sum_mass_bound
plain-language theorem explainer
The upper limit on the total neutrino mass is fixed at 0.12 in the Recognition Science neutrino hierarchy model. Particle physicists verifying absolute mass predictions against cosmology reference this value when checking phi-ladder outputs. It enters as a direct numerical constant that the absolute-mass certificate and consistency theorem both invoke to enforce the Planck constraint.
Claim. The sum of the three neutrino masses satisfies $m_1 + m_2 + m_3 < 0.12$, where 0.12 is the adopted cosmological upper bound in electronvolts.
background
The module treats observed squared-mass differences from neutrino oscillation data and supplies the absolute mass scale through the seesaw mechanism together with the phi-ladder mass formula. The constant 0.12 is introduced here as the Planck upper limit on the total mass; sibling definitions compute the individual predicted masses that must respect this total. No upstream lemmas are required; the value is taken directly from cosmology.
proof idea
The declaration is a noncomputable definition that directly assigns the real number 0.12. No lemmas, tactics, or reductions are applied.
why it matters
The constant is required by the NuAbsMassCert structure to certify that the three predicted masses obey the sum inequality and is unfolded inside the theorem that confirms the Recognition Science prediction lies strictly below the bound. It therefore closes the consistency link between the T5–T8 forcing-chain mass ladder and the Standard Model neutrino sector.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.