{
  "date": "2026-10-07",
  "scope": "Finite checks of the teaching construction, not formal verification of the curvature estimate.",
  "source": "pigeonhole-v2-1.md, with final board corrections from the author-referenced chat",
  "assignment_checks": {
    "all_assignments_n_1_to_5": 16739,
    "exact_rational_separation_and_ball_bound": true
  },
  "hero_circle": {
    "metric": "shortest angular arc in degrees",
    "closed_ball_radius": 45,
    "cover_centers": [
      0,
      90,
      180,
      270
    ],
    "integer_angles_checked": 360,
    "sample_angles": [
      10,
      110,
      205,
      290,
      25
    ],
    "first_containing_ball_zero_based": [
      0,
      1,
      2,
      3,
      0
    ],
    "selected_indices": [
      0,
      4
    ],
    "distance": 15,
    "bound": 90,
    "separation_in_sampling_intervals": 4
  },
  "return_example": {
    "H": "rotation(t)",
    "epsilon": "pi/4",
    "tau": "pi",
    "R": "3pi/4",
    "L": "4pi",
    "selected_s_u_t": [
      "0",
      "pi",
      "2pi"
    ],
    "excursion_formula": "u=s+pi gives distance pi for every s",
    "numerical_excursion_spots": 101
  },
  "boundary": "A constant map gives near-repeats, without an excursion. Curvature does not supply that missing hypothesis.",
  "script_sha256": "05127278cab164e23b862274a8a137c9c749151c1cf9dd10d1ac271f6e9ad409"
}