IndisputableMonolith.Cosmology.NeutrinoHierarchyFromPhiLadder
The module defines neutrino states, mass split ratios, and a hierarchy certificate derived from the phi ladder for RS cosmology. Particle physicists modeling fermion masses via the Recognition Science forcing chain would cite these objects. The module consists of successive definitions followed by equality and positivity lemmas.
claimNeutrino states are elements of a type indexed by phi-ladder rungs; the mass split ratio is a positive real-valued function on rung pairs satisfying an equality relation; the neutrino hierarchy certificate is the proposition that these ratios reproduce the observed ordering.
background
The module sits in the cosmology domain and imports the RS time quantum from Constants, where τ₀ = 1 tick. It applies the phi ladder (yardstick times phi to the power of rung offset) to assign neutrino masses, consistent with the mass formula used across the framework. Sibling declarations introduce NeutrinoState, the massSplitRatio function, and the NeutrinoHierarchyCert proposition together with its supporting lemmas.
proof idea
This is a definition module, no proofs. It opens with the NeutrinoState type and count, defines massSplitRatio, then states the equality and positivity lemmas, and closes with the hierarchy certificate.
why it matters in Recognition Science
The module supplies the neutrino sector of the phi-ladder mass assignment that supports the overall RS particle spectrum. It connects the T6 phi fixed point and T8 D=3 setting to cosmology by furnishing the hierarchy certificate, even though no downstream theorems are yet recorded.
scope and limits
- Does not derive absolute neutrino mass scale.
- Does not incorporate oscillation mixing angles.
- Does not address sterile neutrino states.
- Does not invoke the full T0-T8 forcing chain.