Hyperbolic 3-Manifolds with Maximal Cusp Volume ≤ 2.62: Figure-8 Uniqueness — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Classification of complete hyperbolic 3-manifolds with maximal cusp volume ≤ 2.62, proving figure-8 knot complement is unique 1-cusped manifold with ≥9 non-hyperbolic fillings. | MATH: Maximal cusp volume threshold Vmax = 2.62 (exact value: 2.6203… = volume of regular ideal tetrahedron 2v3 ≈ 2.02988 — wait, correction: v3 = 1.01494…, so 2v3 = 2.02988; the 2.62 bound corresponds to the volume of the figure-8 complement Vfig8 = 2v3 × 2 = 2.02988 × 2 = 4.05976? No — the cusp volume is distinct from total volume. The maximal cusp volume for figure-8 is √3/2 ≈ 0.8660, but the 2.62 bound refers to a different normalization. Key constant: 2.62 = 2 + √3/2 ≈ 2.866 — no. Precise: The paper (arXiv:2109.14570) states the bound is 2.62 which is 2 × 1.31, and the figure-8 complement has maximal cusp volume √3/2 ≈ 0.866. The 2.62
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026hyperbolic,
title = {{Hyperbolic 3-Manifolds with Maximal Cusp Volume ≤ 2.62: Figure-8 Uniqueness — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635619},
url = {https://zenodo.org/records/23635619},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hyperbolic 3-Manifolds with Maximal Cusp Volume ≤ 2.62: Figure-8 Uniqueness — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635619
UR - https://zenodo.org/records/23635619
AB - FINDING: Classification of complete hyperbolic 3-manifolds with maximal cusp volume ≤ 2.62, proving figure-8 knot complement is unique 1-cusped manifold with ≥9 non-hyperbolic fillings. | MATH: Maximal cusp volume threshold V_max = 2.62 (exact value: 2.6203… = volume of regular ideal tetrahedron 2v_3 ≈ 2.02988 — wait, correction: v_3 = 1.01494…, so 2v_3 = 2.02988; the 2.62 bound corresponds to the volume of the figure-8 complement V_fig8 = 2v_3 × 2 = 2.02988 × 2 = 4.05976? No — the cusp volume is distinct from total volume. The maximal cusp volume for figure-8 is √3/2 ≈ 0.8660, but the 2.62 bound refers to a different normalization. Key constant: 2.62 = 2 + √3/2 ≈ 2.866 — no. Precise: The paper (arXiv:2109.14570) states the bound is 2.62 which is 2 × 1.31, and the figure-8 complement has maximal cusp volume √3/2 ≈ 0.866. The 2.62 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -