Quantum Energy Conditions from Spectral Thermodynamics: A Falsifiable Framework for Universal Energy Bounds

This paper establishes a rigorous and falsifiable framework for quantum energy conditions derived from spectral thermodynamics.

It unifies operator positivity, Page-curve entropy dynamics, and spectral determinants under a single canonical Fejér–Hardy normalization.

The construction extends the canonical spectral bridge introduced in A Unified Spectral Framework for Quantum Gravity and Unconditional Exterior Resolution of the Quantum Information Paradox, showing that energy conservation, entropy flow, and quantum information are governed by one universal spectral law.

The result is a self-contained and testable closure of the quantum energy conditions problem, linking thermodynamic irreversibility, information recovery, and gravitational energy constraints in a single mathematical framework.

Related work:

Quantum Information Paradox

Spectral Framework for Quantum Gravity

Quantum Arrow of Time

Cosmological Constant Problem

See also: The Tier–Omega Monad: Trans-Recursive Completion of the Everything Equation (DOI: 10.5281/zenodo.17859631), which establishes the unique trans-recursive invariant that terminates all possible meta-law recursion and completes the Everything Equation. This work provides the structural boundary underlying the entire framework developed in the associated papers.