RS_gauge_mass_gaps
plain-language theorem explainer
RS_gauge_mass_gaps records the explicit RS assignment of a common positive gap to the non-abelian gauge sectors and zero to the abelian sector. Physicists resolving the Yang-Mills mass gap via the J-cost on the phi-lattice would cite this as the concrete prediction separating SU(3), SU(2) from U(1). The definition is a direct record construction that binds the three fields without further computation.
Claim. The RS gauge mass gaps are defined by setting the color and weak sectors to the common value $J(φ) = (√5 - 2)/2$ while the hypercharge sector is set to zero.
background
The module derives the Yang-Mills mass gap from the recognition cost functional alone, as one of the seven Millennium problems. The structure GaugeSectorMassGap distinguishes three sectors: color_gap for SU(3) glueballs, weak_gap for SU(2) W/Z bosons, and hyper_gap for the U(1) photon. The J-cost is given by $J(x) = ½(x + x^{-1}) - 1$ on the phi-lattice, with the minimal non-trivial excitation cost Δ = J(φ) = (√5 - 2)/2 forced by the phi-ladder and recognition composition law.
proof idea
This is a definition that directly constructs the GaugeSectorMassGap record by assigning massGap to color_gap and weak_gap while setting hyper_gap to zero.
why it matters
It supplies the concrete values consumed by the downstream theorems mass_gap_asymmetry, SU2_SU3_gapped, U1_gapless, and the YMGapCertificate structure. This completes the QG-005 registry entry by linking the gap asymmetry directly to the phi-forcing chain (T5-T8) and the recognition composition law, confirming non-abelian sectors are gapped while the abelian sector remains gapless.
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