Knot Invariants: Universal Topology Linking Quantum Computing, DNA, and M-Theory — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Knot invariants (Jones, HOMFLY, Chern-Simons) are the same mathematical objects appearing in quantum computing, DNA topology, and M-theory — topology is a universal language of physical structure. | MATH: Jones polynomial V_K(t) ∈ ℤ[t^{±1/2}]; Chern-Simons action S = (k/4π)∫_M Tr(A∧dA + (2/3)A∧A∧A); Witten's result: ⟨W_K⟩ = ∫DA e^{iS} gives knot invariants as partition functions; skein relation: t^{-1}V(L_+) − tV(L_-) = (t^{1/2} − t^{-1/2})V(L_0). | CONNECTION: Jones polynomial evaluated at roots of unity t = e^{2πi/(k+2)} yields quantum dimensions governed by SU(2) representation theory; quantum group parameter q = e^{2πi/(k+2)}; at k=1, q = e^{2πi/3} (cube root of unity, crystallographic A₂ root system angle 120°); at k=3, q = e^{2πi/5} — the golden ratio φ = (1+√5)/2 emerges as quantum dimension [2]_q = q + q^{-1} = 2cos(2π/5) = 1/φ ≈ 0.618. | DEPTH: 9 --- FINDING: The Jones polynomial's evaluation at q = e^{2πi/5} produces quantum dimensions equal to the golden ratio and Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225129771