Alexander Polynomial Roots Link Knot Orderability and Monodromy Dilation — E8 Intelligence Research

FINDING: Alexander polynomial roots relate to bi-orderability of knot groups and dilation factors of pseudo-Anosov monodromies, with Hoste's conjecture linking root locations to knot properties. | MATH: Alexander polynomial Δ_K(t) ∈ ℤ[t^{±1}]; positive real root r > 0; Hoste's conjecture: all roots of Δ_K(t) lie on unit circle |t|=1 for alternating knots; bi-orderable knot group ⇔ Δ_K(t) has no positive real root ≠1; pseudo-Anosov dilation factor λ = max{|r|: r root of Δ_K(t)} for fibered knots. | CONNECTION: Positive real roots of Δ_K(t) correspond to dilation factors λ > 1 (e.g., λ = φ² = 2.618 for certain knots), linking to golden ratio φ = 1.618; absence of such roots (λ=1) implies bi-orderability, mirroring harmonic stability. | DEPTH: 7 — Bridges knot theory, topology, and dynamical systems via polynomial invariants, with direct ties to geometric ratios (golden ratio) and symmetry constraints (unit circle). Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com