Majorana Was Right: The Neutrino's Double Identity, 89 Years Later — A Categorical Theorem: CPT Invariance, ABS Classification, Bott Periodicity mod 8, and Galois Descent Force ψ = ψᶜ

I prove that any neutral spin-½ fermion on a 4D Lorentzian spin manifold (M, g) with w₂ (M) =0, admitting a CPT-stable vacuum sector and carrying no unbroken gauge U (1) charge, must be a Majorana fermion. The Dirac alternative is algebraically excluded. The proof rests on: (i) the CPT theorem (Jost–Streater–Wightman), (ii) the Atiyah–Bott–Shapiro classification of real Clifford modules identifying Cl₃, ₁ (ℝ) ≅ M₄ (ℝ), (iii) Bott periodicity mod 8 with KO-dimension indexing, (iv) Galois descent for Spin (3, 1) -bundles. Seesaw mass MR ≠ 0 is forced; leptogenesis becomes algebraic necessity with floor MR ≳ 10⁹ GeV (thermal) or ≳ TeV (resonant). By 2033 CUPID + LEGEND-1000 + nEXO will cover the IO band. Genuinely falsifiable within a decade. Version 6. 1 — Final manuscript: 8 theorems (all proved), 9 references, complete falsification protocol. Experimental decision by 2033 via CUPID, LEGEND-1000, nEXO covering the inverted ordering band. SHA-256: 94f539c49b4e903573582bb86a2ec11f880e70e4e72ddaa85788967efbe2a310. OpenTimestamps proof attached.