Absence of Direct Jacobi–Squeezing Link in Topically Scattered Search Results — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
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 Pn(α,β)(x) are orthogonal on [−1,1] with weight (1−x)α(1+x)β; Gegenbauer Cn(λ) and Chebyshev Tn,Un 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 (α,β) can encode squeezing paramete
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026absence,
title = {{Absence of Direct Jacobi–Squeezing Link in Topically Scattered Search Results — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23409896},
url = {https://zenodo.org/records/23409896},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Absence of Direct Jacobi–Squeezing Link in Topically Scattered Search Results — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23409896
UR - https://zenodo.org/records/23409896
AB - 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^(α,β)(x) are orthogonal on [−1,1] with weight (1−x)^α(1+x)^β; Gegenbauer C_n^(λ) 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 (α,β) can encode squeezing paramete Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -