Overview
Neutrino oscillations establish a standard but philosophically loaded fact: the states produced and detected by the weak interaction ($\nu_e$, $\nu_\mu$, $\nu_\tau$) are not the states that propagate. The two descriptions are related by the PMNS matrix, and the observed identity of a neutrino depends on which basis the observation accesses. This structural note examines what that means for the ontology of particle identity within the Cosmochrony framework, where particles are invariants of a non-injective projection rather than primitive objects.
The note is deliberately non-quantitative: it derives no mixing angles and no masses, and it retains the standard oscillation formalism as the operational effective description. What it fixes is a reading — which features of the neutrino sector are generic, which require a mechanism, and which structural expectation is falsifiable.
The reversal: alignment, not misalignment, needs a mechanism
- Misalignment is generic. Whenever an interaction basis and a propagation basis coexist, nothing forces them to coincide. Neutral meson systems ($K^0$, $B^0$) exhibit exactly the same structure; the neutrino is distinguished only by being elementary, so the contextuality of its identity cannot be attributed to constituents.
- Alignment requires a stabiliser. In the projective reading, flavour is an invariant of the weak coupling and mass a spectral invariant of the projected residue — distinct invariants of distinct structures. Charged fermions possess projection channels that stabilise their identity between production and detection; neutrinos, singlets under $SU(3)_C \times U(1)_{\mathrm{em}}$, do not. This is a projective reading, not a Standard-Model dynamical statement.
- PMNS is the default, CKM the explanandum. The large leptonic mixing is the unfixed default — consistent with the anarchy hypothesis of Hall, Murayama and Weiner — while the near-diagonal CKM matrix becomes the non-trivial feature to explain. That explanation requires an additional, explicitly conditional assumption: the charged channels must pin the up-type and down-type mass bases to a common projective frame.
- Falsifiable expectation. Sectors with fewer identity-stabilising projection channels should generically exhibit larger mixing between interaction and propagation bases, unless an independent alignment mechanism is present.
Dirac versus Majorana as conjugation resolution
The Dirac-or-Majorana alternative is reread as a question about the resolution of the projection: a Dirac neutrino corresponds to a configuration whose conjugate projected realisations are distinguished, a Majorana neutrino to one whose partial projectability collapses the conjugate classes. Neutrinoless double beta decay then acquires a structural interpretation — it probes whether the projection resolves relational conjugation in the neutral chiral sector. No rate prediction is made.
What is and is not claimed
Standard (imported). Flavour–mass misalignment, oscillations, neutral meson mixing, near-diagonal CKM, large-angle PMNS, anarchy consistency of the oscillation data.
Structural (this note). The stabiliser reading of alignment, the neutrino as a neutral chiral matching mode, the PMNS-default/CKM-explanandum reversal, the conjugation reading of Dirac–Majorana, and the mixing-versus-channels expectation.
Conditional. The common projective frame assumption behind CKM near-alignment (load-bearing, underived).
Open. The quantitative pinning mechanism, the derivation of mixing magnitudes (blocked at the trivial chiral polar class of the present stratum), the Dirac–Majorana resolution criterion, and any oscillation correction.
Relation to the Cosmochrony programme
This is a companion note of the fermionic matter sub-programme, developing the identity-theoretic core of the white paper's description of neutrinos as partially projectable modes. Its quantitative counterparts — the explicit Lorentzian projective residue and the Yukawa sector — remain the primary open deliverables of the sub-programme; the chiral polar factor carrying generation mixing is invisible at the present stratum (PYO). The note also resonates with a pressure point independently identified in the philosophy of particle physics: neutrino mixing challenges a naive one-to-one correspondence between particle type, flavour label, and mass eigenstate.
References
Jérôme Beau. Neutrino Mixing and Projective Particle Identity: A Structural Note. Working paper, 2026. 10.5281/zenodo.21207750