Loaded 6 Holton-McKay graphs

=== HM #0 ===
  Found 3 candidate cuts to test
Selected layout: sage-spring (edge-length CV^2 = 0.0515)
  Cut #0: |S|=10, matching=True
    side 0: max_depth=2, tires=3, k>=2 passed=0
    side 1: max_depth=7, tires=13, k>=2 passed=6
  Cut #1: |S|=30, matching=True
    side 0: max_depth=7, tires=12, k>=2 passed=3
    side 1: max_depth=2, tires=3, k>=2 passed=0
  Cut #2: |S|=8, matching=True
    side 0: max_depth=2, tires=3, k>=2 passed=0
    side 1: max_depth=7, tires=11, k>=2 passed=4
=== HM #1 ===
  Found 3 candidate cuts to test
Selected layout: sage-spring (edge-length CV^2 = 0.0446)
  Cut #0: |S|=10, matching=True
    side 0: max_depth=2, tires=3, k>=2 passed=0
    side 1: max_depth=6, tires=12, k>=2 passed=7
  Cut #1: |S|=30, matching=True
    side 0: max_depth=7, tires=14, k>=2 passed=7
    side 1: max_depth=2, tires=3, k>=2 passed=0
  Cut #2: |S|=8, matching=True
    side 0: max_depth=2, tires=3, k>=2 passed=0
    side 1: max_depth=7, tires=14, k>=2 passed=7
=== HM #2 ===
  Found 3 candidate cuts to test
Selected layout: sage-spring (edge-length CV^2 = 0.0574)
  Cut #0: |S|=30, matching=True
    side 0: max_depth=6, tires=11, k>=2 passed=4
    side 1: max_depth=2, tires=3, k>=2 passed=0
  Cut #1: |S|=18, matching=False
    side 0: max_depth=4, tires=7, k>=2 passed=2
    side 1: max_depth=4, tires=9, k>=2 passed=3
  Cut #2: |S|=20, matching=False
    side 0: max_depth=4, tires=7, k>=2 passed=2
    side 1: max_depth=3, tires=9, k>=2 passed=6
=== HM #3 ===
  Found 3 candidate cuts to test
Selected layout: sage-spring (edge-length CV^2 = 0.0505)
  Cut #0: |S|=28, matching=True
    side 0: max_depth=7, tires=13, k>=2 passed=6
    side 1: max_depth=2, tires=3, k>=2 passed=0
  Cut #1: |S|=10, matching=True
    side 0: max_depth=2, tires=3, k>=2 passed=0
    side 1: max_depth=7, tires=13, k>=2 passed=6
  Cut #2: |S|=30, matching=True
    side 0: max_depth=7, tires=13, k>=2 passed=3
    side 1: max_depth=2, tires=3, k>=2 passed=0
=== HM #4 ===
  Found 3 candidate cuts to test
Selected layout: sage-spring (edge-length CV^2 = 0.0636)
  Cut #0: |S|=30, matching=True
    side 0: max_depth=6, tires=13, k>=2 passed=2
    side 1: max_depth=2, tires=3, k>=2 passed=0
  Cut #1: |S|=20, matching=False
    side 0: max_depth=4, tires=6, k>=2 passed=3
    side 1: max_depth=3, tires=9, k>=2 passed=7
  Cut #2: |S|=20, matching=False
    side 0: max_depth=4, tires=9, k>=2 passed=4
    side 1: max_depth=4, tires=9, k>=2 passed=3
=== HM #5 ===
  Found 3 candidate cuts to test
Selected layout: sage-spring (edge-length CV^2 = 0.0577)
  Cut #0: |S|=30, matching=True
    side 0: max_depth=5, tires=12, k>=2 passed=6
    side 1: max_depth=2, tires=3, k>=2 passed=0
  Cut #1: |S|=20, matching=False
    side 0: max_depth=4, tires=8, k>=2 passed=2
    side 1: max_depth=3, tires=9, k>=2 passed=7
  Cut #2: |S|=20, matching=False
    side 0: max_depth=4, tires=9, k>=2 passed=4
    side 1: max_depth=4, tires=9, k>=2 passed=3

=== Summary ===
Total cut tires examined: 287
Cut tires with k >= 2: 154
k>=2 tires passing (|π| >= 6 with full S_3 orbit): 107
Counterexamples (k>=2 without full orbit): 0
