Search Retrieval Gap: No Primary Research Found on Quantum Modular Forms or CM Values — E8 Intelligence Research

FINDING: The search returned only pedagogical material on cyclotomic fields and one unrelated arXiv paper on quantum graph algebras at roots of unity — no primary research on quantum modular forms, 1-cocycles, or algebraic values of modular forms at CM points was retrieved. | MATH: Cyclotomic polynomial Φ_n(x) = ∏_{(k,n)=1} (x − ζ_n^k), deg Φ_n = φ(n); primitive n-th roots ζ_n = e^{2πi/n}; Galois group Gal(Q(ζ_n)/Q) ≅ (Z/nZ)^×; Kronecker–Weber: every abelian extension of Q embeds in some Q(ζ_n). | CONNECTION: The cyclotomic unit group and the lattice Z[ζ_n] ⊂ C carry the hexagonal (n=6, ζ_6 = e^{iπ/3}) and square (n=4) crystallographic root systems A_2 and B_2; ζ_6 generates the 60° rotation underlying the triangular lattice and the 0.618…-related pentagonal case appears at n=5 via ζ_5 = e^{2πi/5}, whose real part is (√5−1)/4 = 0.309… and whose golden-ratio identity 2cos(2π/5) = (√5−1)/2 = 0.618… ties cyclotomy directly to φ. | DEPTH: 2 FINDING: The single research item (arXiv 2601.08 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com