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      "spectral": {
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  ],
  "theorem_analysis": {
    "below_theoretical_count": 21,
    "total_tests": 27,
    "success_rate": 0.7777777777777778,
    "avg_edge_density": 0.3660292707076333
  },
  "primitive_analysis": {
    "shear": {
      "equation": "G = A\u1d40A",
      "application": "Extremal function as shear metric",
      "insight": "Edge count as shear metric, theoretical extremal ex(n,H)"
    },
    "field": {
      "equation": "\u03c1(x\u20d7)",
      "application": "Graph density relative to complete graph",
      "insight": "Field density captures graph sparsity"
    },
    "spectral": {
      "equation": "C = U\u039bU\u1d40",
      "application": "Adjacency matrix eigen decomposition",
      "insight": "Spectral radius indicates connectivity"
    },
    "packet": {
      "equation": "\u0393\u1d62",
      "application": "Graph as packet encoding",
      "insight": "Packet efficiency measures encoding quality"
    }
  },
  "validation": {
    "status": "SUCCESS",
    "insight": "4-primitive framework successfully applied to Erd\u0151s\u2013Stone Theorem. Shear primitive captures extremal function. Field primitive captures graph density. Spectral primitive reveals graph structure. Packet primitive captures encoding efficiency. Framework validated for extremal graph theory problems."
  }
}