Predictive Codimension for Fermion Masses and Mixings: Calibration Gates and a Pre-Registered Programme for the JUNO/DUNE Era
The flavour-model literature contains hundreds of constructions claiming predictions for fermion mass ratios, mixing angles and phases, and no accounting standard for how many of those predictions survive after each construction’s adjustable structure — texture zeros, group and representation choices, modular weights, vevs, phases, and the discrete scan over model catalogues — has responded to the data. We transplant the predictive-codimension and certificate framework of the Gauge Unification Under Audit programme to the flavour sector and calibrate it on the field’s own history before scoring any contemporary model. Gate G1: the Gatto–Sartori–Tonin relation tan θC = √(md/ms) scores as a genuinely blind νpred = 1 prediction passing at 0.4% on modern inputs, while its two-sector descendant, spending one free phase, widens the point prediction to a 37% consistency band — the Case P → Case A decay exhibited algebraically. Gate G2: the Fritzsch six-zero texture predicted |Vcb| ∈ [0.086, 0.207] over its entire phase freedom; the measured 0.0408 lies a factor 2.1 below the band floor, an honest exclusion, and its four-zero descendants restored agreement by parameter addition — the same decay, exhibited historically. With the scale set by a hit, a kill, and the accommodation between them, the paper registers the programme: frozen observable protocol, hypotheses with predeclared kill bands, catalogue look-elsewhere pricing, and — time-critical — a pre-registered adjudication table for the published neutrino-model literature, to be deposited before JUNO and DUNE report the mass ordering, octant and δCP. A first cross-programme audit is then executed at the GUT–flavour seam: the running-blind double-ratio invariants — the flavour analogue of the programme’s mediator-blind functionals — exclude the minimal-SU(5) relation Yd = Ye^T by a factor 10.4 immune to running, thresholds and tan β; a 1,728-triple Clebsch-catalogue scan collapses to a single surviving invariant point, the Georgi–Jarlskog class, uniquely at determinant one; and on frozen lattice-correlated inputs the mixing-exact blind invariant gives Rℓ/Rq = 3.360 ± 0.028 against the Georgi–Jarlskog value 3 — the 1979 relation cornered at twelve sigma within its declared class, and the gated operator-existence search then closes the case with a structural theorem: the complete published SU(5)/Pati–Salam Clebsch algebra — renormalisable, dimension-five, and messenger-split operators with their higher-order products — generates only factors of the form ±2ᵃ·3ᵇ, while the data demand an effective factor within one sigma of 10/3, whose prime content includes 5. No operator anyone has written can reach it; every candidate the algebra supplies (9, 10.1, 12 in the squared double-ratio) is excluded at 3.7σ or worse on the frozen inputs. All numerical results herein carry the pilot label pending the registration timestamp.
Authors
- JONATHAN CHARLES DOWNES
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-08-24
- DOI
- https://doi.org/10.5281/zenodo.22083498
- Primary Topic
- Neutrino Physics Research
- Type
- preprint