A neutrino born one flavour arrives another. That swap is impossible for a massless particle — so the oscillation is a direct proof that neutrinos have mass. The engine computes the two-flavour survival probability live, and the mass-proof is a check the machine can fail.
source Pontecorvo (1957), Mesonium and antimesonium, ZhETF 33, 549 → Sov. Phys. JETP 6, 429 (1958); Maki, Nakagawa & Sakata (1962), Prog. Theor. Phys. 28, 870 — neutrino mixing. INSPIRE 42736 · pre-arXiv originals, no stable full-text link → AMBER. Rendered, not quoted.
Two flavour states are rotations of two mass states by a mixing angle θ. Propagation advances each mass state's phase at its own rate — set by its mass. The phases drift apart, the flavour content re-mixes.
Survival: Pₓ = 1 − sin²(2θ)·sin²(1.27·Δm²·L/E). Units: Δm² in eV², L in km, E in GeV. The constant 1.27 folds in ℏ, c and the eV²·km/GeV conversion.
Appearance is the complement: Pₒ = sin²(2θ)·sin²(…). Two flavours, one unit of probability.
Born one flavour, arrive another — Pontecorvo 1957, then the MNS mixing matrix (1962). The oscillation is the quantum interference of the-wavefunction across kilometres, the same coherence that lets a phase survive a journey.
Neighbour sphere: the-wavefunction — superposition here becomes a macroscopic, measurable flavour beat. The interference is not a metaphor; it is the mechanism.
A live re-check, independent of the panel. It recomputes the mass-proof invariant — at Δm²=0 there must be no oscillation — and confirms unitarity. If window 6 tampers with the phase law, this flips red.
Mixing angle θ, mass-squared splitting Δm² (eV²), baseline L (km), energy E (GeV). Defaults sit near the atmospheric channel: near-maximal mixing, Δm² ≈ 2.5×10⁻³ eV².
The proven result: probability is conserved (Pₓ+Pₒ=1), the source is pure (L=0 ⇒ Pₓ=1), and the swap exists only when Δm²≠0.
“Flavour change could be a classical mixing — a rate, not a phase. Why invoke mass?” Answer: a classical rate gives monotone decay, never the sinusoidal return of the original flavour. The oscillation's periodicity in L/E is the fingerprint of an interference phase ∝ Δm². No mass difference, no phase, no oscillation.
Neutrinos are massless (Standard Model, pre-1998). → Super-Kamiokande / SNO measured the oscillation; a nonzero Δm² requires nonzero mass.
The solar-neutrino deficit means the Sun's model is wrong. → The flux was right; ⅔ of νₑ oscillated to other flavours before arrival.
Oscillation measures the absolute masses. → It measures only the difference Δm² and the mixing angle — the scale and ordering stay open. AMBER
Planted void: force the phase to ignore Δm² (treat it as 1). Now a massless neutrino (Δm²=0) would still oscillate — the mass-proof collapses. The Witness (7) catches it live.