A Spectral Criterion for Emergent Gravity
Abstract
We give a source-resolved spectral criterion for long-range tensor exchange between conserved matter sources. Exact channel elimination preserves the propagation kernel together with the source and readout maps and the direct response. Common-space estimates control the residue at the displaced critical root of a finite approximation. A positive Källen-Lehmann representation identifies this residue with a zero-invariant-mass atom even at a continuum endpoint. For a complete positive Lorentz-covariant conserved stress tensor we classify the null-shell measure and prove that its TT atomic weight vanishes. A reduced compact spectral realisation instead carries internal tensor vertices into an external two-helicity response. Conservation reduces the leading vertex of localised stationary matter to its total energy. The mixed residue then factorises into the two energies and a common propagation coefficient. Spatial resolvent estimates determine the potential and force with finite-size corrections. Normalisation through the matter vertex leaves one dimensional calibration for the overall Planck scale. The spectral residue fixes the dimensionless exchange strength. The resulting response admits an Einstein-matter effective description under the stated positivity and helicity assumptions together with universal soft coupling and local nonlinear consistency.
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BibTeX
@misc{guo2026spectral,
title = {{A Spectral Criterion for Emergent Gravity}},
author = {Jinku Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.21621},
eprint = {2607.21621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.21621},
}
RIS
TY - UNPB
TI - A Spectral Criterion for Emergent Gravity
AU - Jinku Guo
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2607.21621
UR - https://arxiv.org/abs/2607.21621
AB - We give a source-resolved spectral criterion for long-range tensor exchange between conserved matter sources. Exact channel elimination preserves the propagation kernel together with the source and readout maps and the direct response. Common-space estimates control the residue at the displaced critical root of a finite approximation. A positive Källen-Lehmann representation identifies this residue with a zero-invariant-mass atom even at a continuum endpoint. For a complete positive Lorentz-covariant conserved stress tensor we classify the null-shell measure and prove that its TT atomic weight vanishes. A reduced compact spectral realisation instead carries internal tensor vertices into an external two-helicity response. Conservation reduces the leading vertex of localised stationary matter to its total energy. The mixed residue then factorises into the two energies and a common propagation coefficient. Spatial resolvent estimates determine the potential and force with finite-size corrections. Normalisation through the matter vertex leaves one dimensional calibration for the overall Planck scale. The spectral residue fixes the dimensionless exchange strength. The resulting response admits an Einstein-matter effective description under the stated positivity and helicity assumptions together with universal soft coupling and local nonlinear consistency.
ER -