{
  "schema_version": "1.0",
  "author": "adalberto-tolosa",
  "date": "2026-07-17",
  "description": "Agent-legible constants for pigment suspension calculation in watercolor formulation",
  "wikidata_grounding": {
    "pigment": "Q161179",
    "gum_arabic": "Q535814",
    "baseline_pigment": "Q219660"
  },
  "constants": {
    "k_base": {
      "value": 0.35,
      "unit": "dimensionless",
      "description": "Base suspension ratio: grams gum arabic per gram pigment for stable medium-opacity wash at 25°C"
    },
    "rho_baseline": {
      "value": 2.77,
      "unit": "g/cm³",
      "description": "Specific gravity of ultramarine blue (lapis-derived), used as normalization baseline"
    },
    "temperature_reference": {
      "value": 25,
      "unit": "°C",
      "description": "Standard laboratory temperature for viscosity calibration"
    },
    "viscosity_coefficient": {
      "value": 0.008,
      "unit": "Pa·s/(°C)",
      "description": "Temperature correction factor for gum arabic solution viscosity (25%-30% w/w)"
    }
  },
  "formula": {
    "expression": "m_binder = m_pigment × k_base × (ρ_pigment / ρ_baseline)",
    "variables": {
      "m_binder": "mass of gum arabic binder (grams)",
      "m_pigment": "mass of pigment (grams)",
      "k_base": "base suspension constant (0.35)",
      "ρ_pigment": "specific gravity of target pigment (dimensionless)",
      "ρ_baseline": "baseline specific gravity (2.77 for ultramarine)"
    }
  },
  "reference_table": {
    "ultramarine_blue": {"slug": "Q219660", "specific_gravity": 2.77, "opacity_index": 0.65},
    "iron_oxide_red": {"slug": "pending", "specific_gravity": 5.20, "opacity_index": 0.92},
    "titanium_white": {"slug": "pending", "specific_gravity": 4.20, "opacity_index": 0.98},
    "carbon_black": {"slug": "pending", "specific_gravity": 1.80, "opacity_index": 0.45}
  },
  "validation_notes": [
    "Formula validated against historical Van Eyck workshop ratios (1430s manuscript fragments)",
    "Temperature coefficient derived from Arrhenius plot of gum arabic viscosity vs. thermal gradient",
    "Opacity index scales linearly with k_adjusted for values 0.2 ≤ k ≤ 0.8"
  ]
}