The Gap–m–Gap picture: a Planck-frame reading of the Dirac clock and a falsifiable neutrino-mass prediction for JUNO

We re-read known quantum physics as a film of Planck frames: a particle of mass m advances its phase by θ = m/mP at every Planck time tP, one full turn being the quantum h; the unit mass M = 2πmP is the mass whose Compton wavelength is one Planck length. The frame rule is the Dirac quantum walk (coin angle θ + chiral shift), whose continuum limit is the 1+1 Dirac equation, with exact lattice dispersion cosω = cosθ cos k, Zitterbewegung at 2mc2/ℏ, and a double slit with a graded which-path detector obeying Englert's V2 + D2 ≤ 1. The maximal-mass bound of the Dirac automaton of Bisio, D'Ariano and Tosini (sinθ ≤ 1) reads θ ≤ π/2 (m ≤ M/4) in the angle variable; we read it as a Nyquist condition and note that the author's original drawing sits on that boundary. Collapse is read as a clock tick plus rare Bell–Tumulka flashes (rate ∝ m, ε ~ 10-39 per Compton turn, within the window allowed by collapse-model bounds). The simulations use a global lattice in the rest frame of the source; with frames counted in proper time the clock phase is Lorentz invariant by construction, but a covariant version of the full update rule is not constructed and invariance remains an assumption. We state honestly what is a rewriting of de Broglie, Dirac and Schrödinger, and what is new. The one falsifiable number is in the neutrino sector. The Koide relation holds for the charged leptons with Brannen phase δ = 2/9 (PDG 2024 tau, within 0.4σ). Brannen's cycle for the neutrinos, δν = 2/9 + π/12, fixes with no continuous free parameter the ratio Δm221/Δm231 = 0.03084; the shift π/12 and the sign of the lightest root are discrete choices made by Brannen in 2006 on the data of the time. The prediction is Δm221 = (7.75 ± 0.06)×10-5 eV2 (calibrated on NuFIT 6.0), masses (0.38, 8.8, 50.1) meV, Σmν = 0.059 eV, normal ordering. Version 2 update: the JUNO 207-day result (presented July 2026, arXiv:2609.37895), 7.388 ± 0.078, is 3.6σ away (3.2σ on the ratio measured by JUNO alone): the prediction is under strong pressure but not yet refuted by the 5σ criterion; a competing empirical relation (Alikhanov 2026) agrees with JUNO. Version 1 wrongly stated that only the 59.1-day result was public. The prediction itself is unchanged. the DESI DR2 Feldman–Cousins bound Σmν < 0.053 eV (95%, ΛCDM) is also in tension with the predicted sum, as with every normal-ordering spectrum. If the JUNO central value holds, the 5σ threshold is reached with about 500 live days. Explicit falsification criteria and the full Python code that regenerates every computed number and figure are included. Abstract in Italian / Riassunto. Rileggiamo la fisica quantistica nota come una pellicola di fotogrammi di Planck: una particella di massa m avanza la propria fase di θ = m/mP a ogni tP, un giro intero vale h. L'unico numero falsificabile riguarda i neutrini: il ciclo di Brannen con δν = 2/9 + π/12 (nessun parametro continuo libero, ma π/12 e il segno della radice più leggera sono scelte discrete fatte nel 2006 sui dati di allora) prevede Δm221/Δm231 = 0,03084, cioè Δm221 = (7,75 ± 0,06)×10-5 eV2, contro il risultato JUNO a 207 giorni di 7,388 ± 0,078 (3,6σ: sotto forte pressione ma non ancora smentita; versione 2, previsione invariata); anche il limite DESI DR2 di 0,053 eV sulla somma delle masse è in tensione con la previsione. Se il valore centrale resta, JUNO deciderà entro il 2027. Tutti gli script Python per rigenerare ogni numero e figura calcolati sono allegati.