Paper CCLXXX — The 12C(α,γ)16O S-factor as a κ=0→κ=−1 Hyperbolic-Core Enhancement: a Fano-Node Photon Closure Linking the CLIX Ni–Co Boundary Root to the GWTC-4 Pair-Instability Constraint

Response to Antonini et al. (2026, Nature Astronomy, arXiv:2509.04637) and Tong et al. (2026, Nature, arXiv:2509.04151). The GW-inferred 12C(α,γ)16O S-factor S(300)=268+195-116 keV·b runs above the laboratory value 140±21 keV·b. The OOB framework derives the excess as a κ=−1 hyperbolic-core enhancement E=(1−√6/28)^−7=1.898, giving S_core = 1.898×140 = 266 keV·b, −0.02σ on the GW central value. The enhancement is fixed by framework structure (shared √6/28 root with CXXXVIII S8 and CLIX Ni–Co); the only external input is the laboratory S-factor. Honest flags: ratio prediction, reciprocal-compression step interpretive, GW 1σ cannot discriminate exponent. Community: one-octonion-brane-bulk.