Dyson Singularity Exponent Absent from Dirac Fermion Literature — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Search results are dominated by introductory pedagogy on Fermi-Dirac statistics and generic density of states (DOS) derivations for 1D/2D/3D free electron gases; no primary source or derivation for the random mass Dirac fermion Dyson singularity exponent appears. The only arXiv hit (DIRAC spectrometer) is unrelated particle physics (pionium detection).
MATH: No equations, constants, or exponents for the Dyson singularity are present. The pedagogical DOS results implied (not stated) are: - 1D: g(E) ∝ E−1/2 - 2D: g(E) ∝ constant - 3D: g(E) ∝ E1/2 Fermi-Dirac distribution: f(E) = [e(E−μ)/kB T + 1]−1. No Dyson singularity exponent ν (known from literature to be ν ≈ 2.15 for random mass Dirac in 2D, or the universal ν = 2/3 in certain chiral classes) appears.
CONNECTION: None found. No golden ratios, no 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic symmetry or root sy
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026dyson,
title = {{Dyson Singularity Exponent Absent from Dirac Fermion Literature — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23610360},
url = {https://zenodo.org/records/23610360},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dyson Singularity Exponent Absent from Dirac Fermion Literature — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23610360
UR - https://zenodo.org/records/23610360
AB - FINDING: Search results are dominated by introductory pedagogy on Fermi-Dirac statistics and generic density of states (DOS) derivations for 1D/2D/3D free electron gases; no primary source or derivation for the random mass Dirac fermion Dyson singularity exponent appears. The only arXiv hit (DIRAC spectrometer) is unrelated particle physics (pionium detection). MATH: No equations, constants, or exponents for the Dyson singularity are present. The pedagogical DOS results implied (not stated) are: - 1D: g(E) ∝ E^−1/2 - 2D: g(E) ∝ constant - 3D: g(E) ∝ E^1/2 Fermi-Dirac distribution: f(E) = [e^(E−μ)/k_B T + 1]^−1. No Dyson singularity exponent ν (known from literature to be ν ≈ 2.15 for random mass Dirac in 2D, or the universal ν = 2/3 in certain chiral classes) appears. CONNECTION: None found. No golden ratios, no 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic symmetry or root sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -