IndisputableMonolith.Physics.NeutrinoMassExactness
This module states the hypothesis that the sum of neutrino masses aligns with the φ-ladder mass formula and satisfies the cosmological bound ∑ m_ν < 0.12 eV. Particle physicists and cosmologists testing Recognition Science predictions against oscillation and CMB data would cite it. The module is a scaffold whose TODO requires deriving the sum from the gap series in the master mass law.
claimThe sum of neutrino masses obeys $\sum m_\nu < 0.12$ eV and is consistent with the φ-ladder where each mass equals the yardstick times $\phi^{r-8+\mathrm{gap}(Z)}$ for the relevant rung and gap.
background
The module imports Constants, which defines the fundamental RS time quantum τ₀ = 1 tick, and Masses.MassLaw. The latter states that every stable recognition state occupies a rung on the φ-ladder and that mass m is proportional to coherence energy E_coh scaled by sector yardstick and rung position. The hypothesis applies this ladder to neutrinos while invoking the cosmological upper bound on their mass sum.
proof idea
This is a hypothesis module marked as scaffold; no formal proofs are present. The structure consists of a single stated bound together with a TODO directing future derivation of the mass sum from the gap series m = Σ φ^{r-8+gap(Z)}.
why it matters in Recognition Science
The module supplies a hypothesis interface that extends the master mass law of Masses.MassLaw to the neutrino sector. It addresses the cosmological bound ∑ m_ν < 0.12 eV as part of checking φ-ladder consistency for light fermions. It touches the open question of higher-order Clag corrections needed to resolve any remaining discrepancy.
scope and limits
- Does not derive the neutrino mass sum from the gap series.
- Does not compute individual neutrino masses or mixing parameters.
- Does not incorporate higher-order Clag corrections.
- Does not compare against specific experimental datasets beyond the stated bound.