The Neutrino-Mass Mechanism Census: Every Class That Generates Neutrino Mass, Its Producing Test, Its Price, and Its Standing Against the Bounds

Neutrinos have mass and the Standard Model gives them none. Oscillation measures two splittings, Δm²₂₁ = (7.53 ± 0.18) × 10⁻⁵ eV² and |Δm²₃₂| ≈ 2.5 × 10⁻³ eV² (PDG 2024), so at least two of the three neutrinos are massive. Oscillation does not measure the lightest mass, does not settle the ordering, and says nothing about the mechanism. This paper is a census of mechanisms, built the way the charge census (TP-4) was built: the candidate set closed in advance, each class given its producing test and its price, the verdict stated over the closed set and at full size. Eight classes are registered: type-I seesaw, type-II seesaw, type-III seesaw, radiative generation, extra-dimensional dilution, Dirac mass by Yukawa coupling alone, mass from spontaneous lepton-number breaking, and clockwork chains. Each class is graded against the bounds that were live when this census was taken: cosmology's sum, Σm_ν < 0.12 eV at 95% confidence (Planck 2018 with baryon acoustic oscillations; the DESI 2024 combination tightens it to < 0.072 eV, model-dependent in both cases), the direct kinematic bound m_β < 0.45 eV (KATRIN, 2025), and the neutrinoless double-beta-decay half-life limits, T > 3.8 × 10²⁶ yr in ¹³⁶Xe (KamLAND-Zen, 2024) and T > 1.9 × 10²⁶ yr in ⁷⁶Ge (LEGEND-200 combined, 2025). The census's result is a class statement: over the eight classes registered in advance, no mechanism that generates neutrino mass is confirmed, no class is dead, and every class still standing pays for the smallness of the mass in one of three currencies — a heavy scale no instrument has seen, a light sector no instrument has seen, or a small number written in by hand. Variants inside classes have died, and §3 prints the dead ones where they fall. What the census buys is a grading instrument: any future claim to have found the mechanism can be placed in one row of the table, and its price read off. Grades carried verbatim from TP-2 (The Unpaired Face), printed in Section 5, not improved: the sterile-partner price CONSTRAINS; Koide NOT DERIVED; ρ = 1 NOT DERIVED. Grades, collected: census COMPLETE as a census; neutrino mass mechanism: NOT IDENTIFIED, by this census or by the literature it grades; the triplet Majoron variant: dead (LEP).