Greedy 1-Skeleton Homology Basis on Genus-2 Surfaces: A Pedagogical Review — E8 Intelligence Research

FINDING: Homology basis computation on genus-2 surfaces is algorithmic via greedy 1-skeleton methods, but the search results are pedagogical videos, not primary research — no new mathematical result is presented. | MATH: No equations, constants, or ratios are extracted from these sources; they reference standard algebraic topology (simplicial homology, Mayer–Vietoris sequence, homotopy basis of genus-g surface with 2g fundamental cycles). | CONNECTION: Genus-2 surface has Euler characteristic χ = 2 − 2g = −2; its fundamental group has 4 generators with one relation — this is a hyperbolic surface whose optimal pants decomposition relates to Fenchel–Nielsen coordinates, but no golden-ratio or base-60 link appears in the given material. | DEPTH: 2 — These are expository videos on existing topology; no novel insight, no harmonic constants, no crystallographic or number-theoretic resonance. The only faint connection: genus-2 surfaces admit constant negative curvature (hyperbolic geometry), Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-18
DOI
https://doi.org/10.5281/zenodo.23446756
Primary Topic
Geometric and Algebraic Topology
Type
preprint
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Greedy 1-Skeleton Homology Basis on Genus-2 Surfaces: A Pedagogical Review — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
preprint

Greedy 1-Skeleton Homology Basis on Genus-2 Surfaces: A Pedagogical Review — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Homology basis computation on genus-2 surfaces is algorithmic via greedy 1-skeleton methods, but the search results are pedagogical videos, not primary research — no new mathematical result is presented. | MATH: No equations, constants, or ratios are extracted from these sources; they reference standard algebraic topology (simplicial homology, Mayer–Vietoris sequence, homotopy basis of genus-g surface with 2g fundamental cycles). | CONNECTION: Genus-2 surface has Euler characteristic χ = 2 − 2g = −2; its fundamental group has 4 generators with one relation — this is a hyperbolic surface whose optimal pants decomposition relates to Fenchel–Nielsen coordinates, but no golden-ratio or base-60 link appears in the given material. | DEPTH: 2 — These are expository videos on existing topology; no novel insight, no harmonic constants, no crystallographic or number-theoretic resonance. The only faint connection: genus-2 surfaces admit constant negative curvature (hyperbolic geometry), Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
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