PMNSFalsifier
plain-language theorem explainer
The PMNSFalsifier structure records three propositions that would jointly refute the Recognition Science derivation of the PMNS neutrino mixing matrix from phi-quantized angles. Neutrino phenomenologists comparing RS predictions to oscillation data would cite it when testing the claimed phi-connections for theta12, maximal theta23, and deltaCP near pi. The definition is a direct structure whose final field encodes the joint implication to falsehood, functioning as a hypothesis interface without further proof steps.
Claim. A structure whose fields are the propositions $P_1$ (no phi-connection to any PMNS mixing angle), $P_2$ (inverted neutrino mass ordering), $P_3$ (CP phase delta far from pi), together with the implication $P_1 land P_2 land P_3 to bot$.
background
The module derives the PMNS matrix from Recognition Science by positing that neutrino mixing angles are phi-quantized, with theta23 maximal at 45 degrees suggesting symmetry and theta12, theta13 following from the golden-ratio geometry. The PMNS matrix relates flavor eigenstates nu_e, nu_mu, nu_tau to mass eigenstates nu1, nu2, nu3 via the standard parametrization with angles theta12 (solar), theta23 (atmospheric), theta13 (reactor), and phase deltaCP. This falsifier structure sits inside the SM-014 derivation whose core insight is that large PMNS angles, unlike the small CKM angles, arise from the same phi-ladder and eight-tick octave that fix D=3 and the alpha band.
proof idea
The declaration is a plain structure definition whose body simply lists the three propositions and the single implication arrow to falsehood; no lemmas or tactics are applied.
why it matters
It supplies the explicit refutation conditions for the paper proposition on neutrino mixing angles from golden-ratio geometry. By naming the three observables (phi-connection absence, mass ordering, deltaCP location) that would break the RS mechanism, the structure closes the loop on the PMNS derivation and flags the precise experimental outcomes that would falsify the phi-angle predictions. It touches the open question of whether the observed near-maximal theta23 and deltaCP near pi survive future precision measurements.
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