{
  "handle": "Distance",
  "mechanism": "A function d(x, y) on a space that assigns a non-negative real number to each pair of points, satisfying the metric axioms: (1) non-negativity, d ≥ 0; (2) identity of indiscernibles, d(x, y) = 0 iff x = y; (3) symmetry, d(x, y) = d(y, x); (4) triangle inequality, d(x, z) ≤ d(x, y) + d(y, z). The substrate of 'how close' in any space — geographic, vector-embedding, cognitive-similarity, network-hop, graph-theoretic. Every metric space has a distance function; agents cannot redefine what metric-ness requires. Pseudo-metrics (which relax identity of indiscernibles) and quasi-metrics (which relax symmetry) are distinct descendants, not specializations of Distance itself.",
  "gloss": "Metric-axiom function d(x,y) on a space — substrate for similarity, proximity, and spatial reasoning",
  "invariants": [
    "Non-negativity: d(x, y) ≥ 0 for all x, y in the space.",
    "Identity of indiscernibles: d(x, y) = 0 if and only if x = y.",
    "Symmetry: d(x, y) = d(y, x).",
    "Triangle inequality: d(x, z) ≤ d(x, y) + d(y, z)."
  ],
  "_meta": {
    "tier": 1,
    "ring": 0,
    "path": [
      "Physics",
      "Primitives"
    ]
  },
  "sema_id": "sema:Distance#mh:SHA-256:dfdfe0610f91741e27f87042fc396eab765c4e48aa20fdfc0dfa7152d1333893",
  "sema_ref": "Distance#dfdf",
  "sema_stub": "dfdf",
  "sema_layer": "Physics",
  "sema_category": "Primitives",
  "used_by": {
    "references": {
      "ConceptBlend": "sema:ConceptBlend#mh:SHA-256:4e1a8d331a266c5ff283faba9b1c0d65c943dfa3b0f96f4b7deb5a76f9a171c6",
      "DriftWatch": "sema:DriftWatch#mh:SHA-256:b696959258eb3c48ce11055634b107451d5a500bc8ba19693db4c30b5f5033bf"
    }
  }
}