IndisputableMonolith.Verification.NeutrinoReferenceIndexCheck
Verification module that pins the reference rung indices used for neutrino masses on the Recognition Science phi-ladder. Experimental or model-facing work that quotes RS neutrino mass placements would cite it as the fixed index table. The file is essentially a named constant and check scaffold rather than a deep proof development.
claimThe module records a reference index $n$ (and any associated checks) for placing neutrino masses on the $\varphi$-ladder via the RS mass formula $\mathrm{yardstick}\cdot\varphi^{r-8+\mathrm{gap}(Z)}$. It is a verification anchor, not a dynamical derivation of the indices from first principles.
background
Recognition Science places particle masses on a discrete $\varphi$-ladder. The mass formula is yardstick times $\varphi$ raised to (rung minus 8 plus a charge-dependent gap). Neutrinos sit at specific rungs of that ladder; those rungs must be fixed once and for all if later numerical or experimental comparisons are to be reproducible.
This module lives in the Verification domain. Its only external import is Mathlib, so it does not pull in the forcing chain (T0–T8), the Recognition Composition Law, or the J-cost calculus. The local object exposed to siblings is a natural-number index $n$ standing for the neutrino reference rung (or a small family of such indices).
The theoretical setting is therefore bookkeeping: freeze the neutrino reference indices that downstream mass and mixing checks will quote, rather than re-derive the ladder structure itself.
proof idea
This is a definition and check module, not a theorem development. Structure is: declare the reference index (or indices) as a named natural, optionally assert elementary numerical bounds or equalities against the expected RS neutrino placement, and stop. No upstream lemmas from the forcing chain or mass-formula proofs are applied here.
why it matters in Recognition Science
Without a frozen neutrino reference index, every later claim about RS neutrino masses, mass-squared differences, or mixing angles would silently depend on an ad-hoc rung choice. The module supplies that freeze point inside Verification so that numerical audits and paper tables share one source of truth.
It does not itself close any step of the T0–T8 forcing chain, nor does it prove the mass formula. It feeds parent verification and phenomenology layers that compare ladder predictions to oscillation data. Open questions (exact gap assignments, sterile sectors, absolute mass scale) remain outside its scope; only the reference index bookkeeping is local.
scope and limits
- Does not derive neutrino rungs from the forcing chain or RCL.
- Does not prove the RS mass formula or fix yardstick, $\varphi$, or gap functions.
- Does not compare to oscillation data or bound absolute neutrino masses.
- Does not address sterile neutrinos or non-ladder mass mechanisms.
- Does not import or re-prove J-uniqueness, eight-tick structure, or $D=3$.