IndisputableMonolith.Cosmology.NeutrinoMass3_FromPhiLadder
Packages cost bounds and a certificate placing the third neutrino mass on the Recognition Science phi-ladder. Cosmologists matching RS rungs to oscillation or sum-of-masses data would cite the NuMass3Cert bundle. The module assembles a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate rather than a single closed-form mass identity.
claimIntroduces a domain cost, proves it nonnegative, fixes a strictly positive canonical threshold, and supplies an inhabited certificate that the third neutrino mass lies on the $\varphi$-ladder in the sense of the RS mass formula (yardstick times $\varphi$ to a rung offset).
background
Recognition Science assigns particle masses on a discrete $\varphi$-ladder via yardstick $\times \varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$, with $\varphi$ the unique self-similar fixed point forced at T6. Neutrino masses are the lightest charged-sector-adjacent entries, so a dedicated cosmology module is needed to pin the third species against that ladder.
The module imports RS constants (including the fundamental tick) and the J-cost layer. Sibling definitions supply a domain cost with an evaluation identity, prove nonnegativity, fix a canonical positive threshold, and bundle the data into a certificate type together with an inhabited witness.
proof idea
Definition-and-certificate module, not a deep forcing proof. It defines the domain cost, records the pointwise evaluation identity, proves nonnegativity, introduces a strictly positive canonical threshold, then packages these into the NuMass3Cert structure with an inhabited instance. Argument structure is assembly of cost positivity and threshold data into a reusable certificate.
why it matters in Recognition Science
Gives the third-neutrino rung certificate for RS cosmology comparisons to oscillation parameters and cosmological mass-sum bounds. No downstream uses are recorded yet, so it is presently a leaf packaging step toward full three-flavor ladder matching. It sits on the phi-ladder mass formula and the T6 uniqueness of $\varphi$; the eight-tick and $D=3$ landmarks are ambient but not re-proved here.
scope and limits
- Does not derive absolute eV-scale masses from first principles alone.
- Does not prove uniqueness of the rung against all oscillation fits.
- Does not treat sterile neutrinos or inverted/nonstandard hierarchies.
- Does not close the full three-flavor cosmological mass-sum bound.
- Does not re-derive T5–T8 forcing; it consumes phi and cost infrastructure.