# hv4/ -- the Hulek-Verrill fourfold sector (main text Section 4, Proposition 4.1, Table 5; SM Section S7)

- `hv4.json` / `.txt`: Hodge numbers and chi/24 = 30; the S_6-invariant rank-5 lattice with Gram5 (Eq. (45); det 6480,
  signature (3,2)), W5 = diag(1,6,15,6,1), N_flux = Q(g)/2 (Eq. (46)), u = Gram5 g (Eq. (50)), the residual monodromy
  M_d (SM Eq. (S7.3)); the Picard-Fuchs operator L5 (Eq. (51)) with symbol, exponents and the holomorphic series; the
  cut n_2 <= 751 with the dyadic interval for mu_lo (SM Eq. (S7.7)), the caps (27,11,7,11,27) and the box R
  (Eq. (47)); the frame map C to the rational period basis of SM Section S7.3 (Eq. (S7.11); integral, det 6,
  C^T Sigma_th C = Gram5), the printed monodromy matrices and their pull-backs, and the three vanishing classes with
  their reflections (Eqs. (S7.12)-(S7.13)); the counts of Table S12 in both units (signed flux vectors: 59,360 in
  the cut, 55,516 / 3,872 / 230 off-cone <= 30 / off-cone <= 3 / on-cone <= 3; classes under <M_d>: 58,388,
  4,048 = 3,818 + 230 at N_flux <= 3); the 28 vacua in R at 12 positions (SM Tables S14-S15) with class
  representative, charge, n_2, position, ball radius and |W| lower bound; the three certified vacua of Table 5 /
  SM Table S16 (charge 4 inside R; charges 3 and 2 above R) with full stored digit strings, radii, |W| bounds and
  e^-K; the field-sign table of SM Table S13, the scan margins, the r = 2 ray and r = 5/2 edge statements
  (Eqs. (S7.9)-(S7.10)); the charge-1 scope statement; the special-point catalogue (eleven points, only 1/64 in R;
  the twelfth point phi = 1 outside R); and the cross-check of the ten fluxes of arXiv:2404.12422 Table 5.1.
- `verify_hv4.py`: the checker (`python3 verify_hv4.py`, `--quick`). It recomputes every lattice and count statement,
  including an independent enumeration of the fluxes in the cut and of their classes under <M_d>, and checks the
  frame identities and the L5 recurrence. The Krawczyk certificates (positions, radii, |W| bounds, e^-K), mu_lo, the
  field signs and block margins are results of certified period evaluation and are quoted here as data; re-deriving
  them requires the period-transport code, which is not part of this folder.