res_nu2_simp
plain-language theorem explainer
res_nu2_simp fixes the solar neutrino rung residue at exactly -231/4. Neutrino mass modelers in the Recognition Science program cite this to anchor the solar scale at rung approximately -58 with the quarter-ladder offset. The proof reduces directly from the atmospheric residue and the fixed 7/2 spacing via substitution and rational normalization.
Claim. The upgraded solar neutrino rung residue satisfies $r_2 = -231/4$, where $r_2$ is obtained by subtracting the fixed spacing $7/2$ from the atmospheric residue $-217/4$.
background
The NeutrinoSector module places neutrino masses on the deep phi-ladder with even integer rungs near -50. The atmospheric generation occupies rung -54 plus a quarter offset, so res_nu3 equals -217/4. The solar generation follows by subtracting the canonical spacing of 7/2, which corresponds to one quarter of the eight-tick cycle and enforces a phi^7 ratio in squared masses.
proof idea
The proof unfolds the definition of res_nu2 as res_nu3 minus nu_spacing. It then applies the simplifications from res_nu3_simp and nu_spacing_eq to substitute the known rationals, after which norm_num reduces the arithmetic to -231/4.
why it matters
This lemma supplies the solar rung for neutrino mass predictions and is invoked by nu2_frac_pred_bounds to establish the predicted mass fraction bounds near 0.00926. It also feeds res_nu1_simp for the lightest generation. In the framework it completes the rung assignments for the neutrino sector under T14, using the phi-ladder and RCL to relate squared-mass ratios to rung differences of 7/2.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.