{
  "edition": "2026-09-28",
  "status": "Geometric checks; conditional surface theorem; no physical stability result",
  "monadAccounting": {
    "sphere": 1,
    "T": 2,
    "O": 1,
    "geometricTypes": 3,
    "pieces": 4,
    "charge": 0,
    "hostChargeAssumed": 0,
    "volumeOverR3": 5.656854249492381,
    "exactVolumeOverR3": "4*sqrt(2)",
    "hcpPrimitiveSphereCount": 2
  },
  "electron": {
    "T": 8,
    "O": 1,
    "chargeNumerator": -6,
    "chargeDenominator": 6,
    "faceContacts": 8,
    "exposedApertures": 24,
    "connected": true
  },
  "electronSymmetryOrder": 48,
  "cagePlusOctah": {
    "T": 8,
    "O": 7,
    "chargeNumerator": 6,
    "chargeDenominator": 6,
    "faceContacts": 25,
    "exposedApertures": 38,
    "connected": true
  },
  "cagePlusOctahCoordinates": [
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      "type": "T",
      "center": [
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        -1,
        -1
      ]
    },
    {
      "type": "T",
      "center": [
        1,
        -1,
        1
      ]
    },
    {
      "type": "T",
      "center": [
        1,
        1,
        -1
      ]
    },
    {
      "type": "T",
      "center": [
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        1,
        1
      ]
    },
    {
      "type": "T",
      "center": [
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        -1,
        -1
      ]
    },
    {
      "type": "T",
      "center": [
        3,
        -1,
        1
      ]
    },
    {
      "type": "T",
      "center": [
        3,
        1,
        -1
      ]
    },
    {
      "type": "T",
      "center": [
        3,
        1,
        1
      ]
    },
    {
      "type": "O",
      "center": [
        0,
        0,
        0
      ]
    },
    {
      "type": "O",
      "center": [
        4,
        0,
        0
      ]
    },
    {
      "type": "O",
      "center": [
        2,
        -2,
        0
      ]
    },
    {
      "type": "O",
      "center": [
        2,
        2,
        0
      ]
    },
    {
      "type": "O",
      "center": [
        2,
        0,
        -2
      ]
    },
    {
      "type": "O",
      "center": [
        2,
        0,
        2
      ]
    },
    {
      "type": "O",
      "center": [
        4,
        2,
        2
      ]
    }
  ],
  "published": {
    "electron": {
      "T": 8,
      "O": 1,
      "chargeNumerator": -6,
      "chargeDenominator": 6,
      "faceContacts": 8,
      "exposedApertures": 24,
      "connected": true,
      "cavityAreaOverR2": 29.667332515315458
    },
    "positron": {
      "T": 2,
      "O": 4,
      "chargeNumerator": 6,
      "chargeDenominator": 6,
      "faceContacts": 5,
      "exposedApertures": 30,
      "connected": true,
      "cavityAreaOverR2": 41.87226251827538
    },
    "proton": {
      "T": 12,
      "O": 9,
      "chargeNumerator": 6,
      "chargeDenominator": 6,
      "faceContacts": 32,
      "exposedApertures": 56,
      "connected": true,
      "cavityAreaOverR2": 108.89673209019476
    }
  },
  "unitHostRadius": {
    "apertureArea": 0.16125448077398064,
    "tetrahWallArea": 2.2051423937301244,
    "octahWallArea": 8.156085826898927,
    "tetrahVoidVolume": 0.20776157700535514,
    "octahVoidVolume": 1.0525408906952785,
    "electronCavityArea": 29.667332515315458,
    "cagePlusOctahCavityArea": 80.86141020754475,
    "sixSeparatedTetrahCavityArea": 17.100961900956282
  },
  "hcp": {
    "neighborCounts": {
      "T": {
        "T": 1,
        "O": 3
      },
      "O": {
        "T": 6,
        "O": 2
      }
    },
    "voronoi": {
      "vertices": 14,
      "edges": 24,
      "faces": 12,
      "volumeOverD3": 0.7071067811865476
    },
    "method": "Finite patch Delaunay cells grouped by circumcenter; numerical cross-check."
  },
  "proofScope": "All finite nonempty face-connected unions of whole FCC interstitial cavities on a fixed undeformed host lattice, q/e=(2O-T)/6=-1. No dynamical or fragmentation conclusion.",
  "sourceSha256": {
    "scripts/check-foundations.py": "dd5a2638b1668065cf796b449e9ef7f03afa599e1599dc9286e6ad68eb54e8c8",
    "dist/lsm-foundations-inputs.json": "f5f3bb543fefb98734b75c7077f47ee3408259a3eb427f9cf648e69655e30741"
  }
}