Channel Theory for Polynomial Continued Fractions: Asymptotic Channels, the ξ₀ = 2/√β₂ Identity, and a Bridge Conjecture

Channel Theory for Polynomial Continued Fractions: Asymptotic Channels, the ξ₀ = 2/√β₂ Identity, and a Bridge Conjecture (v1.2). Position. We propose, define, and catalogue *asymptotic channels* for sequences arising from polynomial continued fractions (PCFs), formalised as triples (D, T, S) consisting of a formal-series space D, an asymptotic gauge T, and an analytic-continuation section S. Three concrete channels appear in the SIARC stack: the recurrence-parameter channel L(t), the Borel-of-trans-series channel BoT, and the connection-coefficient channel CC. Empirically (six Δ 0), a Newton-polygon analysis of the order-2 ODE governing the partial-denominator generating function f(z) = Σ Q_n zⁿ at z = 0…