High-precision independent verification (mpmath, 100 dps)

E0                     = 0.72637710319531682622457710900079947333260905181383131117032
E1                     = 1.83487614894476350466731162827881565766753663879803596280365
E2                     = 3.18874674785991966910811126272038486899985430938813272602603
mu_IR                  = 0.576371368409390901927615490363744461036233332189043738975314
mu_UV                  = 1.98064341524799367642733927485189585205502703407037842453215
sigma_vac              = 0.87868087059910263186553657916885688206452726194232516242456
tau_capture            = 0.0711077474866027876704831665513435581256636542968340672491819
J                      = 0.875798927039864829535248118634483902385075633641225110384766
G                      = 0.767023760604178478865605626591573804545605338559082127563602
M_phys                 = 1.40165394364110616474152417411398940018996713279586526591361
E_phys                 = 0.576371368409390901927615490363744461036233332189043738975314
L_tilde                = 2.60748115341904923917421277384894888554494776965933914547649
b_max                  = 0.537550939458639244302142070579884167204958619411728206525463
b                      = 0.5
D_mag                  = 0.0979133669315815451544177871895149574174932479661956931753648
R_cal                  = -0.052092367854344379142543831447540054878882471658591879019641
r_sec                  = 0.052092367854344379142543831447540054878882471658591879019641
c_IR                   = 0.947907632145655620857456168552459945121117528341408120980359
c_UV                   = 1.25426631205267685020276216585109637872241798225654711336183
epsilon_mix            = 0.41630969276524293177748266999805876253063820000165856932929
det_margin             = 1.01561484964762594768702511964429092193860341584923929807503
kappa                  = 0.657490679870653423390141873696875015862271916401825437673624
actual_gap             = 1.10849904574944667844273451927801618433492758698420465163333
certified_fraction     = 0.593135990862427513569446007827176014961753647720465250066881

Residuals
H_vac_residual                   = 1.071550679e-101
P_idempotence_residual           = 4.464794497e-103
P_selfadjoint_residual           = 0.0
basis_orthogonality_residual     = 2.143101359e-101
E_s_residual                     = 9.492283306e-102
E_u_residual                     = 4.359980987e-101
electric_cross_term              = 5.064507498e-102
full_vacuum_cross_s              = 8.886600363e-102
full_vacuum_cross_u              = 5.973802948e-102
block_reconstruction_residual    = 5.714936956e-101

H-E0 in basis (s,u,vac)
  1.25164820885518024044456255548 0.416309692765242931777482669998 -1.17548238570598650207578211182e-101
  0.416309692765242931777482669998 2.31922048155886928088170611752 -7.34445603879972351514635573619e-102
  -8.995927609945564710095818821e-102 -6.29145362840974465999482217608e-102 3.78430209795027224167853316806e-103

