IndisputableMonolith.Support.RungFractions
This module defines the Rung type for possibly fractional positions on the phi-ladder. Neutrino mass derivations cite it to place neutrinos at deep negative fractional rungs. It supplies constructors ofInt, quarter, half, the toReal conversion, and supporting equality lemmas. The module is purely definitional.
claimA rung $R$ on the $phi$-ladder is an element of $mathbb{Z} + frac{k}{4}mathbb{Z}$ for $k = 0,1,2,3$, equipped with $mathrm{toReal}(R)$ for scaling in mass formulas.
background
Recognition Science places masses on the phi-ladder, with the rung fixing the exponent in the yardstick times phi to the power of rung minus 8 plus gap of Z. Neutrinos are assigned to deep negative even integers near -50, which requires fractional rung support for precise placement and splitting predictions.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module feeds the neutrino mass scale scorecard in NeutrinoMassScaleScoreCard and the T14 neutrino sector formalization in NeutrinoSector. It supplies the rung objects needed for fractional ladder placement and the structural m_3^2 over m_2^2 equals phi^7 relation.
scope and limits
- Does not assign concrete rung numbers to specific neutrinos.
- Does not derive mass values or squared splittings.
- Does not connect rungs to experimental NuFit bands.
- Does not extend the rung concept beyond quarters and halves.