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A Basis-Sensitive Companion to Spectral Dimension: Heat-Kernel Concentration Observables for Diffusion Geometry

James Bowling

Published Mar 8, 2026• 1 citation
Publisher

Abstract

This preprint introduces basis-sensitive coherence observables for self-adjoint generators and benchmarks them against spectral dimensino, disorder localization, and modular-Hamiltonian structure. The results show that the proposed observables capture operator structure not visible to eigenvalue-only diagnostics and can distinguish modular architectures even when entanglement entropy is nearly matched.

DOI
10.5281/zenodo.18912721

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This preprint introduces basis-sensitive coherence observables for self-adjoint generators and benchmarks them against spectral dimensino, disorder localization, and modular-Hamiltonian structure. The results show that the proposed observables capture operator structure not visible to eigenvalue-only diagnostics and can distinguish modular architectures even when entanglement entropy is nearly matched.
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We present a minimal and testable mechanism for the emergence of spacetime from quantum information within the framework of Universal Modular Dynamics (UMD). Starting from the density operator ρ and the modular generator K = −log ρ, we construct a robust operator-level geometry via commutator structures. We demonstrate that all static information-theoretic constructions—including entropy, mutual information, and spectral embeddings—fail to generate a consistent notion of spacetime. We then introduce dynamical diagnostics based on the propagation of distinguishability and show that spacetime emerges if and only if distinguishability propagates with finite speed and maintains locality, forming a light-cone structure. This leads to a phase classification of quantum dynamics into three regimes: no propagation, fast mixing, and localized propagation, the latter uniquely corresponding to emergent spacetime. Our results establish spacetime as a dynamical phase rather than a fundamental structure and provide a concrete, falsifiable criterion for its existence.