r2_lemma61.py (verification run 2, AMR-022-4023)  seed=2029 per=6  numpy 2.5.2 sympy 1.14.0
(A) EXACT identities of the proof
  m = 2: Thales identity True; distance identity (|u| = 1) True
  m = 3: Thales identity True; distance identity (|u| = 1) True
  m = 4: Thales identity True; distance identity (|u| = 1) True
  (A) ALL PASSED  (0.0 s)
(B) RANDOMISED TEST of Lemma 6.1 (sampled hypothesis, sampled conclusion)
  m  n  p          scale*     segments  max(P-1) on [p,y]   mono-viol | at 0.97 scale: segments  max(P-1)  mono-viol
  2  2  centroid   1.951035     300     +0.000e+00        0        300     +0.000e+00        0   
  2  2  x_1        0.597633     300     +0.000e+00        0        300     +0.000e+00        0   
  2  2  random     0.698093     300     +0.000e+00        0        300     +0.000e+00        0   
  2  2  centroid   2.871704     300     +0.000e+00        0        300     +0.000e+00        0   
  2  2  x_1        1.350408     300     +0.000e+00        0        300     +0.000e+00        0   
  2  2  random     0.692450     300     +0.000e+00        0        300     +0.000e+00        0   
  2  3  centroid   1.910213     300     +0.000e+00        0        300     +0.000e+00        0   
  2  3  x_1        0.707036     300     +0.000e+00        0        300     +0.000e+00        0   
  2  3  random     0.750092     300     +0.000e+00        0        300     +0.000e+00        0   
  2  3  centroid   0.601187     300     +0.000e+00        0        300     +0.000e+00        0   
  2  3  x_1        0.606143     300     +0.000e+00        0        300     +0.000e+00        0   
  2  3  random     0.523936     300     +0.000e+00        0        300     +0.000e+00        0   
  2  4  centroid   0.545176     300     +0.000e+00        0        300     +0.000e+00        0   
  2  4  x_1        0.757405     300     +0.000e+00        0        300     +0.000e+00        0   
  2  4  random     1.004241     300     +0.000e+00        0        300     +0.000e+00        0   
  2  4  centroid   0.443117     300     +0.000e+00        0        300     +0.000e+00        0   
  2  4  x_1        0.388006     300     +0.000e+00        0        300     +0.000e+00        0   
  2  4  random     0.582996     300     +0.000e+00        0        300     +0.000e+00        0   
  2  5  centroid   0.602032     300     +0.000e+00        0        300     +0.000e+00        0   
  2  5  x_1        1.499893     300     +0.000e+00        0        300     +0.000e+00        0   
  2  5  random     0.639103     300     +0.000e+00        0        300     +0.000e+00        0   
  2  5  centroid   0.629528     300     +0.000e+00        0        300     +0.000e+00        0   
  2  5  x_1        0.922689     300     +0.000e+00        0        300     +0.000e+00        0   
  2  5  random     1.089897     300     +0.000e+00        0        300     +0.000e+00        0   
  2  6  centroid   0.470352     300     +0.000e+00        0        300     +0.000e+00        0   
  2  6  x_1        0.504136     300     +0.000e+00        0        300     +0.000e+00        0   
  2  6  random     0.334544     300     +0.000e+00        0        300     +0.000e+00        0   
  2  6  centroid   0.470798     300     +0.000e+00        0        300     +0.000e+00        0   
  2  6  x_1        0.645338     300     +0.000e+00        0        300     +0.000e+00        0   
  2  6  random     0.861923     300     +0.000e+00        0        300     +0.000e+00        0   
  2  7  centroid   0.737695     300     +0.000e+00        0        300     +0.000e+00        0   
  2  7  x_1        0.572784     300     +0.000e+00        0        300     +0.000e+00        0   
  2  7  random     0.596060     300     +0.000e+00        0        300     +0.000e+00        0   
  2  7  centroid   0.810997     300     +0.000e+00        0        300     +0.000e+00        0   
  2  7  x_1        1.076935     300     +0.000e+00        0        300     +0.000e+00        0   
  2  7  random     0.375092     300     +0.000e+00        0        300     +0.000e+00        0   
  3  2  centroid   0.816851     300     +0.000e+00        0        300     +0.000e+00        0   
  3  2  x_1        3.000000     300     +0.000e+00        0        300     +0.000e+00        0   
  3  2  random     0.456701     300     +0.000e+00        0        300     +0.000e+00        0   
  3  2  centroid   1.447418     300     +0.000e+00        0        300     +0.000e+00        0   
  3  2  x_1        0.593305     300     +0.000e+00        0        300     +0.000e+00        0   
  3  2  random     1.741801     300     +0.000e+00        0        300     +0.000e+00        0   
  3  3  centroid   0.461986     300     +0.000e+00        0        300     +0.000e+00        0   
  3  3  x_1        1.233101     300     +0.000e+00        0        300     +0.000e+00        0   
  3  3  random     0.473190     300     +0.000e+00        0        300     +0.000e+00        0   
  3  3  centroid   0.560852     300     +0.000e+00        0        300     +0.000e+00        0   
  3  3  x_1        0.574759     300     +0.000e+00        0        300     +0.000e+00        0   
  3  3  random     0.349434     300     +0.000e+00        0        300     +0.000e+00        0   
  3  4  centroid   0.406860     300     +0.000e+00        0        300     +0.000e+00        0   
  3  4  x_1        0.791412     300     +0.000e+00        0        300     +0.000e+00        0   
  3  4  random     0.521974     300     +0.000e+00        0        300     +0.000e+00        0   
  3  4  centroid   0.434363     300     +0.000e+00        0        300     +0.000e+00        0   
  3  4  x_1        0.790741     300     +0.000e+00        0        300     +0.000e+00        0   
  3  4  random     0.849655     300     +0.000e+00        0        300     +0.000e+00        0   
  3  5  centroid   0.404068     300     +0.000e+00        0        300     +0.000e+00        0   
  3  5  x_1        0.388464     300     +0.000e+00        0        300     +0.000e+00        0   
  3  5  random     0.582170     300     +0.000e+00        0        300     +0.000e+00        0   
  3  5  centroid   0.322456     300     +0.000e+00        0        300     +0.000e+00        0   
  3  5  x_1        0.499973     300     +0.000e+00        0        300     +0.000e+00        0   
  3  5  random     0.499974     300     +0.000e+00        0        300     +0.000e+00        0   
  3  6  centroid   0.454782     300     +0.000e+00        0        300     +0.000e+00        0   
  3  6  x_1        0.747861     300     +0.000e+00        0        300     +0.000e+00        0   
  3  6  random     0.443432     300     +0.000e+00        0        300     +0.000e+00        0   
  3  6  centroid   0.429144     300     +0.000e+00        0        300     +0.000e+00        0   
  3  6  x_1        0.581815     300     +0.000e+00        0        300     +0.000e+00        0   
  3  6  random     0.471631     300     +0.000e+00        0        300     +0.000e+00        0   
  3  7  centroid   0.251658     300     +0.000e+00        0        300     +0.000e+00        0   
  3  7  x_1        0.382727     300     +0.000e+00        0        300     +0.000e+00        0   
  3  7  random     0.439447     300     +0.000e+00        0        300     +0.000e+00        0   
  3  7  centroid   0.334717     300     +0.000e+00        0        300     +0.000e+00        0   
  3  7  x_1        0.636294     300     +0.000e+00        0        300     +0.000e+00        0   
  3  7  random     0.351436     300     +0.000e+00        0        300     +0.000e+00        0   
  4  2  centroid   0.981724     300     +0.000e+00        0        300     +0.000e+00        0   
  4  2  x_1        1.753235     300     +0.000e+00        0        300     +0.000e+00        0   
  4  2  random     0.750373     300     +0.000e+00        0        300     +0.000e+00        0   
  4  2  centroid   0.636384     300     +0.000e+00        0        300     +0.000e+00        0   
  4  2  x_1        0.633548     300     +0.000e+00        0        300     +0.000e+00        0   
  4  2  random     0.545981     300     +0.000e+00        0        300     +0.000e+00        0   
  4  3  centroid   0.421519     300     +0.000e+00        0        300     +0.000e+00        0   
  4  3  x_1        0.780346     300     +0.000e+00        0        300     +0.000e+00        0   
  4  3  random     0.341303     300     +0.000e+00        0        300     +0.000e+00        0   
  4  3  centroid   0.547807     300     +0.000e+00        0        300     +0.000e+00        0   
  4  3  x_1        0.591534     300     +0.000e+00        0        300     +0.000e+00        0   
  4  3  random     0.454210     300     +0.000e+00        0        300     +0.000e+00        0   
  4  4  centroid   0.454322     300     +0.000e+00        0        300     +0.000e+00        0   
  4  4  x_1        0.820126     300     +0.000e+00        0        300     +0.000e+00        0   
  4  4  random     0.481937     300     +0.000e+00        0        300     +0.000e+00        0   
  4  4  centroid   0.520671     300     +0.000e+00        0        300     +0.000e+00        0   
  4  4  x_1        0.594727     300     +0.000e+00        0        300     +0.000e+00        0   
  4  4  random     0.483401     300     +0.000e+00        0        300     +0.000e+00        0   
  4  5  centroid   0.697266     300     +0.000e+00        0        300     +0.000e+00        0   
  4  5  x_1        0.671095     300     +0.000e+00        0        300     +0.000e+00        0   
  4  5  random     0.267429     300     +0.000e+00        0        300     +0.000e+00        0   
  4  5  centroid   0.374942     300     +0.000e+00        0        300     +0.000e+00        0   
  4  5  x_1        0.772027     300     +0.000e+00        0        300     +0.000e+00        0   
  4  5  random     0.334809     300     +0.000e+00        0        300     +0.000e+00        0   
  4  6  centroid   0.337299     300     +0.000e+00        0        300     +0.000e+00        0   
  4  6  x_1        0.769053     300     +0.000e+00        0        300     +0.000e+00        0   
  4  6  random     0.330635     300     +0.000e+00        0        300     +0.000e+00        0   
  4  6  centroid   0.389282     300     +0.000e+00        0        300     +0.000e+00        0   
  4  6  x_1        0.434421     300     +0.000e+00        0        300     +0.000e+00        0   
  4  6  random     0.281877     300     +0.000e+00        0        300     +0.000e+00        0   
  4  7  centroid   0.512869     300     +0.000e+00        0        300     +0.000e+00        0   
  4  7  x_1        0.580995     300     +0.000e+00        0        300     +0.000e+00        0   
  4  7  random     0.403567     300     +0.000e+00        0        300     +0.000e+00        0   
  4  7  centroid   0.288986     300     +0.000e+00        0        300     +0.000e+00        0   
  4  7  x_1        0.596466     300     +0.000e+00        0        300     +0.000e+00        0   
  4  7  random     0.298828     300     +0.000e+00        0        300     +0.000e+00        0   
  segments tested: 64800; configurations with a violation: 0
  (B) ALL PASSED  (42.9 s)
(C) CONTROL: two far clusters (disconnected E) must fail the sampled hypothesis
  hypothesis on the sample: False (must be False)
TOTAL: ALL CHECKS PASSED  (42.9 s)
