WP-1325 out of sample: TOPAS's laws on the WO3 ramp, the form test first
machine   Darwin arm64, 10 CPUs, python 3.12.10, numpy 2.5.4
rietx     1.10.0.dev0 at 7d7cb7bc, compiled kernels on
load      7.91 8.92 7.06
window    patterns 0..99 (0-based), 100 patterns, T 300 -> 90 K
seeds     per pattern the better chain: 31 forward, 69 backward; Σχ² 1334689.0; Rwp 12.73-14.66 %
laws      9 edges a0 + g/(exp(θ/T)-1), θ 125.370423 K held; 5 angles quadratic in T; joint plan ['scale_bkg', 'disp', 'cell', 'strain'], B held at the chain's
anchor    TOPAS: 12.87 % for 184 parameters over 11 patterns, 12.81 % for 1163 over 100

all laws  2176.1 s; status converged; iters [2, 7, 13, 23]; Rwp 13.694 %; χ² 1366201.0 with 1633 free; χ²r 2.344, f 2.890

FORM TEST VERDICTS (recorded before any comparison)
  m_a      phases.0.cell.a        patterns 100 of 100  verdict REJECTED
           freed     215.0 /  98 dof (cut  122.1,  2.19/dir, p 9.55e-11) REJECT
           tied      454.6 /  98 dof (cut  122.1,  4.64/dir, p 2.56e-47) REJECT
  m_b      phases.0.cell.b        patterns 100 of 100  verdict REJECTED
           freed     326.0 /  98 dof (cut  122.1,  3.33/dir, p 2.8e-26) REJECT
           tied      378.7 /  98 dof (cut  122.1,  3.86/dir, p 1.28e-34) REJECT
  m_c      phases.0.cell.c        patterns 100 of 100  verdict REJECTED
           freed     137.2 /  98 dof (cut  122.1,  1.40/dir, p 0.00556) REJECT
           tied      177.2 /  98 dof (cut  122.1,  1.81/dir, p 1.69e-06) REJECT
  m_beta   phases.0.cell.beta     patterns 100 of 100  verdict kept
           freed      29.0 /  97 dof (cut  121.0,  0.30/dir, p 1) keep
           tied       60.9 /  97 dof (cut  121.0,  0.63/dir, p 0.998) keep
  t_a      phases.1.cell.a        patterns 100 of 100  verdict kept
           freed      12.9 /  98 dof (cut  122.1,  0.13/dir, p 1) keep
           tied      304.5 /  98 dof (cut  122.1,  3.11/dir, p 5.11e-23) REJECT
  t_b      phases.1.cell.b        patterns 100 of 100  verdict kept
           freed     110.9 /  98 dof (cut  122.1,  1.13/dir, p 0.176) keep
           tied       43.9 /  98 dof (cut  122.1,  0.45/dir, p 1) keep
  t_c      phases.1.cell.c        patterns 100 of 100  verdict kept
           freed     118.3 /  98 dof (cut  122.1,  1.21/dir, p 0.0795) keep
           tied      112.0 /  98 dof (cut  122.1,  1.14/dir, p 0.158) keep
  t_alpha  phases.1.cell.alpha    patterns 100 of 100  verdict kept
           freed       8.5 /  97 dof (cut  121.0,  0.09/dir, p 1) keep
           tied       10.0 /  97 dof (cut  121.0,  0.10/dir, p 1) keep
  t_beta   phases.1.cell.beta     patterns 100 of 100  verdict kept
           freed     110.1 /  97 dof (cut  121.0,  1.14/dir, p 0.171) keep
           tied      130.4 /  97 dof (cut  121.0,  1.34/dir, p 0.0135) REJECT
  t_gamma  phases.1.cell.gamma    patterns 100 of 100  verdict kept
           freed      25.8 /  97 dof (cut  121.0,  0.27/dir, p 1) keep
           tied       11.8 /  97 dof (cut  121.0,  0.12/dir, p 1) keep
  p_a      phases.2.cell.a        patterns 100 of 100  verdict kept
           freed     100.6 /  98 dof (cut  122.1,  1.03/dir, p 0.409) keep
           tied       48.0 /  98 dof (cut  122.1,  0.49/dir, p 1) keep
  p_b      phases.2.cell.b        patterns 100 of 100  verdict kept
           freed      53.9 /  98 dof (cut  122.1,  0.55/dir, p 1) keep
           tied       28.3 /  98 dof (cut  122.1,  0.29/dir, p 1) keep
  p_c      phases.2.cell.c        patterns 100 of 100  verdict REJECTED
           freed     383.1 /  98 dof (cut  122.1,  3.91/dir, p 2.42e-35) REJECT
           tied      382.8 /  98 dof (cut  122.1,  3.91/dir, p 2.78e-35) REJECT
  p_beta   phases.2.cell.beta     patterns 100 of 100  verdict kept
           freed      27.0 /  97 dof (cut  121.0,  0.28/dir, p 1) keep
           tied       61.6 /  97 dof (cut  121.0,  0.63/dir, p 0.998) keep
  joint      1941.9 / 1367 dof (cut 1454.1,  1.42/dir, p 8.4e-23) REJECT
  diag PARAMETRIC_FORM_REJECTED: parametric tie 'm_a' does not describe phases.0.cell.a across 100 of its 100 patterns with the other laws' targets freed: freeing the target in each would remove 215.0 times χ²_red·f² of χ², past the 95 % point 122.1 of χ² for 98 directions
  diag PARAMETRIC_FORM_REJECTED: parametric tie 'm_b' does not describe phases.0.cell.b across 100 of its 100 patterns with the other laws' targets freed: freeing the target in each would remove 326.0 times χ²_red·f² of χ², past the 95 % point 122.1 of χ² for 98 directions
  diag PARAMETRIC_FORM_REJECTED: parametric tie 'm_c' does not describe phases.0.cell.c across 100 of its 100 patterns with the other laws' targets freed: freeing the target in each would remove 137.2 times χ²_red·f² of χ², past the 95 % point 122.1 of χ² for 98 directions
  diag PARAMETRIC_FORM_REJECTED: parametric tie 'p_c' does not describe phases.2.cell.c across 100 of its 100 patterns with the other laws' targets freed: freeing the target in each would remove 383.1 times χ²_red·f² of χ², past the 95 % point 122.1 of χ² for 98 directions

VISIBILITY, from the seeding chain: per target, the patterns whose fit held the phase unseen, and those whose cell sat on the chain's window (±1.5 % edge, TOPAS's angle window)
  m_a      unseen   0; on a bound   0
  m_b      unseen   0; on a bound   0
  m_c      unseen   0; on a bound   0
  m_beta   unseen   0; on a bound   0
  t_a      unseen   0; on a bound   0
  t_b      unseen   0; on a bound   0
  t_c      unseen   0; on a bound   0
  t_alpha  unseen   0; on a bound   0
  t_beta   unseen   0; on a bound   0
  t_gamma  unseen   0; on a bound   0
  p_a      unseen   0; on a bound   1 at T [293]
  p_b      unseen   0; on a bound   4 at T [297, 293, 286, 284]
  p_c      unseen   0; on a bound   0
  p_beta   unseen   0; on a bound  35 at T [297, 295, 293, 290, 288, 286, 284, 282, 271, 263, 255, 250, 248, 246, 244, 242, 240, 238, 236, 233, 231, 229, 227, 225, 223, 221, 219, 216, 214, 212, 210, 208, 206, 204, 202]

COMPARISONS
untied    3501.0 s; status converged; iters [2, 3, 15, 165]; Rwp 13.531 %; χ² 1333788.3 with 3000 free; χ²r 2.294, f 2.897
all laws    2176.1 s converged iters [2, 7, 13, 23] Rwp 13.694 % | refit Δχ²   32412.7 for 1367 fewer free; F/f²  1.23, p 7.69e-09
          joint reading's gain   38014.5 for 1367 (refit Δχ² 32412.7 for 1367)
diagnostics, all laws: ['BISO_NEGATIVE', 'BOUND_HIT', 'FLOOR_HIT', 'HIGH_CORRELATION', 'PARAMETRIC_FORM_REJECTED']
diagnostics, untied:   ['BISO_NEGATIVE', 'BOUND_HIT', 'FLOOR_HIT']
held in the all-laws fit (0): [] 

coefficients (all-laws fit) beside TOPAS's
  m_a      d0            7.30011 ± 0.000506
  m_a      d1        0.001318485 ± 0.00032
  m_b      d0           7.501368 ± 0.000503
  m_b      d1         0.02031743 ± 0.00032
  m_c      d0           7.659308 ± 0.000581
  m_c      d1         0.01799176 ± 0.000364
  m_beta   1            90.98944 ± 0.00282
  m_beta   T        -0.001330715 ± 7.72e-05
  m_beta   T^2      1.266974e-06 ± 7.47e-07
  t_a      d0           7.318231 ± 0.000538
  t_a      d1        -0.00658336 ± 0.00046
  t_b      d0           7.488525 ± 0.000495
  t_b      d1         0.01982781 ± 0.000419
  t_c      d0           7.655819 ± 0.000827
  t_c      d1         0.01944885 ± 0.000648
  t_alpha  1            88.85969 ± 0.00363
  t_alpha  T         0.001629811 ± 7.18e-05
  t_alpha  T^2      1.875826e-05 ± 1.15e-06
  t_beta   1             90.8388 ± 0.00405
  t_beta   T         -0.00174269 ± 7.81e-05
  t_beta   T^2     -4.485579e-05 ± 1.23e-06
  t_gamma  1            90.77599 ± 0.0038
  t_gamma  T        0.0007453797 ± 7.83e-05
  t_gamma  T^2     -2.297921e-05 ± 1.22e-06
  p_a      d0           5.274014 ± 0.000289
  p_a      d1        0.006759397 ± 0.000404
  p_b      d0           5.159135 ± 0.000271
  p_b      d1        0.003322277 ± 0.000375
  p_c      d0           7.660223 ± 0.000402
  p_c      d1         0.01309255 ± 0.000586
  p_beta   1            91.70281 ± 0.00546
  p_beta   T         0.001085735 ± 0.000196
  p_beta   T^2      9.996455e-06 ± 1.65e-06
  TOPAS edges (a0 + g): m_a: 7.29683 + 0.00249, m_b: 7.50572 + 0.01699, m_c: 7.65825 + 0.01767, t_a: 7.31006 + -0.00010, t_b: 7.48913 + 0.01774, t_c: 7.65431 + 0.02119, p_a: 5.27377 + 0.00504, p_b: 5.15835 + 0.00331, p_c: 7.66032 + 0.01104

each law against the chain's trajectory: weighted χ²_red of the chain points about the law's curve (points with an esd only)
  m_a      n 100  χ²_red     2.68  max |z|   3.59  mean chain esd 0.00243
  m_b      n 100  χ²_red     4.48  max |z|   4.25  mean chain esd 0.00235
  m_c      n 100  χ²_red     1.19  max |z|   3.41  mean chain esd 0.00322
  m_beta   n 100  χ²_red     0.51  max |z|   2.20  mean chain esd 0.04194
  t_a      n 100  χ²_red     0.84  max |z|   1.51  mean chain esd 0.00202
  t_b      n 100  χ²_red     1.50  max |z|   2.87  mean chain esd 0.00180
  t_c      n 100  χ²_red     0.39  max |z|   1.39  mean chain esd 0.00290
  t_alpha  n 100  χ²_red     1.02  max |z|   2.95  mean chain esd 0.03618
  t_beta   n 100  χ²_red     5.89  max |z|   5.62  mean chain esd 0.03883
  t_gamma  n 100  χ²_red     1.88  max |z|   4.08  mean chain esd 0.03900
  p_a      n 100  χ²_red     4.30  max |z|   9.50  mean chain esd 0.00538
  p_b      n 100  χ²_red     3.63  max |z|   9.71  mean chain esd 0.00474
  p_c      n 100  χ²_red     1.33  max |z|   2.71  mean chain esd 0.00730
  p_beta   n 100  χ²_red     0.58  max |z|   2.96  mean chain esd 0.11555

figure    form_trajectories_0_99.png in the scratch directory
