{
  "tool": "vein-integrity-calculator",
  "author": "billy-harris",
  "location": "Shrewsbury, Massachusetts",
  "version": "1.0.0",
  "calibration_date": "2026-07-17",
  "governing_equation": {
    "formulation": "F_c = μ × A × k",
    "von_mises_reference": "Q901396",
    "description": "Critical shear force for metallic seam under torsional load"
  },
  "variables": {
    "mu": {
      "symbol": "μ",
      "unit": "GPa",
      "description": "Shear modulus of alloy",
      "sources": {
        "pure_gold": {
          "value": 27,
          "wikidata": "Q897",
          "note": "Elemental gold shear modulus"
        },
        "gold_silver_24k": {
          "value": 31,
          "note": "Traditional kintsugi binding alloy"
        },
        "gold_copper_22k": {
          "value": 38,
          "note": "High-strength variant for structural repairs"
        },
        "bronze_reference": {
          "value": 70,
          "note": "Copper-tin alloy baseline"
        }
      }
    },
    "area": {
      "symbol": "A",
      "unit": "mm²",
      "description": "Cross-sectional area of joint interface"
    },
    "k_factor": {
      "symbol": "k",
      "unit": "dimensionless",
      "range": [0.7, 1.4],
      "description": "Geometric interlock factor accounting for fracture surface complexity",
      "values": {
        "smooth_joint": 0.7,
        "moderate_interlock": 0.9,
        "interlocked_fracture": 1.1,
        "fracture_locked": 1.4
      }
    }
  },
  "output": {
    "primary": {
      "symbol": "F_c",
      "unit": "MN",
      "description": "Critical shear force before seam failure"
    },
    "derived": {
      "tonnes_force": {
        "conversion": "1 tonne-force ≈ 9.807 kN",
        "description": "Equivalent compressive load capacity"
      }
    }
  },
  "validation_example": {
    "scenario": "Shrewsbury Pressure Vessel Prototype",
    "inputs": {
      "mu": 38,
      "area_mm2": 23.5,
      "k": 1.2
    },
    "expected_output": {
      "force_MN": 1.069,
      "tonnes": 109.0
    }
  },
  "citations": [
    {
      "entity": "shear_strength",
      "wikidata": "Q901396",
      "url": "https://www.wikidata.org/wiki/Q901396"
    },
    {
      "entity": "kintsugi_technique",
      "wikidata": "Q2740942",
      "url": "https://www.wikidata.org/wiki/Q2740942"
    },
    {
      "entity": "gold_element",
      "wikidata": "Q897",
      "url": "https://www.wikidata.org/wiki/Q897"
    }
  ],
  "related_work": [
    {
      "citizen": "julio-torres",
      "work": "Friction Coefficient Lab",
      "relation": "complementary tribology analysis"
    }
  ]
}