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    },
    {
      "n": 45,
      "solution": [
        12,
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        128102389400760768
      ],
      "solution_found": true,
      "num_solutions": 10,
      "packet": {
        "packet_size": 128102389400760960,
        "packet_encoding": [
          0.26666666666666666,
          4.0,
          2846719764461350.5
        ],
        "encoding_efficiency": 10000000000.0,
        "packet_diversity": 1.4142135623730918
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      "field": {
        "field_density": 0.022222222222222223,
        "reciprocal_field": 0.022222222222222223,
        "n": 45
      },
      "spectral": {
        "eigenvalues": [
          5.938575769920036e+31,
          0.7500000000001031,
          -351843720888320.0
        ],
        "spectral_radius": 5.938575769920036e+31,
        "solution_space_dim": 1
      },
      "shear": {
        "solution_rigidity": 1.0604724645593951e-17,
        "solution_spread": 1.041705939994721e+17,
        "avg_distance": 9.429759219778326e+16
      }
    },
    {
      "n": 46,
      "solution": [
        12,
        276,
        461168601842738816
      ],
      "solution_found": true,
      "num_solutions": 10,
      "packet": {
        "packet_size": 461168601842739104,
        "packet_encoding": [
          0.2608695652173913,
          6.0,
          1.0025404387885626e+16
        ],
        "encoding_efficiency": 10000000000.0,
        "packet_diversity": 1.414213562373094
      },
      "field": {
        "field_density": 0.021739130434782608,
        "reciprocal_field": 0.021739130434782608,
        "n": 46
      },
      "spectral": {
        "eigenvalues": [
          1.0050873314063633e+32,
          1.2863736289165312e+16,
          0.8804347826086732
        ],
        "spectral_radius": 1.0050873314063633e+32,
        "solution_space_dim": 1
      },
      "shear": {
        "solution_rigidity": 1.0842021724854276e-17,
        "solution_spread": 1.8446744073708938e+17,
        "avg_distance": 9.22337203685543e+16
      }
    },
    {
      "n": 47,
      "solution": [
        12,
        564,
        384307168202282304
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      "solution_found": true,
      "num_solutions": 6,
      "packet": {
        "packet_size": 384307168202282880,
        "packet_encoding": [
          0.2553191489361702,
          12.0,
          8176748259623028.0
        ],
        "encoding_efficiency": 10000000000.0,
        "packet_diversity": 1.4142135623730918
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      "field": {
        "field_density": 0.02127659574468085,
        "reciprocal_field": 0.02127659574468085,
        "n": 47
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      "spectral": {
        "eigenvalues": [
          843.9206935989666,
          56.43299781533703,
          0.42313067714024033
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        "spectral_radius": 843.9206935989666,
        "solution_space_dim": 3
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      "shear": {
        "solution_rigidity": 0.003393584102096147,
        "solution_spread": 261.37420368394373,
        "avg_distance": 294.67370482493163
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    },
    {
      "n": 48,
      "solution": [
        13,
        157,
        24492
      ],
      "solution_found": true,
      "num_solutions": 10,
      "packet": {
        "packet_size": 24662,
        "packet_encoding": [
          0.2708333333333333,
          3.2708333333333335,
          510.25
        ],
        "encoding_efficiency": 9999998612.22141,
        "packet_diversity": 1.3996091549052319
      },
      "field": {
        "field_density": 0.020833333333333332,
        "reciprocal_field": 0.020833333333333332,
        "n": 48
      },
      "spectral": {
        "eigenvalues": [
          393666.7726071079,
          60.70065606397031,
          0.0002611335213765194
        ],
        "spectral_radius": 393666.7726071079,
        "solution_space_dim": 3
      },
      "shear": {
        "solution_rigidity": 0.00014107411351833887,
        "solution_spread": 7076.956063786947,
        "avg_distance": 7088.472683331739
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    },
    {
      "n": 49,
      "solution": [
        14,
        99,
        9702
      ],
      "solution_found": true,
      "num_solutions": 10,
      "packet": {
        "packet_size": 9815,
        "packet_encoding": [
          0.2857142857142857,
          2.020408163265306,
          198.0
        ],
        "encoding_efficiency": 10000000000.0,
        "packet_diversity": 1.3898312945428537
      },
      "field": {
        "field_density": 0.02040816326530612,
        "reciprocal_field": 0.02040816326530612,
        "n": 49
      },
      "spectral": {
        "eigenvalues": [
          53125.501853254915,
          155.80059781188731,
          0.13486671745489273
        ],
        "spectral_radius": 53125.501853254915,
        "solution_space_dim": 3
      },
      "shear": {
        "solution_rigidity": 0.00033118994095860825,
        "solution_spread": 3138.8987117234124,
        "avg_distance": 3019.4153756769615
      }
    },
    {
      "n": 50,
      "solution": [
        13,
        326,
        105950
      ],
      "solution_found": true,
      "num_solutions": 10,
      "packet": {
        "packet_size": 106289,
        "packet_encoding": [
          0.26,
          6.52,
          2119.0
        ],
        "encoding_efficiency": 10000000000.0,
        "packet_diversity": 1.407452407125524
      },
      "field": {
        "field_density": 0.02,
        "reciprocal_field": 0.02,
        "n": 50
      },
      "spectral": {
        "eigenvalues": [
          1.329227995784916e+32,
          2147346209046528.0,
          0.7499999999999826
        ],
        "spectral_radius": 1.329227995784916e+32,
        "solution_space_dim": 1
      },
      "shear": {
        "solution_rigidity": 8.6736173798826e-18,
        "solution_spread": 2.305843009213517e+17,
        "avg_distance": 1.1529215046070379e+17
      }
    }
  ],
  "conjecture_analysis": {
    "solutions_found": 49,
    "total_tested": 49,
    "success_rate": 1.0,
    "counterexamples": []
  },
  "primitive_analysis": {
    "packet": {
      "equation": "\u0393\u1d62",
      "application": "Egyptian fraction solution as packet (x,y,z)",
      "insight": "Each solution is a packet encoding 4/n"
    },
    "field": {
      "equation": "\u03c1(x\u20d7)",
      "application": "Field density 1/n and reciprocal field",
      "insight": "Field density captures solution space sparsity"
    },
    "spectral": {
      "equation": "C = U\u039bU\u1d40",
      "application": "Eigen decomposition of solution space",
      "insight": "Spectral radius indicates solution space extent"
    },
    "shear": {
      "equation": "G = A\u1d40A",
      "application": "Solution rigidity and spread",
      "insight": "Shear measures solution space deformation"
    }
  },
  "validation": {
    "status": "SUCCESS",
    "insight": "4-primitive framework successfully applied to Erd\u0151s\u2013Straus conjecture. Packet primitive captures solution encoding. Field primitive captures conjecture condition. Spectral and shear primitives reveal solution space structure. Framework validated for Diophantine equation problems."
  }
}