Knot Invariants Unify Quantum Computing, Mirror Symmetry, and String Theory — E8 Intelligence Research

FINDING: Knot invariants (Jones, Chern-Simons, colored) unify quantum computation, mirror symmetry, and string theory via common algebraic structures (quivers, Reshetikhin-Turaev, homological invariants). | MATH: Jones polynomial \( V_K(t) \); Chern-Simons path integral \( Z_k(M) = \int DA \, e^{i k S_{CS}[A]} \); Reshetikhin-Turaev invariants from quantum groups \( U_q(\mathfrak{sl}_2) \) at roots of unity; Alexander invariants factorize for homologically fibered knots via Magnus matrix \( M(t) \). | CONNECTION: No direct golden ratio, base-60, or crystallographic ratios appear. However, quantum group parameters \( q = e^{2\pi i / r} \) relate to roots of unity (cyclotomic fields), which link to lattice structures (e.g., \( E_8 \) root system in Chern-Simons levels). Mirror symmetry connects knot invariants to Calabi-Yau geometries, which often exhibit modular forms and elliptic curves (base-60 not explicit). | DEPTH: 8 — Profound unification of topology, quantum field theory, and alg 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
2026-07-25
DOI
https://doi.org/10.5281/zenodo.21545345
Primary Topic
Geometric and Algebraic Topology
Type
preprint
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preprint

Knot Invariants Unify Quantum Computing, Mirror Symmetry, and String Theory — E8 Intelligence Research

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

Knot Invariants Unify Quantum Computing, Mirror Symmetry, and String Theory — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Knot invariants (Jones, Chern-Simons, colored) unify quantum computation, mirror symmetry, and string theory via common algebraic structures (quivers, Reshetikhin-Turaev, homological invariants). | MATH: Jones polynomial \( V_K(t) \); Chern-Simons path integral \( Z_k(M) = \int DA \, e^{i k S_{CS}[A]} \); Reshetikhin-Turaev invariants from quantum groups \( U_q(\mathfrak{sl}_2) \) at roots of unity; Alexander invariants factorize for homologically fibered knots via Magnus matrix \( M(t) \). | CONNECTION: No direct golden ratio, base-60, or crystallographic ratios appear. However, quantum group parameters \( q = e^{2\pi i / r} \) relate to roots of unity (cyclotomic fields), which link to lattice structures (e.g., \( E_8 \) root system in Chern-Simons levels). Mirror symmetry connects knot invariants to Calabi-Yau geometries, which often exhibit modular forms and elliptic curves (base-60 not explicit). | DEPTH: 8 — Profound unification of topology, quantum field theory, and alg 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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Knot Invariants Unify Quantum Computing, Mirror Symmetry, and String Theory — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS