IndisputableMonolith.Cosmology.NeutrinoHierarchyFromPhiLadder
This module defines neutrino states and certifies their mass hierarchy via the phi-ladder in RS cosmology. Cosmologists modeling neutrino masses in RS-native units would cite its mass split ratio and hierarchy certificate. The module consists of type definitions, a count lemma, an equality lemma, a positivity lemma, and a top-level certificate, all built on the imported Constants module.
claimNeutrino state type; mass split ratio function $m_i/m_j$ on the phi-ladder; neutrino hierarchy certificate asserting three-state structure with positive ratios derived from rung differences.
background
The module imports Constants, whose sole documented content is the fundamental RS time quantum $ au_0 = 1$ tick. It sits in the cosmology domain and applies the phi-ladder mass placement (yardstick times $\phi$ to a power involving rung minus 8 plus gap(Z)) to neutrinos. Sibling definitions introduce the neutrino state type, the mass split ratio, its equality to a phi expression, its positivity, and the top-level hierarchy certificate.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the neutrino hierarchy objects that extend the phi-ladder mass formula into cosmology. It connects the Recognition Science mass placement rule to the three-neutrino sector and the eight-tick octave, providing the concrete objects needed for later cosmological derivations even though no downstream uses are recorded yet.
scope and limits
- Does not assign absolute masses in eV units.
- Does not treat mixing angles or CP phases.
- Does not compare normal versus inverted ordering numerically.
- Does not incorporate experimental bounds or oscillation data.