant Problem smallness, stability, universality, and empirical testability while remaining consistent with General Relativity and Quantum Field Theory.

This paper forms part of a larger unified framework that includes:

• Spectral Thermodynamics and the Quantum Arrow of Time (DOI: 10.5281/zenodo.17545541)

• Unconditional Exterior Resolution of the Quantum Information Paradox via a Canonical Spectral Bridge (DOI: 10.5281/zenodo.17540398)

• A Unified Spectral Framework for Quantum Gravity (DOI: 10.5281/zenodo.17538401)

Together, these works establish a coherent spectral foundation linking quantum information, gravity, and vacuum energy under a single mathematical architecture.

This work provides the structural foundation for subsequent Tier-0 classifications of cosmological dark components. In particular, it underlies the companion analyses Dark Matter as Record-Silent Curvature: A Law-Level Classification Within the Tier-0 Framework (Zenodo DOI: https://doi.org/10.5281/zenodo.18261716) and Dark Energy as a Closure Background: A Tier-0 Law-Level Classification (Zenodo DOI: https://doi.org/10.5281/zenodo.18278767), which apply the same admissibility principles to the distinct observational profiles of dark matter and dark energy.