MERLIN SCIENCE — q-Zeilberger Algorithm Computes Quantum A-Polynomials via Holonomic Re — E8 Intelligence Research

Here's the narration for the MERLIN SCIENCE video: --- The finding is this: the q-Zeilberger algorithm gives us a systematic, algorithmic way to compute quantum A-polynomials for knots, directly from the colored Jones polynomial. That's a bridge from quantum invariants to classical geometry, and it's now refereed and reproducible. Let me set the field. For decades, the colored Jones polynomial has been a central object in quantum topology. But it's a sequence of polynomials, one for each integer N, and extracting geometric information from that sequence has been more art than science. The quantum A-polynomial changes that. It's a single operator, acting on the colored Jones polynomial, and it encodes the entire recurrence structure. The mechanism is creative telescoping. The q-Zeilberger algorithm takes the colored Jones polynomial, treats it as a holonomic sequence, and derives a q-difference equation that it satisfies. That equation is the quantum A-polynomial. The operators are Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com