Single-Anchor Mass Identity, Coherent Equal-Z Response (No Per-Flavor Tuning)

We present four theory results that require no experimental input. First, at a single universal anchor scale µ, the mass-display map for each species collapses to a closed form in the charge index Z and the golden ratio φ,

fi(µ, mi) = ln(1 + Zi/φ) / ln φ,

which yields two immediate consequences: (i) all members of an equal-Z family share the same anchor display (equal-Z degeneracy), and (ii) anchor ratios within a family are pure powers set by rung differences (φ^∆r). Second, we prove a meta-theorem: if the anchor is chosen by a standard stationarity principle and the resulting fixed point depends smoothly and convexly on shared kernel or policy parameters, then equal-Z families respond coherently to any shared deformation at the anchor; any per-flavor tweak necessarily breaks equal-Z degeneracy. Hence, per-flavor tuning at the anchor is forbidden.

Third, we derive a discrete charge–parity structure for leptons from writhe parity of the neutral three-cycle: trivial writhe enforces a Dirac branch with an exactly vanishing neutrinoless double-beta amplitude, while nontrivial writhe fixes a Majorana branch with maximal phase δ = ±π/2 and a narrow, computable interval for the effective double-beta mass. Finally, under three austere neutral-sector locks—Dirac identity, zero neutral residue at the anchor, and neutral transport shared with the charged sectors—the unique neutrino rung triplet admitted by the constructor fails the oscillation-ratio acceptance test for both orderings. Because the ratio depends only on rung differences, no adjustment of transport or scale can rescue it. This constitutes a neutrino no-go within the single-anchor, no-tuning framework and cleanly identifies the minimal relaxation sites for any future closure.