mass_gap_from_phi
plain-language theorem explainer
Recognition Science equates the Yang-Mills mass gap exactly to the J-cost functional evaluated at the golden ratio phi. Workers deriving particle spectra from cost minimization would cite the equality when anchoring the lowest excitation to the phi fixed point. The proof is a direct one-line reference to the prior theorem Jcost_phi_eq_massGap.
Claim. The mass gap satisfies $J(phi) = Delta$, where $J$ is the J-cost functional, $phi$ the self-similar fixed point, and $Delta$ the Yang-Mills mass gap constant.
background
The module derives the full 4D Lorentzian metric signature from the J-cost functional and the T0-T8 forcing chain. J-cost quantifies deviation from recognition balance; phi is the unique self-similar fixed point forced by T6. The mass gap is the lowest excitation energy in the Yang-Mills sector, expressed via the phi-ladder mass formula.
proof idea
One-line wrapper that applies the upstream theorem Jcost_phi_eq_massGap, which itself reduces to Jcost_phi_exact.
why it matters
The equality anchors the mass gap to J(phi) inside the Recognition framework, supporting the module's derivation of spacetime from cost minimization. It realizes T5 J-uniqueness and T6 phi forcing in the mass spectrum. The result feeds the spacetime emergence theorems that obtain eta = diag(-1,+1,+1,+1) with zero free parameters.
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