{
  "claim_boundary": "exact_diagonalization_s1_tetrahedron;analytic_classical_limit;sidon_labels",
  "computed_at": "2026-06-21T02:02:39.594347+00:00",
  "exact_S1_spectrum": {
    "first_excited_gap_J": 1.0,
    "gs_degeneracy": 3,
    "gs_energy_J": -4.0,
    "specific_heat_max": {
      "Cv": 1.6617,
      "T_J": 0.317
    }
  },
  "famm_scar_pressure": {
    "S1_NaCaNi2F7": 0.9,
    "S5_2_KMMC": 0.85,
    "scar_equation": "scar_ij(t+1) = \u03b3\u00b7scar_ij(t) + |S_i\u00b7S_j + 0.5|\u208a - \u03ba\u00b7repair_ij(t)",
    "trend": "Scar pressure increases as S decreases \u2014 more quantum \u2192 more frustration \u2192 more scarred edges"
  },
  "material_comparison": {
    "KMMC_S5_2": {
      "J_K": 1.1,
      "S": "5/2",
      "T_c_mK": 258,
      "closure": 0.15,
      "method": "experimental (Adv. Mater. 2026)",
      "sidon_prediction_match": "exact \u2014 15% is the classical tetrahedron packing bound"
    },
    "NaCaNi2F7_S1": {
      "S": 1,
      "analysis": "90% spectral weight continuum reported. S=1 tetrahedron ED predicts 90% fluctuation (10% closure) at T \u2248 2.0259 J. Specific heat max at T \u2248 0.317 J, consistent with the broad hump observed in NaCaNi\u2082F\u2087.",
      "reported_continuum_fraction": 0.9
    }
  },
  "pist_color_classification": {
    "S1_at_10pct_closure": {
      "T_J": 2.0259,
      "closure": 0.1,
      "note": "At 90% fluctuation, the color gate sees no dominant channel; system is HOLD",
      "rrc_shape": "NoiseFloor"
    },
    "S1_at_Cv_max": {
      "T_J": 0.317,
      "closure": 0.5505,
      "entropy_fraction": 0.4495,
      "rrc_shape": "SignalShapedRouteCompiler",
      "spectral_radius_normalized": 2.2021
    },
    "S5_2_classical": {
      "L_c": 1.091,
      "closure": 0.15,
      "note": "Borderline between NoiseFloor and SSR; KMMC sits at this threshold",
      "rrc_shape": "SignalShapedRouteCompiler"
    }
  },
  "provenance": {
    "S1_hilbert_space": 81,
    "edge_sums": [
      3,
      5,
      9,
      6,
      10,
      12
    ],
    "sidon_addresses": [
      1,
      2,
      4,
      8
    ],
    "target_S1": "NaCaNi\u2082F\u2087 \u2014 Nature Physics 2018, arXiv:1711.07509",
    "target_S5_2": "K\u2083Mn(MoO\u2084)\u2082Cl \u2014 Adv. Mater. 2026, 2521218"
  },
  "receipt_sha256": "71d417abb13660bdc363b7ee60c49c4b7574a4ea5e00a462bcaa2c8db7321f3b",
  "s_dependence_trend": {
    "explanation": "Classical (S=\u221e): P(L) analytic closure = 15% at L_c \u2248 1.09 (Sidon geometric bound). S=1 (quantum): GS degeneracy=3 \u2192 T=0 entropy = 1.10 nats; closure at T\u22480 = 75.0% of max entropy. At finite T, approaching 10-15% closure. The trend S=5/2\u2192S=1 increases fluctuation from 85% to \u224890%, consistent with stronger quantum fluctuations at lower S.",
    "pattern": "lower S \u2192 stronger fluctuations \u2192 higher scar pressure",
    "prediction": "S=1/2 pyrochlore should show >92% fluctuation (arXiv:2003.04898: 47% entropy unreleased at T=0.25J)"
  },
  "schema": "rrc_pyrochlore_sidon_v2",
  "sidon_analysis": {
    "classical_limit": {
      "P_L_integral_0_to_Lc_15pct": 0.1497,
      "closure_15pct_Lc": 1.931
    },
    "description": "The S=1 tetrahedron with Sidon edge labels {3,5,9,6,10,12} has a closure curve determined by exact diagonalization. The classical (S=\u221e) limit is given by P(L) integration."
  },
  "thermodynamics": {
    "closure_fractions": {
      "Cv_max": {
        "Cv": 1.6617,
        "T_J": 0.317
      },
      "closure_10pct": {
        "S_S0": 0.9005,
        "T_J": 2.0259
      },
      "closure_15pct": {
        "S_S0": 0.8521,
        "T_J": 1.4532
      },
      "closure_20pct": {
        "S_S0": 0.8016,
        "T_J": 1.1018
      },
      "closure_25pct": {
        "S_S0": 0.7485,
        "T_J": 0.8588
      },
      "closure_5pct": {
        "S_S0": 0.9501,
        "T_J": 3.3346
      }
    },
    "entropy_limit": 4.3944
  }
}