Absence of Direct Jacobi–Squeezing Link in Topically Scattered Search Results — E8 Intelligence Research

Abstract

FINDING: Search results are **topically scattered** — no direct paper or derivation linking Jacobi polynomials to two-mode squeezing thermal-state nonclassicality appears in the returned set. The hits are pedagogical videos (Jacobi/Gegenbauer/Chebyshev), a collocation method demo, a zeros lecture, a moduli-space talk (Abel–Jacobi), and a quantum Jacobi forms talk — none containing the target closed-form result. | MATH: No new equations, constants, or ratios are extractable from these titles/descriptions. The only implicit mathematics: Jacobi polynomials \(P_n^{(\alpha,\beta)}(x)\) are orthogonal on \([-1,1]\) with weight \((1-x)^\alpha(1+x)^\beta\); Gegenbauer \(C_n^{(\lambda)}\) and Chebyshev \(T_n,U_n\) are special cases. Abel–Jacobi maps relate to periods of differentials — no explicit numeric constants given. | CONNECTION: **None directly supported.** However, the *absence* is itself informative: Jacobi polynomials' parameter pairs \((\alpha,\beta)\) can encode squeezing paramete Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com