CP Asymmetry as a Lorentz Boost: A Class-D Protection Hierarchy and a Closed-Form Hyperbolic Law in Casas–Ibarra Space

This work studies the algebraic structure underlying the necessary conditions for a spectral matter–antimatter asymmetry, using the real elliptic Ginibre ensemble S = H + gA in its Altland–Zirnbauer class-D form. In odd dimension the spectrum has the exact shape n = 2k+1 — k positive modes, k negative modes bound by particle-hole conjugation, and one protected neutral Majorana mode.Three groups of results are established, each derived from first principles and verified by high-statistics simulation and exact symbolic computation at a fixed seed. First, a four-layer protection hierarchy assigns every structural feature of the spectrum to its exact algebraic guardian: the ±Re symmetry and the neutral Re = 0 mode are guarded by reality (and oddness); the spectral protection |λ| = 0 by antisymmetry and oddness; and the Majorana self-conjugacy by reality and antisymmetry together. Second, it is proved that a purely real structure has an exactly vanishing spectral asymmetry ε = 0, while complex structure is necessary for ε ≠ 0 — the exact spectral counterpart of the leptogenesis statement ε₁ ∝ Im[(Y†Y)²]. Third, working in the standard Casas–Ibarra parametrization, where the complex orthogonal matrix R = exp(so(3,ℂ)) ≅ SO(3,1) carries the high-scale phases to which low-energy neutrino data are blind, it is shown that CP violation is exactly the boost (non-compact) component of R: rotations leave the Hermitian form Y†Y invariant and preserve ε for any Yukawa, while boosts generate it. The dependence on boost rapidity is derived in closed form, ε(η) = c₁ sinh(2η) + c₂ sinh(4η), with coefficients given explicitly by the Yukawa structure; the hyperbolic (rather than trigonometric) character is the quantitative signature of the boost.The scope is stated plainly. This work does not derive the baryon-to-photon ratio η, does not predict the CP-violating phase, and does not claim to solve baryogenesis. The CP-violating input remains external, exactly as it is in every accepted mechanism; the connection to Sakharov's conditions is labelled as a structural analogy, not a quantitative bridge. The contribution is a clean algebraic classification of the structural prerequisites for a spectral asymmetry and an exact reformulation of the functional form and algebraic location in which the CP-violating ingredient enters the seesaw parametrization. Two seductive but spurious numerical patterns encountered during the analysis are explicitly identified and rejected.A complete Python script reproducing every numerical and symbolic result (fixed seed 12345; requires numpy, scipy, sympy) accompanies the paper.