{
  "id": "BS-MIN-01",
  "version": "1.0",
  "kind": "public_worked_example",
  "scope": "Fixed labelled four-vertex family and 2D orthogonal projection",
  "configuration": {
    "P1": [
      0,
      0,
      0
    ],
    "P2": [
      1,
      0,
      0
    ],
    "P3": [
      0,
      1,
      0
    ],
    "P4": "(1,1,t), t real"
  },
  "projection": "pi(x,y,z)=(x,y)",
  "ordered_squared_distance_pairs": [
    "12",
    "13",
    "23",
    "14",
    "24",
    "34"
  ],
  "ordered_squared_distance_formulas": [
    "1",
    "1",
    "2",
    "2+t^2",
    "1+t^2",
    "1+t^2"
  ],
  "result": "Projection is invariant under t. One P4-incident squared distance determines |t|; for t nonzero, +t and -t remain unless orientation-sensitive evidence is provided. They are equivalent modulo E(3) but not modulo SE(3) with labels fixed.",
  "evidence_type": "exact derivation and finite executable check; not a Lean theorem",
  "artifact_urls": [
    "https://shadow.golge.ai/evidence/bs-min-01/",
    "https://shadow.golge.ai/evidence/bs-min-01/verify.py.txt",
    "https://shadow.golge.ai/evidence/bs-min-01/check-output.txt",
    "https://shadow.golge.ai/evidence/bs-min-01/Projection.lean.txt",
    "https://shadow.golge.ai/evidence/bs-min-01/lean-check-output.txt"
  ],
  "falsifiability": "A counterexample to the displayed formulas in the specified coordinate family invalidates the statement; broad rigidity-threshold generalizations are not asserted.",
  "limitations": [
    "No physical interpretation is established.",
    "Finite Python test is not a universal proof.",
    "Parameterization and labelled base-plane assumptions are essential."
  ],
  "formal_demonstrator": {
    "source": "https://shadow.golge.ai/evidence/bs-min-01/Projection.lean.txt",
    "toolchain": "leanprover/lean4:v4.33.0-rc1",
    "check_output": "https://shadow.golge.ai/evidence/bs-min-01/lean-check-output.txt",
    "scope": "projection invariance and concrete non-injectivity; no distance-rigidity formalization"
  }
}