A complete first-principles study of the real parts of the eigenvalues of the real elliptic Ginibre ensemble S = H + gA in the strong-coupling limit g → ∞ — and a small voyage in which every result was caught, weighed, and made to confess its origin before it was allowed into the paper. Main results, all proved analytically and verified by an independent high-statistics simulation at a fixed seed: • An exact finite-n variance floor for the real parts that is PARITY-SPLIT: (n−2)/2(n−1) for even n, and exactly 1/2 for odd n — the odd value carried by a single guaranteed real eigenvalue of double variance. • The algebraic reason behind that lonely mode: under multiplication by i, the ensemble sits exactly in Altland–Zirnbauer CLASS D. The odd-n eigenvalue is the topologically protected MAJORANA ZERO-MODE (index ν = 1 odd / 0 even), protected for all couplings. A random-matrix variance turns out to be a statement about topological superconductors. • A genuine odd 1/g correction (decisive at 8σ) that no symmetric Lorentzian can reproduce, traced to eigenvector non-normality, a critical α = 1 heavy tail, and persistently-defective near-real modes. • An exact quasi-independence lemma for the real parts, a Gumbel extreme-value law under one trace constraint, the exact conditional-floor coefficient (n−1)/n(n+2), and asymptotic universality. Everything reached by elementary means — first-order perturbation theory, Wick contraction, trace identities — where the literature uses skew-orthogonal polynomials and Pfaffian processes. Throughout, a strict discipline: no fitting presented as derivation, no manual adjustment, no hidden correction, and every wall named honestly — including the one coefficient a(n) left open for the reason its own α = 1 criticality dictates. A companion Python script reproduces every number in the paper from a fixed seed. No number was forced; every failed guess is recorded as a failure. That honesty is the real treasure. Numerical experiments and verification performed with AI assistance (Claude, Anthropic) as a computational instrument, under the author's strict no-overclaiming discipline.
Abdelilah AHMOURI (Sat,) studied this question.