# charge22/ -- the fully stabilizing flux of charge 22 (main text Section 3.4, Eqs. (40)-(43), Table 4; SM Section S6)

- `charge22.json` / `.txt`: the number field Q(zeta_66) and its real places; delta (generator of the different) and
  the unit eps_S in the power basis with the sign condition (eps_S delta^-1 positive at exactly one real place) and
  the margins; the Gram matrix B of L = (Z[zeta_66], Tr(eps_S delta^-1 x ybar)) (symmetric Toeplitz, first row tau of
  SM Eq. (S6.3); even, det 1, signature (2,18)); M_zeta; the Gram matrix d of Lambda = U + L (det -1, signature (3,19));
  the U-block matrices; the flux matrices gtilde = gtilde_U + M_(1+zeta), g = g_U + M_(1+zeta^-1), S = g gtilde,
  Stilde, and N with g = N d; tr S = 44, N_flux = 22, n_M2 = 2; the characteristic polynomial
  (x^2-6x+1) m(x)^2 with m written out and disc(m); the ten eigenplanes with lambda_k = 2 + 2 cos(2 pi k/66) and the
  sign of the form on each (three positive directions); Lambda cap Sigma^perp = 0; and the identification of
  (Lambda, h), h = 1_U + M_zeta, with entry 0.66.0.1 of the K3Groups database (Kondo's K3 surface with an automorphism
  of order 66): the database Gram matrix G_BH and generator M_BH, the change-of-basis matrix P of SM Eq. (S6.17) with
  det P = 1, P^T G_BH P = d, A^5 P = P h (A = M_BH^T), and the admissible powers [5, 61].
- `charge22_data.gp`: the same integers in PARI/GP syntax.
- `verify_charge22.gp` (PARI/GP) and `verify_charge22.py` (Python 3; mpmath/sympy used if present): recompute delta,
  eps_S and the trace form from their definitions, integrality, evenness, unimodularity and the signatures,
  integrality and adjointness of g and gtilde, tr S = 44, det S = 1, the characteristic polynomial and its
  factorization, irreducibility of m, reality and positivity of the spectrum, the sign of the form on every
  eigenplane, the three positive directions, the two irreducibility facts behind Lambda cap Sigma^perp = 0, and the
  identities of P (including the second isometry for a = 61 obtained by composing with complex conjugation).
  Whether W = 0 at this vacuum is not decided by these data and is not claimed.