PreprintCC BY 4.0Zenodo
The Barbero–Immirzi Parameter, Black-Hole Entropy, and the Area Gap from the R12 Rendering Algebra: McKayFolding, the SU(2)4 Horizon Category, and the Complete Entropy Expansion
Abstract
The Barbero–Immirzi parameter is derived as γBI = ln2/(π√3) = 0.127384 from the rendering algebra R12 = M3(C)⊗ M4(C) of Array Cosmology, as the exact solution of the Domagała–Lewandowski normalization restricted to the puncture spectrum the algebra admits. The restriction is a theorem: the rotation module of M4(C) ∼=Cl(3,1)⊗Cis 1 2 ⊕ 1 2 with Casimir 3 4, so horizon punctures carry spin 1 2 exclusively.
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BibTeX
@misc{lim2026barberoimmirzi,
title = {{The Barbero–Immirzi Parameter, Black-Hole Entropy, and the Area Gap from the R12 Rendering Algebra: McKayFolding, the SU(2)4 Horizon Category, and the Complete Entropy Expansion}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603597},
url = {https://zenodo.org/records/23603597},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Barbero–Immirzi Parameter, Black-Hole Entropy, and the Area Gap from the R12 Rendering Algebra: McKayFolding, the SU(2)4 Horizon Category, and the Complete Entropy Expansion
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603597
UR - https://zenodo.org/records/23603597
AB - The Barbero–Immirzi parameter is derived as γBI = ln2/(π√3) = 0.127384 from the rendering algebra R12 = M3(C)⊗ M4(C) of Array Cosmology, as the exact solution of the Domagała–Lewandowski normalization restricted to the puncture spectrum the algebra admits. The restriction is a theorem: the rotation module of M4(C) ∼=Cl(3,1)⊗Cis 1 2 ⊕ 1 2 with Casimir 3 4, so horizon punctures carry spin 1 2 exclusively.
ER -