mass_ratio
plain-language theorem explainer
mass_ratio defines the ratio of atmospheric to solar neutrino mass-squared differences. Researchers deriving PMNS parameters or neutrino hierarchies in Recognition Science cite it when connecting empirical deltas to the phi-ladder. The definition is a direct division of two real-valued terms supplied by the NeutrinoMassHierarchy module.
Claim. Define the mass ratio as $r = {deltam31_sq} / {deltam21_sq}$, where $deltam31_sq$ and $deltam21_sq$ are the squared mass differences between the third and first, and second and first, neutrino mass eigenstates.
background
The PMNSMatrix module develops the Pontecorvo-Maki-Nakagawa-Sakata matrix for neutrino flavor mixing from Recognition Science, with large angles theta12, theta23, theta13 quantized via phi. Neutrino mass eigenstates nu1, nu2, nu3 relate to flavor states through the PMNS matrix, and the module targets derivation from golden-ratio geometry. Upstream, the mass_ratio theorem in NeutrinoMassFromPhiLadder states that the ratio of adjacent neutrino masses equals phi, with a parallel result for meson masses in MesonSpectrumFromPhiLadder.
proof idea
This is a one-line definition that computes the ratio by dividing deltam31_sq by deltam21_sq. No tactics or lemmas are applied beyond the division; the terms are imported directly from NeutrinoMassHierarchy.
why it matters
This definition supplies the mass-ratio input to neutrinoMassCert and fermionKineticCert, and to darkMatterMassCert. It supports the module comment's approximation of the observed ratio to phi^7 (with 15 percent deviation) and fills the mass-hierarchy slot in the SM-014 derivation of PMNS angles from phi geometry. It ties into the phi-ladder mass formula and the eight-tick octave structure for spectra.
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