What question did this study set out to answer?

Investigate how knot polynomial invariants provide a unified mathematical framework bridging classical fluid dynamics, topological quantum field theory, and quantum computing through braid group representations.

September 14, 2026Open Access

Knot Invariants Unify Fluid Helicity, Chern-Simons Theory, and Quantum Computing — E8 Intelligence Research

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Knot polynomial invariants, including the Jones, Alexander, and HOMFLY-PT polynomials, unify fluid helicity, Chern-Simons theory, and quantum computing via braid group representations. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

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Investigate how knot polynomial invariants provide a unified mathematical framework bridging classical fluid dynamics, topological quantum field theory, and quantum computing through braid group representations.
Formulated mathematical linkages connecting the Jones polynomial, Alexander polynomial, and HOMFLY-PT invariants to physical systems.
Evaluated fluid helicity as linking numbers for disjoint loops and derived Chern-Simons gauge theory invariants using Wilson loop expectation values.
Analyzed algebraic properties across roots of unity, focusing on Temperley-Lieb algebra dimensions and connections to the golden ratio.
Demonstrated that knot polynomial invariants unify fluid helicity, Chern-Simons theory, and topological quantum computing via braid group representations.
Established that evaluating the Jones polynomial at fifth roots of unity ($t=e^{2\pi i/5}$) yields relations to the golden ratio ($\\phi \\approx 1.618$) via $2\cos(2\pi/5) = \phi^{-1}$.
Showed that Temperley-Lieb algebra dimensions evaluated at $q=e^{i\pi/5}$ correspond directly to Fibonacci numbers.

Implication

Mathematical analysis demonstrates unification of fluid helicity, Chern-Simons gauge theory, and quantum computing via knot polynomials, highlighting shared topological foundations across physics.

Abstract

FINDING: Knot polynomial invariants (Jones, Alexander, HOMFLY-PT) unify fluid helicity, Chern-Simons theory, and quantum computing via braid group representations. | MATH: Jones polynomial $V_L(t)$ from Kauffman bracket $ L = ∑smoothings Aᵗʷⁱˢᵗˢ(-A^2-A⁻²)ᶜᵒᵐᵖᵒⁿᵉⁿᵗˢ$, with $t=A⁻⁴$; Alexander polynomial $Δ_K(t)$ from Seifert matrix; HOMFLY-PT $P(a,z)$ generalizes both; helicity $H = ∫ A\,d^3x$ equals linking number for disjoint loops; Chern-Simons action $SCS = k/4π∫ Tr(A dA + 2/3A^3)$ yields knot invariants as Wilson loop expectation values. | CONNECTION: Jones polynomial at roots of unity: $t=e2π i/5$ gives $V_L(e2π i/5)$ related to golden ratio $φ = 1.618$ via $2cos(2π/5) = φ⁻¹ = 0.618$; Temperley-Lieb algebra dimension at $q=eiπ/5$ is Fibonacci number $F_n$, linking to 0.618; Alexander polynomial at $t=-1$ gi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b3660926e14a848b252e https://doi.org/10.5281/zenodo.22701666

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Implication

Mathematical analysis demonstrates unification of fluid helicity, Chern-Simons gauge theory, and quantum computing via knot polynomials, highlighting shared topological foundations across physics.

Knot Invariants Unify Fluid Helicity, Chern-Simons Theory, and Quantum Computing — E8 Intelligence Research

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Knot Invariants Unify Fluid Helicity, Chern-Simons Theory, and Quantum Computing — E8 Intelligence Research

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Cite This Study

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