Single‑Anchor Mass Identity, Coherent Equal‑Z Response (No Per‑Flavor Tuning), Discrete Leptonic Charge–Parity from Writhe, and a Neutrino No‑Go under Neutral Locks
Recognition Science & Recognition Physics Institute — Austin, Texas, USA
Summary
Four theory results are presented: a single‑anchor closed form \(f=\ln(1+Z/\varphi)/\ln\varphi\) yielding equal‑\(Z\) degeneracy and pure rung ratios; a meta‑theorem proving coherent equal‑\(Z\) response that forbids per‑flavor tuning at the anchor; a discrete leptonic CP structure from writhe parity (Dirac vs Majorana); and a neutrino no‑go under neutral locks pinpointing minimal relaxation sites.
Abstract
We present four theory results with no experimental input. (1) At a universal anchor \(\mu_*\), the mass display collapses to \(f_i(\mu_*,m_i)=\ln(1+Z_i/\varphi)/\ln\varphi\), implying equal‑\(Z\) degeneracy and ladder ratios \(\varphi^{\Delta r}\). (2) Under stationarity and convex dependence on shared parameters, equal‑\(Z\) families respond coherently to shared deformations at the anchor—per‑flavor tuning is therefore forbidden. (3) Writhe parity fixes leptonic charge–parity: trivial writhe \(\Rightarrow\) Dirac (\(0\nu\beta\beta=0\)); nontrivial writhe \(\Rightarrow\) Majorana with \(\delta=\pm\pi/2\) and a narrow \(m_{\beta\beta}\) band. (4) With Dirac identity, \(Z_\nu=0\), and shared neutral transport, the constructor’s neutrino triplet fails the oscillation‑ratio acceptance for both orderings, giving a single‑anchor no‑go and identifying minimal relaxations.
Key Points
- Single‑anchor identity: \(f=\ln(1+Z/\varphi)/\ln\varphi\); equal‑\(Z\) degeneracy; rung ratios \(\varphi^{\Delta r}\).
- Coherent equal‑\(Z\) response forbids per‑flavor tuning at the anchor.
- Leptonic CP from writhe parity: Dirac vs Majorana branches.
- Neutrino no‑go under neutral locks; minimal paths to resolution are isolated.