IndisputableMonolith.Support.RungFractions
Support.RungFractions defines the type of a possibly fractional rung on the phi-ladder together with quarter, half, and toReal operations. Neutrino mass modelers cite it when placing neutrinos on the deep ladder at even integers near -50. The module supplies only definitions and equalities with no proofs.
claimA rung $r$ on the $phi$-ladder may be fractional. The constructors ofInt, quarter, and half produce such rungs, and toReal embeds them into the reals, satisfying quarter_eq and half_eq.
background
Recognition Science places masses on the phi-ladder via yardstick times phi to the power (rung minus 8 plus gap(Z)). The supplied doc-comment states that a rung may be fractional. NeutrinoSector places neutrinos on even integers in the -50 range of this ladder, while NeutrinoMassScaleScoreCard uses fractional placements to match NuFIT Delta m squared bands and the structural relation m_3 squared over m_2 squared equals phi to the 7.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies rung infrastructure that feeds NeutrinoSector (T14 neutrino sector derivation on the deep ladder) and NeutrinoMassScaleScoreCard (phase 2 predictions for fractional rung placement and phi^7 structure in squared splittings). It enables the hypothesis that neutrinos occupy even integers near -50 while allowing the fractional adjustments required for mass-scale comparisons.
scope and limits
- Does not derive numerical mass values or squared splittings.
- Does not connect rungs to the J-function or the forcing chain T0-T8.
- Does not address Berry creation threshold or Z_cf equals phi^5.
- Does not prove uniqueness of rung assignments for any particle.