{
 "id": "su7_km25",
 "group": "SU(7)",
 "orbifold": {
  "name": "S1/Z2 x S1/Z2",
  "note": "their eqs. (11)-(13); two parities on the fifth circle, one on the sixth"
 },
 "source": {
  "paper": "Y. Komori, N. Maru, arXiv:2503.04090",
  "extracted_from": "research/smeft_formalization/part_vii/amin_closed_form.py",
  "chain": "amin_closed_form.py extracts terms(), GAUGE and T1 from part_vi/su7_anchor_mh.py, which derives the gauge weights from their eqs. (63)-(67)",
  "generated": "2026-08-26"
 },
 "gauge": [
  [
   -1.0,
   1,
   2
  ],
  [
   -2.0,
   1,
   1
  ],
  [
   -3.5,
   -1,
   1
  ]
 ],
 "reps": {
  "7": {
   "(+,+)": [
    [
     1.0,
     -1,
     1
    ]
   ],
   "(+,-)": [
    [
     1.0,
     1,
     1
    ]
   ]
  },
  "28": {
   "(+,+)": [
    [
     1.0,
     1,
     2
    ],
    [
     4.0,
     -1,
     1
    ],
    [
     1.0,
     1,
     1
    ]
   ],
   "(+,-)": [
    [
     1.0,
     -1,
     2
    ],
    [
     4.0,
     1,
     1
    ],
    [
     1.0,
     -1,
     1
    ]
   ]
  },
  "48": {
   "(+,+)": [
    [
     1.0,
     1,
     2
    ],
    [
     8.0,
     -1,
     1
    ],
    [
     2.0,
     1,
     1
    ]
   ],
   "(+,-)": [
    [
     1.0,
     -1,
     2
    ],
    [
     8.0,
     1,
     1
    ],
    [
     2.0,
     -1,
     1
    ]
   ]
  },
  "84": {
   "(+,+)": [
    [
     1.0,
     -1,
     3
    ],
    [
     1.0,
     -1,
     2
    ],
    [
     4.0,
     1,
     2
    ],
    [
     11.0,
     -1,
     1
    ],
    [
     4.0,
     1,
     1
    ],
    [
     1.0,
     -1,
     1
    ]
   ],
   "(+,-)": [
    [
     1.0,
     1,
     3
    ],
    [
     1.0,
     1,
     2
    ],
    [
     4.0,
     -1,
     2
    ],
    [
     11.0,
     1,
     1
    ],
    [
     4.0,
     -1,
     1
    ],
    [
     1.0,
     1,
     1
    ]
   ]
  }
 },
 "published_rows": [
  {
   "label": "(1)",
   "bulk": [
    {
     "rep": "28",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 1
    },
    {
     "rep": "84",
     "parities": [
      1,
      1
     ],
     "multiplicity": 4
    }
   ],
   "published": {
    "alpha_min": 0.043,
    "m_h": 126.8,
    "invR5": 3.8
   },
   "ours": {
    "D8": 15,
    "A4": 258,
    "G": 59.57501900391759
   }
  },
  {
   "label": "(2)",
   "bulk": [
    {
     "rep": "28",
     "parities": [
      1,
      1
     ],
     "multiplicity": 1
    },
    {
     "rep": "84",
     "parities": [
      1,
      1
     ],
     "multiplicity": 4
    }
   ],
   "published": {
    "alpha_min": 0.081,
    "m_h": 125.5,
    "invR5": 2.0
   },
   "ours": {
    "D8": 29,
    "A4": 271,
    "G": 84.57891079557112
   }
  },
  {
   "label": "(3)",
   "bulk": [
    {
     "rep": "28",
     "parities": [
      1,
      1
     ],
     "multiplicity": 1
    },
    {
     "rep": "48",
     "parities": [
      1,
      1
     ],
     "multiplicity": 3
    },
    {
     "rep": "84",
     "parities": [
      1,
      1
     ],
     "multiplicity": 2
    }
   ],
   "published": {
    "alpha_min": 0.021,
    "m_h": 125.1,
    "invR5": 7.5
   },
   "ours": {
    "D8": 9,
    "A4": 189,
    "G": 103.66790493566285
   }
  },
  {
   "label": "(4)",
   "bulk": [
    {
     "rep": "7",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 1
    },
    {
     "rep": "48",
     "parities": [
      1,
      1
     ],
     "multiplicity": 2
    },
    {
     "rep": "84",
     "parities": [
      1,
      1
     ],
     "multiplicity": 3
    }
   ],
   "published": {
    "alpha_min": 0.026,
    "m_h": 126.4,
    "invR5": 6.1
   },
   "ours": {
    "D8": 11,
    "A4": 223,
    "G": 85.08525197676323
   }
  },
  {
   "label": "(5)",
   "bulk": [
    {
     "rep": "7",
     "parities": [
      1,
      1
     ],
     "multiplicity": 1
    },
    {
     "rep": "7",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 1
    },
    {
     "rep": "84",
     "parities": [
      1,
      1
     ],
     "multiplicity": 4
    }
   ],
   "published": {
    "alpha_min": 0.043,
    "m_h": 126.2,
    "invR5": 3.8
   },
   "ours": {
    "D8": 15,
    "A4": 255,
    "G": 64.41537389287674
   }
  }
 ],
 "anchor": {
  "label": "published row (2)",
  "bulk": [
   {
    "rep": "28",
    "parities": [
     1,
     1
    ],
    "multiplicity": 1
   },
   {
    "rep": "84",
    "parities": [
     1,
     1
    ],
    "multiplicity": 4
   }
  ],
  "caveat": "the row where our alpha agrees best with theirs (1.03x); across the 5 rows the ratio runs 1.03x to 2.08x; the Higgs-mass window is decided by the summed potential (see Hierarchy)"
 },
 "constants": {
  "ceiling_GeV": 10034.0,
  "ceiling_A4": 215,
  "ceiling_8D": 1,
  "anchor_band": [
   1.03,
   2.08
  ],
  "note": "ceiling_GeV is the RELAXATION's bound -- Part VII section 8, eq. (24), certified by an exact rational dual for arbitrary content on the seed as printed; its own vertex is empty, and the levels below it are in `ceilings`. The band is the row-wise range of alpha_ours/alpha_theirs, Part VI section 7"
 },
 "ceilings": {
  "relaxation": {
   "GeV": 10034.0,
   "A4": 215,
   "8D": 1,
   "bounds": "any bulk content, on the gauge seed as printed -- the LP dual's bound",
   "attained": false,
   "source": "ceiling_ilp.py, Part VII eq. (24); the vertex (215, 1) is EMPTY once G is written in {1, ln 2, ln 3}: no content of any size can pay for it in G, short by 0.067 in a budget of 681 (certify_212_215.py)"
  },
  "attained": {
   "GeV": 10013,
   "A4": 212,
   "8D": 1,
   "bounds": "any bulk content whose electroweak point is STATIONARY",
   "attained": true,
   "witness": [
    {
     "rep": "7",
     "parities": [
      1,
      1
     ],
     "multiplicity": 17
    },
    {
     "rep": "7",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 2
    },
    {
     "rep": "28",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 57
    }
   ],
   "source": "vacuum_constraint.py section 3 and certify_212_215.py, Part VII eq. (32); the witness sits in a FALSE vacuum -- deeper at alpha = 1 by 316"
  },
  "true_vacuum": {
   "GeV": 9218,
   "A4": 104,
   "8D": 1,
   "bounds": "any bulk content whose electroweak point is its TRUE vacuum (W > 0), with m_h anywhere in the window",
   "attained": true,
   "witness": [
    {
     "rep": "7",
     "parities": [
      1,
      1
     ],
     "multiplicity": 16
    },
    {
     "rep": "28",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 1
    },
    {
     "rep": "48",
     "parities": [
      1,
      1
     ],
     "multiplicity": 1
    },
    {
     "rep": "48",
     "parities": [
      1,
      -1
     ],
     "multiplicity": 4
    },
    {
     "rep": "84",
     "parities": [
      1,
      1
     ],
     "multiplicity": 1
    }
   ],
   "witness_W": 2.5,
   "exact": {
    "alpha": 0.01756,
    "m_h": 126.0,
    "GeV": 9157
   },
   "source": "vacuum_constraint.py section 3, Part VII eq. (36); [8]'s stability criterion carried inside the integer program. `exact` is the same witness minimised on the untruncated polylogarithmic potential"
  },
  "measured_mh": {
   "GeV": 9087,
   "A4": 101,
   "8D": 1,
   "m_h": 125.2,
   "m_h_err": 0.11,
   "bounds": "any true-vacuum content at the Higgs mass the Higgs actually has",
   "attained": true,
   "unconstrained_GeV": 9871,
   "unconstrained_A4": 206,
   "source": "higgs_window.py, Part VII eq. (37); the one-sigma band does not move the vertex"
  },
  "asymptote_GeV": 2678.2,
  "asymptote_source": "asymptotic_ray.py, Part VII eq. (27): the Lambert-W limit the per-rung ceiling falls to, approached from above and never reached; it carries no gauge quantity at all",
  "per_rung": [
   {
    "8D": 1,
    "A4": 215,
    "GeV": 10034.0
   },
   {
    "8D": 3,
    "A4": 336,
    "GeV": 6266.5
   },
   {
    "8D": 5,
    "A4": 436,
    "GeV": 5137.3
   },
   {
    "8D": 7,
    "A4": 533,
    "GeV": 4562.1
   },
   {
    "8D": 9,
    "A4": 630,
    "GeV": 4208.7
   },
   {
    "8D": 15,
    "A4": 918,
    "GeV": 3653.1
   },
   {
    "8D": 21,
    "A4": 1209,
    "GeV": 3390.2
   },
   {
    "8D": 33,
    "A4": 1800,
    "GeV": 3138.3
   },
   {
    "8D": 45,
    "A4": 2397,
    "GeV": 3016.6
   },
   {
    "8D": 65,
    "A4": 3400,
    "GeV": 2912.7
   },
   {
    "8D": 99,
    "A4": 5112,
    "GeV": 2831.6
   },
   {
    "8D": 129,
    "A4": 6630,
    "GeV": 2796.2
   },
   {
    "8D": 201,
    "A4": 10272,
    "GeV": 2753.6
   },
   {
    "8D": 301,
    "A4": 15335,
    "GeV": 2728.4
   },
   {
    "8D": 501,
    "A4": 25470,
    "GeV": 2708.4
   }
  ],
  "per_rung_source": "ceiling_ilp.py: the relaxation's ceiling on each odd rung, on the seed as printed -- the teeth Part VII section 10 reads the likelihood at"
 },
 "gauge_seeds": {
  "published": {
   "label": "as printed in arXiv:2503.04090, eq. (68)",
   "weights": [
    2,
    0.5
   ],
   "bracket": [
    2,
    4,
    7
   ],
   "gauge": [
    [
     -1.0,
     1,
     2
    ],
    [
     -2.0,
     1,
     1
    ],
    [
     -3.5,
     -1,
     1
    ]
   ],
   "five": [
    -18,
    -27,
    -39,
    0,
    -3
   ],
   "parity_of_8D": "odd",
   "ceiling_GeV": 10034.0,
   "ceiling_8D": 1,
   "note": "four degrees of freedom in the periodic channel and one in the antiperiodic: five, where a six-dimensional gauge field has four. Theorem 1 (8D odd) holds on this seed"
  },
  "candidate": {
   "label": "candidate parity-resolved split, Part VII section 13",
   "weights": [
    1.5,
    0.5
   ],
   "bracket": [
    1.5,
    3,
    6
   ],
   "gauge": [
    [
     -0.75,
     1,
     2
    ],
    [
     -1.5,
     1,
     1
    ],
    [
     -3.0,
     -1,
     1
    ]
   ],
   "five": [
    -13.5,
    -18.0,
    -30.0,
    0.0,
    -3.0
   ],
   "parity_of_8D": "even",
   "ceiling_GeV": 7376,
   "ceiling_8D": 2,
   "ceiling_A4": 272.5,
   "note": "three and one, which is four; the ghost subtraction lands in the periodic sector. 8D is even, A4 half-integral, the hypothesis of Theorem 1 is not met, Theorem 2 and the 2W theorem survive, and the relaxation ceiling drops one rung to 8D = 2. The true-vacuum level is NOT recomputed on this branch"
  },
  "shift": {
   "2A4": 9,
   "8D": 9,
   "2U": 9,
   "V": 0,
   "2W": 0
  },
  "source": "gauge_ghost_seed.py, ceiling_ilp_coset.py, seed_shift_character.py"
 },
 "escape_assignments": {
  "rows": [
   {
    "l": [
     "1/2",
     "1/2",
     "0"
    ],
    "X_Q": "-1/9",
    "A": [
     "1/6",
     "1/6",
     "-1/3"
    ],
    "nus": [
     "-1",
     "-1",
     "-1/2"
    ],
    "realisable": true
   },
   {
    "l": [
     "1/2",
     "1/2",
     "-1/2"
    ],
    "X_Q": "-1/18",
    "A": [
     "1/3",
     "1/3",
     "-2/3"
    ],
    "nus": [
     "-1",
     "-1"
    ],
    "realisable": false
   },
   {
    "l": [
     "1/2",
     "1/2",
     "-1"
    ],
    "X_Q": "0",
    "A": [
     "1/2",
     "1/2",
     "-1"
    ],
    "nus": [
     "-1",
     "-1",
     "1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "1/2",
     "0",
     "0"
    ],
    "X_Q": "-1/18",
    "A": [
     "1/3",
     "-1/6",
     "-1/6"
    ],
    "nus": [
     "-1",
     "-1/2",
     "-1/2"
    ],
    "realisable": true
   },
   {
    "l": [
     "1/2",
     "0",
     "-1"
    ],
    "X_Q": "1/18",
    "A": [
     "2/3",
     "1/6",
     "-5/6"
    ],
    "nus": [
     "-1"
    ],
    "realisable": false
   },
   {
    "l": [
     "1/2",
     "-1/2",
     "-1/2"
    ],
    "X_Q": "1/18",
    "A": [
     "2/3",
     "-1/3",
     "-1/3"
    ],
    "nus": [
     "-1"
    ],
    "realisable": false
   },
   {
    "l": [
     "1/2",
     "-1/2",
     "-1"
    ],
    "X_Q": "1/9",
    "A": [
     "5/6",
     "-1/6",
     "-2/3"
    ],
    "nus": [
     "-1",
     "1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "1/2",
     "-1",
     "-1"
    ],
    "X_Q": "1/6",
    "A": [
     "1",
     "-1/2",
     "-1/2"
    ],
    "nus": [
     "-1",
     "1/2",
     "1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "0",
     "0",
     "-1/2"
    ],
    "X_Q": "1/18",
    "A": [
     "1/6",
     "1/6",
     "-1/3"
    ],
    "nus": [
     "-1/2",
     "-1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "0",
     "0",
     "-1"
    ],
    "X_Q": "1/9",
    "A": [
     "1/3",
     "1/3",
     "-2/3"
    ],
    "nus": [
     "-1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "0",
     "-1/2",
     "-1/2"
    ],
    "X_Q": "1/9",
    "A": [
     "1/3",
     "-1/6",
     "-1/6"
    ],
    "nus": [
     "-1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "0",
     "-1",
     "-1"
    ],
    "X_Q": "2/9",
    "A": [
     "2/3",
     "-1/3",
     "-1/3"
    ],
    "nus": [
     "1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "-1/2",
     "-1/2",
     "-1"
    ],
    "X_Q": "2/9",
    "A": [
     "1/6",
     "1/6",
     "-1/3"
    ],
    "nus": [
     "1/2"
    ],
    "realisable": false
   },
   {
    "l": [
     "-1/2",
     "-1",
     "-1"
    ],
    "X_Q": "5/18",
    "A": [
     "1/3",
     "-1/6",
     "-1/6"
    ],
    "nus": [
     "1/2",
     "1/2"
    ],
    "realisable": false
   }
  ],
  "count": 14,
  "realisable": 2,
  "source": "su7_realisable.py, Part VI §4 (an independent re-derivation of the fourteen of su7_family_u1.py); brane-quark charge family-universal, a = -(sum l)/9; right-handed neutrinos from the singlet ladder, up to three",
  "one_generation": {
   "X_Q": "-1/6",
   "channels_forcing_it": [
    "su2_x",
    "x2_y",
    "x_y2"
   ],
   "uncancellable": [
    "x_grav",
    "x3"
   ],
   "value": "1",
   "source": "su7_anomaly_channels.py, Part VI §3"
  },
  "hosting": {
   "0": [
    "21",
    "28"
   ],
   "1": [
    "84"
   ],
   "2": [],
   "3": [],
   "parities": {
    "21@0": [
     -1,
     1
    ],
    "84@1": [
     1,
     1
    ]
   },
   "source": "su7_family_u1.py steps 6-7 and su7_realisable.py step 1: the 35 hosts L at rung 1 and not e_R; the 48 is real (Prop. 2)"
  },
  "qphi": {
   "supply": [
    [
     "1/2",
     "7"
    ],
    [
     "1",
     "28"
    ],
    [
     "3/2",
     "84"
    ]
   ],
   "minimal_halfline": "1/3",
   "strict_halfline": "1",
   "scan": {
    "values": 18648,
    "disagreements": 0
   },
   "source": "su7_qphi.py steps 2, 6, 7"
  },
  "residual": {
   "Z": {
    "1/2": 1,
    "1": 2,
    "3/2": 3
   },
   "pairs_collapse_to": "1/2",
   "source": "su7_residual_group.py"
  }
 },
 "coordinates": {
  "names": [
   "A4",
   "8D",
   "2U",
   "V",
   "2W"
  ],
  "generators": {
   "7(+,+)": [
    0,
    -6,
    2,
    0,
    2
   ],
   "7(+,-)": [
    1,
    8,
    0,
    0,
    -2
   ],
   "28(+,+)": [
    17,
    16,
    40,
    0,
    6
   ],
   "28(+,-)": [
    4,
    2,
    34,
    0,
    -6
   ],
   "48(+,+)": [
    18,
    0,
    48,
    0,
    12
   ],
   "48(+,-)": [
    8,
    28,
    36,
    0,
    -12
   ],
   "84(+,+)": [
    68,
    10,
    346,
    0,
    18
   ],
   "84(+,-)": [
    109,
    80,
    168,
    81,
    -18
   ]
  },
  "gauge": [
   -18,
   -27,
   -39,
   0,
   -3
  ],
  "invariant_factors": [
   2,
   72,
   2592
  ],
  "index": 373248,
  "probes": {
   "the paper's witness": [
    104,
    1,
    565,
    0,
    5
   ],
   "\\cite{KM25} row (1)": [
    258,
    15,
    1379,
    0,
    63
   ],
   "\\cite{KM25} row (2)": [
    271,
    29,
    1385,
    0,
    75
   ],
   "\\cite{KM25} row (3)": [
    189,
    9,
    837,
    0,
    75
   ],
   "\\cite{KM25} row (4)": [
    223,
    11,
    1095,
    0,
    73
   ],
   "\\cite{KM25} row (5)": [
    255,
    15,
    1347,
    0,
    69
   ]
  },
  "source": "lattice_lift.py and congruences.py; rank 5, kernel of dimension 3"
 },
 "wedge": {
  "w_diagonal_interval": [
   0.5869565217391305,
   1.0384615384615385
  ],
  "fitted": [
   {
    "repair": "their formulas, w = 1",
    "w28": 1.0,
    "w84": 1.0,
    "D2_donated": 2.375,
    "D3_donated": -0.125,
    "headline": true
   },
   {
    "repair": "(I) a_min only        s6",
    "w28": 1.081,
    "w84": 0.827,
    "D2_donated": 1.88825,
    "D3_donated": -0.17925,
    "headline": true
   },
   {
    "repair": "(II) curvature only   s6",
    "w28": 1.037,
    "w84": 1.03,
    "D2_donated": 2.5615,
    "D3_donated": -0.0135,
    "headline": true
   },
   {
    "repair": "(I)+(II) both columns s6",
    "w28": 0.825,
    "w84": 0.923,
    "D2_donated": 1.73625,
    "D3_donated": -0.57125,
    "headline": true
   },
   {
    "repair": "per-row lam, lowest   s4",
    "w28": 0.8,
    "w84": 0.8,
    "D2_donated": 1.225,
    "D3_donated": -0.775,
    "headline": true
   },
   {
    "repair": "per-row lam, highest  s4",
    "w28": 0.962,
    "w84": 0.962,
    "D2_donated": 2.1565,
    "D3_donated": -0.2485,
    "headline": true
   },
   {
    "repair": "EDGE: w at which (2) dies",
    "w28": 0.5869565217391305,
    "w84": 0.5869565217391305,
    "D2_donated": 0.0,
    "D3_donated": -1.4673913043478262,
    "headline": false
   }
  ],
  "w48_largest_repair": 5.59,
  "source": "su7_repair_space.py part A: D(2) donated = -27/8 + 2 w28 + (15/4) w84 must stay positive and D(3) donated = -27/8 + 2 w28 + (5/4) w84 negative; w(7) and w(48) appear in neither, so the headline lives in a plane and the largest repair the anchor asks for is identically invisible to it"
 },
 "sixth_row": {
  "ratio_with48": 1.9400183150183148,
  "ratio_no48": 1.1993396497272466,
  "candidates": [
   {
    "kind": "48-rich, large alpha",
    "content": "1 x 28(+1,-1) + 1 x 28(+1,+1) + 1 x 48(+1,+1) + 3 x 84(+1,+1)",
    "bulk": [
     {
      "rep": "28",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 1
     },
     {
      "rep": "28",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     },
     {
      "rep": "48",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     },
     {
      "rep": "84",
      "parities": [
       1,
       1
      ],
      "multiplicity": 3
     }
    ],
    "n48": 1,
    "a_ours": 0.07341681295233493,
    "mh_ours": 126.24708619751308
   },
   {
    "kind": "no 48, small alpha",
    "content": "1 x 28(+1,+1) + 1 x 7(+1,+1) + 2 x 84(+1,+1)",
    "bulk": [
     {
      "rep": "28",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     },
     {
      "rep": "7",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     },
     {
      "rep": "84",
      "parities": [
       1,
       1
      ],
      "multiplicity": 2
     }
    ],
    "n48": 0,
    "a_ours": 0.028757157097695128,
    "mh_ours": 130.9976513109146
   }
  ],
  "source": "su7_sixth_row.py (Part VI section 7): the confound is that n(48) and the published alpha are rank-correlated across their five rows; these two publishable contents break the lock, and the committed numbers -- a_ours divided by 1.94 or by 1.20 according to the reading -- were fixed in print before any such row exists"
 },
 "collider": {
  "coupling_ratio": "sqrt(2)",
  "alphas_run": {
   "aZ": 0.118,
   "MZ": 91.1876,
   "nf": 6,
   "source": "collider_dictionary.py: one-loop, crude on purpose -- the width is a 10%-level statement"
  },
  "branches": [
   {
    "name": "ceiling at the measured m_h",
    "invR5_TeV": 9.09,
    "alphas": 0.0735,
    "GoverM": 0.147,
    "Gamma_GeV": 1337
   },
   {
    "name": "ceiling with the true vacuum",
    "invR5_TeV": 9.22,
    "alphas": 0.0734,
    "GoverM": 0.147,
    "Gamma_GeV": 1354
   },
   {
    "name": "ceiling for arbitrary content",
    "invR5_TeV": 10.03,
    "alphas": 0.0729,
    "GoverM": 0.146,
    "Gamma_GeV": 1463
   },
   {
    "name": "contents that afford the escape",
    "invR5_TeV": 3.97,
    "alphas": 0.0789,
    "GoverM": 0.158,
    "Gamma_GeV": 626
   }
  ],
  "resummation": {
   "eft_coefficient": -0.20873605782007704,
   "invR5_used_TeV": 3.97,
   "width_shift_at_zero": 0.975704156834996,
   "ratios_chi_1p5": {
    "3.3": {
     "9.09": 1.3635305816920371,
     "3.97": 3.1601237326629743
    },
    "3.9": {
     "9.09": 1.5159967926787838,
     "3.97": 4.129944848321026
    },
    "4.5": {
     "9.09": 1.6989831274937304,
     "3.97": 5.301748523089522
    },
    "5.1": {
     "9.09": 1.9141651181992847,
     "3.97": 6.675107810188199
    },
    "6.5": {
     "9.09": 2.549821427696582,
     "3.97": 10.646352237447008
    }
   },
   "source": "kk_resummation.py: F(t) = pi R5 sqrt(-t) coth(pi R5 sqrt(-t)); the withdrawn width correction tends to 1/(1+(2 alpha_s)^2) at t -> 0, which no self-energy below threshold may do"
  },
  "lambda8_TeV": {
   "escape": 7.79,
   "measured_mh": 18.48
  },
  "bins": {
   "mjj_TeV": [
    2.7,
    3.3,
    3.9,
    4.5,
    5.1,
    6.5,
    9.0
   ],
   "chi": [
    1.5,
    2,
    3,
    4,
    5,
    6,
    8,
    10,
    12,
    14,
    16
   ],
   "source": "kk_dijet_lo.py, the LO recast's own grid"
  },
  "teeth": {
   "min_dchi2": 12.0,
   "at_8D": 1,
   "at_TeV": 10.03,
   "threshold": 3.84,
   "next_tooth_dchi2": 244,
   "escape_dchi2": "beyond a thousand",
   "half_quantum": {
    "TeV": 14.19,
    "dchi2": -6.0
   },
   "source": "QUOTED from the published Part VII, eq. (combchi): the 77-point chi^2, truncated teeth -- both stated choices made the unfavourable way; the profiling recipe lives in make_fig_chi2.py and is not re-derived here"
  }
 },
 "screen": {
  "K_over_g4": 2.245624109666417,
  "at_theirs": [
   {
    "case": "(1)",
    "a_theirs": 0.043,
    "mh": 126.8,
    "F2": 16.201554847093597,
    "F1": -0.29516161990390444,
    "K": 1.3545946669390485,
    "g4": 0.6032152313951914
   },
   {
    "case": "(2)",
    "a_theirs": 0.081,
    "mh": 125.5,
    "F2": 53.57221241877249,
    "F1": -0.11331976984100134,
    "K": 1.3888615460712812,
    "g4": 0.6184746325499657
   },
   {
    "case": "(3)",
    "a_theirs": 0.021,
    "mh": 125.1,
    "F2": -2.4488323500549747,
    "F1": -0.1945352141452601,
    "K": null,
    "g4": null
   },
   {
    "case": "(4)",
    "a_theirs": 0.026,
    "mh": 126.4,
    "F2": 0.6096095336246989,
    "F1": -0.25630388722191233,
    "K": 4.209151395215051,
    "g4": 1.8743793215865998
   },
   {
    "case": "(5)",
    "a_theirs": 0.043,
    "mh": 126.2,
    "F2": 16.25199731721468,
    "F1": -0.29571660705304836,
    "K": 1.3460910587286767,
    "g4": 0.5994284853526247
   }
  ],
  "source": "su7_anchor_mh.py section B (Part VI): K = m_h a_min / sqrt(F''(a_min)) = 2 m_W sqrt(3/(16 pi^6)) g4 for every row of every content; invariant under F -> lambda F, so it does not test the normalisation"
 },
 "escape": {
  "host": "84(+,+)",
  "cost8": 10,
  "min_8D": 11,
  "ceiling_GeV": 3967.4,
  "ceiling_A4": 727,
  "ceiling_8D": 11,
  "ratio": 2.53,
  "note": "donating the host takes cost8/8 off D, and D must stay positive, so a content can afford the escape iff 8D >= min_8D. The per-rung ceiling is monotone decreasing in D, so that bound moves the ceiling itself: ceiling_GeV against the unconstrained one. It bounds the content BEFORE the donation, not the world after"
 },
 "size_curve": [
  {
   "N": 5,
   "contents": 1286,
   "in_window": 1,
   "with_host": 1,
   "can_pay": 1,
   "best_invR5": 1924,
   "best_8D": 29,
   "best_invR5_paying": 1924,
   "best_8D_paying": 29
  },
  {
   "N": 6,
   "contents": 3002,
   "in_window": 3,
   "with_host": 3,
   "can_pay": 3,
   "best_invR5": 2182,
   "best_8D": 21,
   "best_invR5_paying": 2182,
   "best_8D_paying": 21
  },
  {
   "N": 7,
   "contents": 6434,
   "in_window": 15,
   "with_host": 15,
   "can_pay": 13,
   "best_invR5": 3604,
   "best_8D": 7,
   "best_invR5_paying": 2573,
   "best_8D_paying": 15
  },
  {
   "N": 8,
   "contents": 12869,
   "in_window": 30,
   "with_host": 29,
   "can_pay": 22,
   "best_invR5": 9138,
   "best_8D": 1,
   "best_invR5_paying": 2683,
   "best_8D_paying": 13
  },
  {
   "N": 9,
   "contents": 24309,
   "in_window": 62,
   "with_host": 58,
   "can_pay": 47,
   "best_invR5": 9138,
   "best_8D": 1,
   "best_invR5_paying": 2858,
   "best_8D_paying": 11
  },
  {
   "N": 10,
   "contents": 43757,
   "in_window": 110,
   "with_host": 99,
   "can_pay": 86,
   "best_invR5": 9138,
   "best_8D": 1,
   "best_invR5_paying": 2972,
   "best_8D_paying": 11
  },
  {
   "N": 11,
   "contents": 75581,
   "in_window": 212,
   "with_host": 184,
   "can_pay": 167,
   "best_invR5": 9138,
   "best_8D": 1,
   "best_invR5_paying": 2974,
   "best_8D_paying": 11
  },
  {
   "N": 12,
   "contents": 125969,
   "in_window": 388,
   "with_host": 332,
   "can_pay": 307,
   "best_invR5": 9156,
   "best_8D": 1,
   "best_invR5_paying": 2975,
   "best_8D_paying": 11
  },
  {
   "N": 13,
   "contents": 203489,
   "in_window": 670,
   "with_host": 562,
   "can_pay": 525,
   "best_invR5": 9156,
   "best_8D": 1,
   "best_invR5_paying": 2975,
   "best_8D_paying": 11
  },
  {
   "N": 14,
   "contents": 319769,
   "in_window": 1097,
   "with_host": 906,
   "can_pay": 857,
   "best_invR5": 9156,
   "best_8D": 1,
   "best_invR5_paying": 3017,
   "best_8D_paying": 11
  }
 ],
 "multiplets": {
  "source": "Komori & Maru, arXiv:2503.04090",
  "equations": {
   "7": "(41)",
   "28": "(69)",
   "48": "(57)",
   "84": "(70)"
  },
  "note": "Multiplets of SU(3)_C x SU(2)_L with their three Z2 parities.  For a fermion representation the signs are relative to (xi_R, eta_R, eta'_R) as the paper prints them; the 48 is eq. (57), printed with absolute parities because the gauge sector shares the decomposition.  Charges are c = r-1, r-3, ... > 0 (eq. (71) and the note below it).  Sign s = eta*eta'*P5*P5' (eq. (72)); for the gauge field s = P5*P5' (eq. (58)).",
  "fields": [
   "label",
   "P6",
   "P5",
   "P5p",
   "colour",
   "r"
  ],
  "gauge_weight": {
   "periodic": 1.0,
   "antiperiodic": 0.25
  },
  "decomposition": {
   "7": [
    [
     "(3,1)",
     1,
     -1,
     -1,
     3,
     1
    ],
    [
     "(1,2)",
     -1,
     -1,
     1,
     1,
     2
    ],
    [
     "(1,1)",
     -1,
     1,
     -1,
     1,
     1
    ],
    [
     "(1,1)'",
     -1,
     1,
     1,
     1,
     1
    ]
   ],
   "28": [
    [
     "(3,2)",
     -1,
     -1,
     1,
     3,
     2
    ],
    [
     "(1,3)",
     1,
     -1,
     -1,
     1,
     3
    ],
    [
     "(1,2)",
     1,
     1,
     -1,
     1,
     2
    ],
    [
     "(1,2)'",
     1,
     1,
     1,
     1,
     2
    ]
   ],
   "48": [
    [
     "(1,3)",
     1,
     1,
     1,
     1,
     3
    ],
    [
     "(1,2)",
     1,
     -1,
     1,
     1,
     2
    ],
    [
     "(1,2bar)",
     1,
     -1,
     1,
     1,
     2
    ],
    [
     "(1,2)'",
     1,
     -1,
     -1,
     1,
     2
    ],
    [
     "(1,2bar)'",
     1,
     -1,
     -1,
     1,
     2
    ],
    [
     "(3,2bar)",
     -1,
     1,
     -1,
     3,
     2
    ],
    [
     "(3bar,2)",
     -1,
     1,
     -1,
     3,
     2
    ]
   ],
   "84": [
    [
     "(6,2)",
     -1,
     -1,
     1,
     6,
     2
    ],
    [
     "(3,3)",
     1,
     -1,
     -1,
     3,
     3
    ],
    [
     "(3,2)",
     1,
     1,
     1,
     3,
     2
    ],
    [
     "(3,2)'",
     1,
     1,
     -1,
     3,
     2
    ],
    [
     "(1,4)",
     -1,
     -1,
     1,
     1,
     4
    ],
    [
     "(1,3)",
     -1,
     1,
     -1,
     1,
     3
    ],
    [
     "(1,3)'",
     -1,
     1,
     1,
     1,
     3
    ],
    [
     "(1,2)",
     -1,
     -1,
     1,
     1,
     2
    ],
    [
     "(1,2)'",
     -1,
     -1,
     1,
     1,
     2
    ],
    [
     "(1,2)''",
     -1,
     -1,
     -1,
     1,
     2
    ]
   ]
  },
  "produced_by": "ghu-lab/build/make_data_multiplets.py",
  "verified_against": "data/su7_km25.json reps + gauge, term table by term table"
 },
 "inverse": {
  "certificates": {
   "floor": "identity (II) demands an A_4 below that of the EMPTY content, and multiplicities are non-negative. This is the obstruction the extremal direction never meets: it closes the scale from BELOW, and it is what makes the reachable set bounded rather than a half-line.",
   "cone": "(A_4, 8D) lies outside the moment cone generated by the eight multiplets. Not even a REAL content -- fractional multiplicities allowed -- sits there.",
   "congruence": "the lattice law 8D = 2 A_4 + 3 (mod 6), Part VII Theorem 2. An integer obstruction: it holds at any size, and it holds on either gauge seed.",
   "dual": "an exact rational Farkas pair (lambda, nu): the smallest G a real content can have at this rung already lies outside the interval the target box allows. A bound with a witness, not a search.",
   "exhaustion": "the rung is a FINITE set -- of the eight generators only 7(+,+) has A_4 = 0, so at fixed A_4 the other seven are bounded and 7(+,+) is then pinned by 8D -- and the finite set was enumerated with nothing landing in the box."
  },
  "not_certificates": {
   "rung": "the rung cannot meet the box at all once (II) fixes mu as a function of x. Cheap, and it is a real exclusion of that rung -- but of the RUNG, not of the target.",
   "budget": "the enumeration ran past its declared budget. This is NOT a certificate and never prints as one: 'we stopped looking' must not read as 'there is none'."
  },
  "screen": "W > 0 is a SCREEN, not a certificate: Part VII eq. (34) compares the two symmetric points only, so every design is put on the exact potential before it is delivered.",
  "dual_vertices": {
   "lower": [
    [
     "-2760913347279289022424017578967/3000000000000000000000000000000",
     "231049060186648436472410707153/2000000000000000000000000000000"
    ],
    [
     "-3971002069519070260092946064803/3750000000000000000000000000000",
     "3927834023173023420030982021601/10000000000000000000000000000000"
    ]
   ],
   "upper": [
    [
     "434676409720027345291383939271/375000000000000000000000000000",
     "346573590279972654708616060729/3000000000000000000000000000000"
    ]
   ]
  },
  "k_max": 21,
  "published": {
   "k_band": [
    1,
    3,
    5,
    7
   ],
   "bands": [
    {
     "k8D": 1,
     "bottom": 8897.457324783607,
     "top": 9967.119825496062,
     "top_LP": 10034.021039019786,
     "enumerated": 423631,
     "in_window": 1769,
     "n_W": 430,
     "bottom_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 4
      }
     ],
     "top_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 17
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 2
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 57
      }
     ],
     "closed_below": {
      "dual": 29
     },
     "A4_cap": 215,
     "A4_first": 74,
     "bottom_A4": 74,
     "top_A4": 212,
     "top_W": 9156.174055989379,
     "top_W_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 16
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 4
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      }
     ]
    },
    {
     "k8D": 3,
     "bottom": 5257.9787698220225,
     "top": 6215.347006976357,
     "top_LP": 6266.49784914276,
     "enumerated": 3888823,
     "in_window": 4495,
     "n_W": 191,
     "bottom_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 19
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 18
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 5
      }
     ],
     "top_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 30
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 2
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 83
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      }
     ],
     "closed_below": {
      "dual": 34
     },
     "A4_cap": 336,
     "A4_first": 90,
     "bottom_A4": 90,
     "top_A4": 324,
     "top_W": 5477.839325578678,
     "top_W_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 6
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 5
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      }
     ]
    },
    {
     "k8D": 5,
     "bottom": 4057.9350878652594,
     "top": 5103.210574272533,
     "top_LP": 5137.318665568311,
     "enumerated": 15802014,
     "in_window": 8434,
     "n_W": 1594,
     "bottom_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 8
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 8
      },
      {
       "rep": "28",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 5
      }
     ],
     "top_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 38
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 2
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 108
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      }
     ],
     "closed_below": {
      "dual": 37
     },
     "A4_cap": 436,
     "A4_first": 97,
     "bottom_A4": 97,
     "top_A4": 424,
     "top_W": 4269.567158802665,
     "top_W_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 7
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      }
     ]
    },
    {
     "k8D": 7,
     "bottom": 3455.87778063836,
     "top": 4440.735641770118,
     "top_LP": 4562.093002617042,
     "enumerated": 48907996,
     "in_window": 13915,
     "n_W": 1961,
     "bottom_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 13
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 14
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 6
      }
     ],
     "top_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 38
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 119
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      }
     ],
     "closed_below": {
      "dual": 39
     },
     "A4_cap": 533,
     "A4_first": 104,
     "bottom_A4": 104,
     "top_A4": 479,
     "top_W": 3688.327697782909,
     "top_W_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 13
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 6
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 2
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      }
     ]
    }
   ],
   "ladder": [
    {
     "k8D": 1,
     "lo": 8897.540257667888,
     "hi": 9157.088151918197,
     "gap_above": null
    },
    {
     "k8D": 3,
     "lo": 5258.155622841155,
     "hi": 5445.5771214473225,
     "gap_above": [
      5445.5771214473225,
      8897.540257667888
     ]
    },
    {
     "k8D": 5,
     "lo": 4058.195991274372,
     "hi": 4258.565000475089,
     "gap_above": [
      4258.565000475089,
      5258.155622841155
     ]
    },
    {
     "k8D": 7,
     "lo": 3456.2047491656344,
     "hi": 3617.0206937797134,
     "gap_above": [
      3617.0206937797134,
      4058.195991274372
     ]
    }
   ],
   "band_ends": [
    {
     "k8D": 1,
     "which": "floor",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 4
      }
     ],
     "closed": 8897.457324783607,
     "exact": 8897.540257667888,
     "exact_mh": 125.58265810263109,
     "false_vacua_passed": 0
    },
    {
     "k8D": 1,
     "which": "top",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 16
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 4
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      }
     ],
     "closed": 9156.174055989379,
     "exact": 9157.088151918197,
     "exact_mh": 125.984280598191,
     "false_vacua_passed": 0
    },
    {
     "k8D": 3,
     "which": "floor",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 19
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 18
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 5
      }
     ],
     "closed": 5257.9787698220225,
     "exact": 5258.155622841155,
     "exact_mh": 126.95892099498224,
     "false_vacua_passed": 0
    },
    {
     "k8D": 3,
     "which": "top",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 8
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      }
     ],
     "closed": 5443.134240631868,
     "exact": 5445.5771214473225,
     "exact_mh": 125.86939492299435,
     "false_vacua_passed": 4
    },
    {
     "k8D": 5,
     "which": "floor",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 8
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 8
      },
      {
       "rep": "28",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 5
      }
     ],
     "closed": 4057.9350878652594,
     "exact": 4058.195991274372,
     "exact_mh": 125.51253534175115,
     "false_vacua_passed": 0
    },
    {
     "k8D": 5,
     "which": "top",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 21
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 4
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      }
     ],
     "closed": 4255.276326042109,
     "exact": 4258.565000475089,
     "exact_mh": 125.36626799717757,
     "false_vacua_passed": 13
    },
    {
     "k8D": 7,
     "which": "floor",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 13
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 14
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 6
      }
     ],
     "closed": 3455.87778063836,
     "exact": 3456.2047491656344,
     "exact_mh": 125.77015070960306,
     "false_vacua_passed": 0
    },
    {
     "k8D": 7,
     "which": "top",
     "content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 12
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 1
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 3
      },
      {
       "rep": "84",
       "parities": [
        1,
        1
       ],
       "multiplicity": 2
      }
     ],
     "closed": 3613.227306510282,
     "exact": 3617.0206937797134,
     "exact_mh": 125.28590673101206,
     "false_vacua_passed": 31
    }
   ],
   "gap": {
    "lo": 6215.347006976357,
    "hi": 8897.457324783607,
    "width": 2682.11031780725,
    "lo_LP": 6266.49784914276
   },
   "gap_note": "between the rung-3 ceiling and the rung-1 floor. The ends are rounded INWARD, never to nearest: an interval that says 'nothing here' is a negative claim, and rounding to nearest can put an occupied point inside it.",
   "verified_rung1": {
    "n_window": 1769,
    "n_Wpos": 430,
    "n_true": 430,
    "lo": 8897.457324783607,
    "hi": 9156.174055989379,
    "lo_content": [
     {
      "rep": "7",
      "parities": [
       1,
       1
      ],
      "multiplicity": 2
     },
     {
      "rep": "7",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 3
     },
     {
      "rep": "28",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     },
     {
      "rep": "48",
      "parities": [
       1,
       1
      ],
      "multiplicity": 4
     }
    ],
    "hi_content": [
     {
      "rep": "7",
      "parities": [
       1,
       1
      ],
      "multiplicity": 16
     },
     {
      "rep": "28",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 1
     },
     {
      "rep": "48",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     },
     {
      "rep": "48",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 4
     },
     {
      "rep": "84",
      "parities": [
       1,
       1
      ],
      "multiplicity": 1
     }
    ]
   },
   "pdg_window": {
    "n": 81,
    "n_points": 1,
    "lo": 8967.465585390897,
    "hi": 8967.465585390897,
    "lo_content": [
     {
      "rep": "7",
      "parities": [
       1,
       1
      ],
      "multiplicity": 10
     },
     {
      "rep": "28",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 2
     },
     {
      "rep": "48",
      "parities": [
       1,
       1
      ],
      "multiplicity": 4
     },
     {
      "rep": "48",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 3
     }
    ],
    "hi_content": [
     {
      "rep": "7",
      "parities": [
       1,
       1
      ],
      "multiplicity": 10
     },
     {
      "rep": "28",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 2
     },
     {
      "rep": "48",
      "parities": [
       1,
       1
      ],
      "multiplicity": 4
     },
     {
      "rep": "48",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 3
     }
    ]
   }
  },
  "candidate": {
   "seeds": {
    "published": {
     "A4": "-18",
     "k8D": -27,
     "G": -23.98362997908106,
     "W2": "-3"
    },
    "ghost": {
     "A4": "-27/2",
     "k8D": -18,
     "G": -17.72779229160082,
     "W2": "-3"
    }
   },
   "lp_caps": {
    "2": 545,
    "4": 751,
    "6": 951
   },
   "bands": [
    {
     "k8D": 2,
     "bottom": 6383.952178724947,
     "top": 7320.789766731146,
     "top_LP": 7376.302771760749,
     "enumerated": 1227070,
     "in_window": 2783,
     "n_W": 577,
     "bottom_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 6
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 7
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 5
      }
     ],
     "top_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 25
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 67
      },
      {
       "rep": "48",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      }
     ],
     "closed_below": {
      "dual(max)": 31
     },
     "t2_cap": 545,
     "bottom_t2": 167,
     "top_t2": 527
    },
    {
     "k8D": 4,
     "bottom": 4535.441486831367,
     "top": 5546.57394713846,
     "top_LP": 5554.221626919528,
     "enumerated": 6570135,
     "in_window": 7593,
     "n_W": 1507,
     "bottom_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 19
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 17
      },
      {
       "rep": "48",
       "parities": [
        1,
        1
       ],
       "multiplicity": 5
      }
     ],
     "top_content": [
      {
       "rep": "7",
       "parities": [
        1,
        1
       ],
       "multiplicity": 30
      },
      {
       "rep": "7",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 1
      },
      {
       "rep": "28",
       "parities": [
        1,
        -1
       ],
       "multiplicity": 97
      }
     ],
     "closed_below": {
      "dual(max)": 34
     },
     "t2_cap": 751,
     "bottom_t2": 187,
     "top_t2": 751
    }
   ],
   "ladder": [
    {
     "k8D": 2,
     "lo": 6384.0906184247115,
     "hi": 6574.135792810597,
     "lo_content": [
      6,
      7,
      0,
      0,
      5,
      0,
      0,
      0
     ],
     "hi_content": [
      27,
      4,
      0,
      0,
      1,
      5,
      1,
      0
     ]
    },
    {
     "k8D": 4,
     "lo": 4535.667423118169,
     "hi": 4719.318906852154,
     "lo_content": [
      19,
      17,
      0,
      0,
      5,
      0,
      0,
      0
     ],
     "hi_content": [
      11,
      1,
      0,
      2,
      0,
      2,
      2,
      0
     ]
    }
   ],
   "gap": {
    "lo": 5546.57394713846,
    "hi": 6383.952178724947,
    "width": 837.3782315864864
   },
   "pdg": {
    "n": 100,
    "n_true": 100,
    "n_points": 1,
    "lo": 6407.695228293932,
    "hi": 6407.695228293932,
    "lo_content": [
     {
      "rep": "7",
      "parities": [
       1,
       1
      ],
      "multiplicity": 16
     },
     {
      "rep": "28",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 2
     },
     {
      "rep": "48",
      "parities": [
       1,
       1
      ],
      "multiplicity": 4
     },
     {
      "rep": "48",
      "parities": [
       1,
       -1
      ],
      "multiplicity": 4
     }
    ]
   },
   "census": {
    "k8D": 2,
    "n_window": 2783,
    "n_W": 577,
    "n_true_coarse": 556,
    "coarse_lo": 6383.952178724947,
    "coarse_hi": 6600.994684757432,
    "above_verified_top": 26,
    "of_those_survive_fine": 0,
    "note": "el censo grueso es cota superior; los extremos son de la caza fina"
   },
   "note": "the candidate parity-resolved seed of Part VII section 13, where 8D is even and A_4 half-integral. The reachable SUBGROUP of Z^2 in (2A_4, 8D) is the same on both seeds -- basis (2, 8) and (0, 6) -- so only the base point moves, and the mod-6 law survives while the odd-eighths corollary does not."
  },
  "rows": [
   {
    "row": "(1)",
    "invR": 2901.333357343979,
    "mh": 143.54658735371913,
    "A4": 258,
    "k8D": 15,
    "hits": 64,
    "own": true,
    "same_rung": true,
    "smallest": [
     0,
     0,
     0,
     1,
     0,
     0,
     4,
     0
    ],
    "W": "63/2"
   },
   {
    "row": "(2)",
    "invR": 1923.9281906647107,
    "mh": 125.85239573466873,
    "A4": 271,
    "k8D": 29,
    "hits": 64,
    "own": true,
    "same_rung": true,
    "smallest": [
     0,
     0,
     1,
     0,
     0,
     0,
     4,
     0
    ],
    "W": "75/2"
   },
   {
    "row": "(3)",
    "invR": 3686.2929826607324,
    "mh": 148.11105831889114,
    "A4": 189,
    "k8D": 9,
    "hits": 64,
    "own": true,
    "same_rung": true,
    "smallest": [
     0,
     0,
     1,
     0,
     3,
     0,
     2,
     0
    ],
    "W": "75/2"
   },
   {
    "row": "(4)",
    "invR": 3426.456154432728,
    "mh": 149.68052860596697,
    "A4": 223,
    "k8D": 11,
    "hits": 64,
    "own": true,
    "same_rung": true,
    "smallest": [
     0,
     1,
     0,
     0,
     2,
     0,
     3,
     0
    ],
    "W": "73/2"
   },
   {
    "row": "(5)",
    "invR": 2902.909316815872,
    "mh": 143.9951603358952,
    "A4": 255,
    "k8D": 15,
    "hits": 64,
    "own": true,
    "same_rung": true,
    "smallest": [
     1,
     1,
     0,
     0,
     0,
     0,
     4,
     0
    ],
    "W": "69/2"
   }
  ],
  "design_table": [
   {
    "target_TeV": 3.0,
    "kmax": 21,
    "tried": 2,
    "false_vacua": 2,
    "verdict": "undecided",
    "proved": false,
    "certificates": {
     "floor": 4,
     "rung": 7,
     "dual": 9,
     "exhaustion": 31,
     "budget": 42
    },
    "without_W": [
     16,
     0,
     0,
     8,
     0,
     1,
     1,
     1
    ]
   },
   {
    "target_TeV": 6.0,
    "kmax": 3,
    "tried": 0,
    "false_vacua": 0,
    "verdict": "no-go",
    "proved": true,
    "certificates": {
     "floor": 1,
     "rung": 2,
     "exhaustion": 10
    },
    "without_W": [
     33,
     3,
     0,
     60,
     1,
     3,
     0,
     0
    ]
   },
   {
    "target_TeV": 6.5,
    "kmax": 1,
    "tried": 0,
    "false_vacua": 0,
    "verdict": "no-go",
    "proved": true,
    "certificates": {
     "floor": 1
    },
    "without_W": null
   },
   {
    "target_TeV": 7.0,
    "kmax": 1,
    "tried": 0,
    "false_vacua": 0,
    "verdict": "no-go",
    "proved": true,
    "certificates": {
     "floor": 1
    },
    "without_W": null
   },
   {
    "target_TeV": 8.0,
    "kmax": 1,
    "tried": 0,
    "false_vacua": 0,
    "verdict": "no-go",
    "proved": true,
    "certificates": {
     "floor": 1
    },
    "without_W": null
   },
   {
    "target_TeV": 9.0,
    "kmax": 1,
    "tried": 1,
    "false_vacua": 0,
    "verdict": "design",
    "invR": 9008.48226663603,
    "A4": 80,
    "k8D": 1,
    "size": 8,
    "content": [
     0,
     1,
     1,
     2,
     4,
     0,
     0,
     0
    ],
    "mh": 126.6180162115633,
    "alpha": 0.017849843651859276,
    "W": "37/2",
    "exact": {
     "alpha": 0.017849443209304948,
     "invR": 9008.684367038108,
     "mh": 126.62131740084537
    }
   },
   {
    "target_TeV": 9.1,
    "kmax": 1,
    "tried": 1,
    "false_vacua": 0,
    "verdict": "design",
    "invR": 9080.935301245767,
    "A4": 92,
    "k8D": 1,
    "size": 14,
    "content": [
     5,
     6,
     0,
     0,
     2,
     0,
     1,
     0
    ],
    "mh": 126.26598332895094,
    "alpha": 0.017707427116889676,
    "W": "37/2",
    "exact": {
     "alpha": 0.017706140859730123,
     "invR": 9081.594982999075,
     "mh": 126.27687573057023
    }
   },
   {
    "target_TeV": 9.5,
    "kmax": 1,
    "tried": 0,
    "false_vacua": 0,
    "verdict": "no-go",
    "proved": true,
    "certificates": {
     "rung": 2,
     "exhaustion": 9
    },
    "without_W": [
     14,
     1,
     0,
     19,
     0,
     2,
     1,
     0
    ]
   }
  ],
  "source": "research/smeft_formalization/part_viii/outputs/inverse_design.json and research/smeft_formalization/part_viii/outputs/reachable_set.json",
  "note": "The bands and their ends are READ. Finding the floor of rung 1 means enumerating 423 631 contents and putting the survivors on the exact potential; the page shows that, it does not re-derive it. What the page DOES re-derive is the decision at a rung -- the certificates and the enumeration -- and it is held to this archive."
 },
 "census": {
  "free": "7(+,+)",
  "step": 6,
  "build_seconds": 0.89,
  "totals": {
   "1": {
    "A4_cap": 215,
    "n_legal_A4": 77,
    "counted": 423631,
    "enumerated": 423631
   },
   "3": {
    "A4_cap": 336,
    "n_legal_A4": 117,
    "counted": 3888823,
    "enumerated": 3888823
   },
   "5": {
    "A4_cap": 436,
    "n_legal_A4": 151,
    "counted": 15802014,
    "enumerated": 15802014
   },
   "7": {
    "A4_cap": 533,
    "n_legal_A4": 183,
    "counted": 48907996,
    "enumerated": 48907996
   }
  },
  "curves": {
   "1": {
    "A4": [
     -13,
     -10,
     -7,
     -4,
     -1,
     2,
     5,
     8,
     11,
     14,
     17,
     20,
     23,
     26,
     29,
     32,
     35,
     38,
     41,
     44,
     47,
     50,
     53,
     56,
     59,
     62,
     65,
     68,
     71,
     74,
     77,
     80,
     83,
     86,
     89,
     92,
     95,
     98,
     101,
     104,
     107,
     110,
     113,
     116,
     119,
     122,
     125,
     128,
     131,
     134,
     137,
     140,
     143,
     146,
     149,
     152,
     155,
     158,
     161,
     164,
     167,
     170,
     173,
     176,
     179,
     182,
     185,
     188,
     191,
     194,
     197,
     200,
     203,
     206,
     209,
     212,
     215
    ],
    "N": [
     1,
     3,
     4,
     5,
     8,
     12,
     15,
     23,
     28,
     35,
     43,
     56,
     69,
     84,
     96,
     118,
     139,
     164,
     189,
     222,
     252,
     292,
     329,
     380,
     430,
     488,
     540,
     615,
     687,
     771,
     850,
     953,
     1052,
     1169,
     1279,
     1424,
     1560,
     1716,
     1868,
     2059,
     2242,
     2455,
     2658,
     2907,
     3149,
     3424,
     3695,
     4021,
     4334,
     4692,
     5039,
     5452,
     5862,
     6316,
     6758,
     7285,
     7795,
     8365,
     8933,
     9587,
     10226,
     10938,
     11638,
     12448,
     13245,
     14118,
     14988,
     15977,
     16947,
     18021,
     19085,
     20282,
     21470,
     22764,
     24052,
     25502,
     26933
    ]
   },
   "3": {
    "A4": [
     -12,
     -9,
     -6,
     -3,
     0,
     3,
     6,
     9,
     12,
     15,
     18,
     21,
     24,
     27,
     30,
     33,
     36,
     39,
     42,
     45,
     48,
     51,
     54,
     57,
     60,
     63,
     66,
     69,
     72,
     75,
     78,
     81,
     84,
     87,
     90,
     93,
     96,
     99,
     102,
     105,
     108,
     111,
     114,
     117,
     120,
     123,
     126,
     129,
     132,
     135,
     138,
     141,
     144,
     147,
     150,
     153,
     156,
     159,
     162,
     165,
     168,
     171,
     174,
     177,
     180,
     183,
     186,
     189,
     192,
     195,
     198,
     201,
     204,
     207,
     210,
     213,
     216,
     219,
     222,
     225,
     228,
     231,
     234,
     237,
     240,
     243,
     246,
     249,
     252,
     255,
     258,
     261,
     264,
     267,
     270,
     273,
     276,
     279,
     282,
     285,
     288,
     291,
     294,
     297,
     300,
     303,
     306,
     309,
     312,
     315,
     318,
     321,
     324,
     327,
     330,
     333,
     336
    ],
    "N": [
     1,
     3,
     5,
     6,
     8,
     12,
     18,
     23,
     31,
     38,
     47,
     56,
     74,
     89,
     105,
     122,
     146,
     170,
     202,
     229,
     266,
     303,
     347,
     390,
     450,
     504,
     570,
     631,
     713,
     796,
     890,
     976,
     1093,
     1203,
     1331,
     1457,
     1615,
     1764,
     1939,
     2105,
     2315,
     2518,
     2748,
     2972,
     3246,
     3508,
     3812,
     4106,
     4457,
     4802,
     5189,
     5565,
     6017,
     6456,
     6946,
     7429,
     7993,
     8546,
     9162,
     9768,
     10473,
     11162,
     11922,
     12681,
     13545,
     14394,
     15334,
     16263,
     17317,
     18361,
     19500,
     20635,
     21915,
     23176,
     24556,
     25931,
     27464,
     28988,
     30642,
     32291,
     34130,
     35947,
     37914,
     39890,
     42065,
     44226,
     46563,
     48899,
     51464,
     54020,
     56766,
     59525,
     62536,
     65532,
     68753,
     71985,
     75497,
     79008,
     82756,
     86521,
     90607,
     94681,
     99032,
     103411,
     108128,
     112844,
     117869,
     122921,
     128361,
     133798,
     139571,
     145389,
     151621,
     157860,
     164487,
     171147,
     178266
    ]
   },
   "5": {
    "A4": [
     -14,
     -11,
     -8,
     -5,
     -2,
     1,
     4,
     7,
     10,
     13,
     16,
     19,
     22,
     25,
     28,
     31,
     34,
     37,
     40,
     43,
     46,
     49,
     52,
     55,
     58,
     61,
     64,
     67,
     70,
     73,
     76,
     79,
     82,
     85,
     88,
     91,
     94,
     97,
     100,
     103,
     106,
     109,
     112,
     115,
     118,
     121,
     124,
     127,
     130,
     133,
     136,
     139,
     142,
     145,
     148,
     151,
     154,
     157,
     160,
     163,
     166,
     169,
     172,
     175,
     178,
     181,
     184,
     187,
     190,
     193,
     196,
     199,
     202,
     205,
     208,
     211,
     214,
     217,
     220,
     223,
     226,
     229,
     232,
     235,
     238,
     241,
     244,
     247,
     250,
     253,
     256,
     259,
     262,
     265,
     268,
     271,
     274,
     277,
     280,
     283,
     286,
     289,
     292,
     295,
     298,
     301,
     304,
     307,
     310,
     313,
     316,
     319,
     322,
     325,
     328,
     331,
     334,
     337,
     340,
     343,
     346,
     349,
     352,
     355,
     358,
     361,
     364,
     367,
     370,
     373,
     376,
     379,
     382,
     385,
     388,
     391,
     394,
     397,
     400,
     403,
     406,
     409,
     412,
     415,
     418,
     421,
     424,
     427,
     430,
     433,
     436
    ],
    "N": [
     1,
     1,
     3,
     5,
     8,
     10,
     13,
     19,
     26,
     31,
     43,
     51,
     62,
     75,
     94,
     111,
     133,
     151,
     180,
     209,
     243,
     275,
     319,
     360,
     413,
     461,
     526,
     589,
     664,
     732,
     827,
     917,
     1020,
     1119,
     1248,
     1371,
     1515,
     1651,
     1825,
     1991,
     2182,
     2369,
     2598,
     2817,
     3071,
     3316,
     3614,
     3905,
     4232,
     4551,
     4935,
     5307,
     5729,
     6140,
     6623,
     7099,
     7629,
     8148,
     8762,
     9356,
     10014,
     10671,
     11424,
     12163,
     12985,
     13794,
     14717,
     15630,
     16629,
     17626,
     18754,
     19862,
     21079,
     22291,
     23648,
     24998,
     26463,
     27922,
     29555,
     31170,
     32923,
     34681,
     36623,
     38550,
     40636,
     42723,
     45026,
     47314,
     49777,
     52251,
     54958,
     57652,
     60556,
     63462,
     66631,
     69796,
     73182,
     76585,
     80286,
     83971,
     87914,
     91878,
     96161,
     100446,
     105014,
     109602,
     114556,
     119503,
     124765,
     130071,
     135760,
     141451,
     147504,
     153589,
     160107,
     166642,
     173559,
     180525,
     187968,
     195423,
     203314,
     211261,
     219722,
     228212,
     237173,
     246201,
     255803,
     265428,
     275573,
     285805,
     296647,
     307534,
     318994,
     330543,
     342760,
     355032,
     367925,
     380934,
     394660,
     408454,
     422931,
     437526,
     452907,
     468382,
     484578,
     500921,
     518118,
     535406,
     553498,
     571758,
     590923
    ]
   },
   "7": {
    "A4": [
     -13,
     -10,
     -7,
     -4,
     -1,
     2,
     5,
     8,
     11,
     14,
     17,
     20,
     23,
     26,
     29,
     32,
     35,
     38,
     41,
     44,
     47,
     50,
     53,
     56,
     59,
     62,
     65,
     68,
     71,
     74,
     77,
     80,
     83,
     86,
     89,
     92,
     95,
     98,
     101,
     104,
     107,
     110,
     113,
     116,
     119,
     122,
     125,
     128,
     131,
     134,
     137,
     140,
     143,
     146,
     149,
     152,
     155,
     158,
     161,
     164,
     167,
     170,
     173,
     176,
     179,
     182,
     185,
     188,
     191,
     194,
     197,
     200,
     203,
     206,
     209,
     212,
     215,
     218,
     221,
     224,
     227,
     230,
     233,
     236,
     239,
     242,
     245,
     248,
     251,
     254,
     257,
     260,
     263,
     266,
     269,
     272,
     275,
     278,
     281,
     284,
     287,
     290,
     293,
     296,
     299,
     302,
     305,
     308,
     311,
     314,
     317,
     320,
     323,
     326,
     329,
     332,
     335,
     338,
     341,
     344,
     347,
     350,
     353,
     356,
     359,
     362,
     365,
     368,
     371,
     374,
     377,
     380,
     383,
     386,
     389,
     392,
     395,
     398,
     401,
     404,
     407,
     410,
     413,
     416,
     419,
     422,
     425,
     428,
     431,
     434,
     437,
     440,
     443,
     446,
     449,
     452,
     455,
     458,
     461,
     464,
     467,
     470,
     473,
     476,
     479,
     482,
     485,
     488,
     491,
     494,
     497,
     500,
     503,
     506,
     509,
     512,
     515,
     518,
     521,
     524,
     527,
     530,
     533
    ],
    "N": [
     1,
     2,
     3,
     5,
     8,
     12,
     15,
     20,
     27,
     35,
     43,
     56,
     67,
     81,
     95,
     118,
     139,
     163,
     187,
     219,
     251,
     292,
     329,
     378,
     428,
     485,
     539,
     615,
     685,
     769,
     848,
     950,
     1051,
     1168,
     1277,
     1422,
     1558,
     1713,
     1867,
     2058,
     2240,
     2453,
     2656,
     2904,
     3147,
     3423,
     3693,
     4019,
     4332,
     4688,
     5037,
     5451,
     5860,
     6314,
     6756,
     7281,
     7793,
     8364,
     8931,
     9585,
     10224,
     10934,
     11636,
     12447,
     13243,
     14116,
     14986,
     15973,
     16945,
     18020,
     19083,
     20280,
     21468,
     22760,
     24050,
     25501,
     26931,
     28487,
     30043,
     31769,
     33487,
     35349,
     37207,
     39266,
     41308,
     43510,
     45727,
     48157,
     50572,
     53179,
     55788,
     58641,
     61491,
     64545,
     67611,
     70952,
     74279,
     77846,
     81430,
     85313,
     89194,
     93337,
     97498,
     102002,
     106495,
     111284,
     116107,
     121293,
     126480,
     132000,
     137550,
     143508,
     149472,
     155798,
     162172,
     168986,
     175811,
     183047,
     190328,
     198097,
     205893,
     214121,
     222414,
     231248,
     240100,
     249445,
     258867,
     268860,
     278894,
     289465,
     300118,
     311411,
     322745,
     334659,
     346684,
     359388,
     372151,
     385565,
     399080,
     413336,
     427678,
     442707,
     457871,
     473846,
     489900,
     506709,
     523673,
     541503,
     559447,
     578206,
     597130,
     616998,
     636988,
     657863,
     678943,
     701022,
     723245,
     746431,
     769831,
     794320,
     818984,
     844674,
     870606,
     897704,
     924998,
     953411,
     982090,
     1012021,
     1042177,
     1073521,
     1105169,
     1138172,
     1171412,
     1205939,
     1240803,
     1277098,
     1313680,
     1351644,
     1389970,
     1429837,
     1470014,
     1511665,
     1553733
    ]
   }
  },
  "curves_low": {
   "9": {
    "A4": [
     -12,
     -9,
     -6,
     -3,
     0,
     3,
     6,
     9,
     12,
     15,
     18,
     21,
     24,
     27,
     30,
     33,
     36,
     39,
     42,
     45,
     48,
     51,
     54,
     57,
     60,
     63,
     66,
     69,
     72,
     75,
     78,
     81,
     84,
     87,
     90,
     93,
     96,
     99,
     102,
     105,
     108,
     111,
     114,
     117,
     120,
     123,
     126,
     129,
     132,
     135,
     138,
     141,
     144,
     147,
     150,
     153,
     156,
     159,
     162,
     165,
     168,
     171,
     174,
     177,
     180,
     183,
     186,
     189,
     192,
     195,
     198,
     201,
     204,
     207,
     210,
     213,
     216,
     219,
     222,
     225,
     228,
     231,
     234,
     237,
     240,
     243,
     246,
     249,
     252,
     255,
     258,
     261,
     264,
     267,
     270,
     273,
     276,
     279,
     282,
     285,
     288,
     291,
     294,
     297,
     300,
     303,
     306,
     309,
     312,
     315,
     318,
     321,
     324,
     327,
     330,
     333,
     336,
     339,
     342,
     345,
     348,
     351,
     354,
     357,
     360,
     363,
     366,
     369,
     372,
     375,
     378,
     381,
     384,
     387,
     390,
     393,
     396,
     399,
     402,
     405,
     408,
     411,
     414,
     417,
     420,
     423,
     426,
     429,
     432,
     435,
     438,
     441,
     444,
     447,
     450,
     453,
     456,
     459,
     462,
     465,
     468,
     471,
     474,
     477,
     480,
     483,
     486,
     489,
     492,
     495,
     498,
     501,
     504,
     507,
     510,
     513,
     516,
     519,
     522,
     525,
     528,
     531,
     534,
     537,
     540,
     543,
     546,
     549,
     552,
     555,
     558,
     561,
     564,
     567,
     570,
     573,
     576,
     579,
     582,
     585,
     588,
     591,
     594,
     597,
     600,
     603,
     606,
     609,
     612,
     615,
     618,
     621,
     624,
     627,
     630,
     633,
     636,
     639,
     642,
     645,
     648,
     651,
     654,
     657,
     660,
     663,
     666,
     669,
     672,
     675,
     678,
     681,
     684,
     687,
     690,
     693,
     696,
     699,
     702,
     705,
     708,
     711,
     714,
     717,
     720,
     723,
     726,
     729,
     732,
     735,
     738,
     741,
     744,
     747,
     750,
     753,
     756,
     759,
     762,
     765,
     768,
     771,
     774,
     777,
     780,
     783,
     786,
     789,
     792,
     795,
     798,
     801,
     804,
     807,
     810,
     813,
     816,
     819,
     822,
     825,
     828,
     831,
     834,
     837,
     840,
     843,
     846,
     849,
     852,
     855,
     858,
     861,
     864,
     867,
     870,
     873,
     876,
     879
    ],
    "N": [
     1,
     3,
     4,
     5,
     8,
     12,
     18,
     23,
     28,
     37,
     47,
     56,
     74,
     87,
     102,
     121,
     146,
     170,
     201,
     227,
     263,
     302,
     347,
     390,
     448,
     502,
     567,
     630,
     713,
     794,
     888,
     974,
     1090,
     1202,
     1330,
     1455,
     1613,
     1762,
     1936,
     2104,
     2314,
     2516,
     2746,
     2970,
     3243,
     3506,
     3811,
     4104,
     4455,
     4800,
     5185,
     5563,
     6016,
     6454,
     6944,
     7427,
     7989,
     8544,
     9161,
     9766,
     10471,
     11160,
     11918,
     12679,
     13544,
     14392,
     15331,
     16261,
     17313,
     18359,
     19499,
     20633,
     21912,
     23174,
     24552,
     25929,
     27463,
     28986,
     30639,
     32289,
     34126,
     35945,
     37913,
     39888,
     42062,
     44224,
     46559,
     48897,
     51463,
     54018,
     56763,
     59523,
     62532,
     65530,
     68752,
     71983,
     75494,
     79006,
     82752,
     86519,
     90606,
     94679,
     99029,
     103409,
     108124,
     112842,
     117868,
     122919,
     128358,
     133796,
     139567,
     145387,
     151620,
     157858,
     164484,
     171145,
     178262,
     185405,
     192957,
     200565,
     208682,
     216812,
     225400,
     234059,
     243263,
     252502,
     262242,
     272055,
     282470,
     292923,
     303927,
     315031,
     326773,
     338566,
     350967,
     363470,
     376679,
     389958,
     403886,
     417936,
     432747,
     447639,
     463252,
     478998,
     495566,
     512236,
     529673,
     547271,
     565771,
     584371,
     603812,
     623438,
     644016,
     664734,
     686365,
     708190,
     731051,
     754065,
     778057,
     802287,
     827623,
     853134,
     879711,
     906532,
     934547,
     962780,
     992139,
     1021780,
     1052711,
     1083863,
     1116243,
     1148943,
     1183010,
     1217338,
     1252980,
     1288964,
     1326427,
     1364178,
     1403336,
     1442883,
     1483995,
     1525431,
     1568388,
     1611754,
     1656800,
     1702217,
     1749240,
     1796726,
     1846009,
     1895688,
     1947093,
     1999004,
     2052821,
     2107089,
     2163192,
     2219845,
     2278539,
     2337716,
     2398852,
     2460602,
     2524499,
     2588936,
     2655470,
     2722653,
     2792133,
     2862209,
     2934495,
     3007497,
     3082937,
     3159021,
     3237469,
     3316686,
     3398481,
     3480989,
     3565995,
     3651839,
     3740430,
     3829773,
     3921769,
     4014683,
     4110486,
     4207124,
     4306580,
     4407007,
     4510493,
     4614885,
     4722254,
     4830688,
     4942349,
     5054983,
     5170773,
     5287695,
     5408032,
     5529439,
     5654157,
     5780097,
     5909649,
     6040331,
     6174533,
     6310056,
     6449365,
     6589898,
     6734141,
     6879789,
     7029451,
     7180422,
     7335299,
     7491691,
     7652286,
     7814292,
     7980441,
     8148181,
     8320351,
     8494047,
     8672073,
     8851821,
     9036242,
     9222270,
     9412867,
     9605298,
     9802620,
     10001687,
     10205557,
     10411370,
     10622337,
     10835144,
     11052996,
     11272946,
     11498278,
     11725579,
     11958198,
     12193014,
     12433490,
     12676082,
     12924231,
     13174724,
     13431153,
     13689815,
     13954326,
     14221323,
     14494530,
     14770128,
     15051840,
     15336185,
     15627055,
     15920438,
     16220236,
     16522841,
     16832245,
     17144335,
     17463150,
     17784912,
     18113800,
     18445534,
     18784294,
     19126193,
     19475529,
     19827876
    ]
   },
   "13": {
    "A4": [
     -13,
     -10,
     -7,
     -4,
     -1,
     2,
     5,
     8,
     11,
     14,
     17,
     20,
     23,
     26,
     29,
     32,
     35,
     38,
     41,
     44,
     47,
     50,
     53,
     56,
     59,
     62,
     65,
     68,
     71,
     74,
     77,
     80,
     83,
     86,
     89,
     92,
     95,
     98,
     101,
     104,
     107,
     110,
     113,
     116,
     119,
     122,
     125,
     128,
     131,
     134,
     137,
     140,
     143,
     146,
     149,
     152,
     155,
     158,
     161,
     164,
     167,
     170,
     173,
     176,
     179,
     182,
     185,
     188,
     191,
     194,
     197,
     200,
     203,
     206,
     209,
     212,
     215,
     218,
     221,
     224,
     227,
     230,
     233,
     236,
     239,
     242,
     245,
     248,
     251,
     254,
     257,
     260,
     263,
     266,
     269,
     272,
     275,
     278,
     281,
     284,
     287,
     290,
     293,
     296,
     299,
     302,
     305,
     308,
     311,
     314,
     317,
     320,
     323,
     326,
     329,
     332,
     335,
     338,
     341,
     344,
     347,
     350,
     353,
     356,
     359,
     362,
     365,
     368,
     371,
     374,
     377,
     380,
     383,
     386,
     389,
     392,
     395,
     398,
     401,
     404,
     407,
     410,
     413,
     416,
     419,
     422,
     425,
     428,
     431,
     434,
     437,
     440,
     443,
     446,
     449,
     452,
     455,
     458,
     461,
     464,
     467,
     470,
     473,
     476,
     479,
     482,
     485,
     488,
     491,
     494,
     497,
     500,
     503,
     506,
     509,
     512,
     515,
     518,
     521,
     524,
     527,
     530,
     533,
     536,
     539,
     542,
     545,
     548,
     551,
     554,
     557,
     560,
     563,
     566,
     569,
     572,
     575,
     578,
     581,
     584,
     587,
     590,
     593,
     596,
     599,
     602,
     605,
     608,
     611,
     614,
     617,
     620,
     623,
     626,
     629,
     632,
     635,
     638,
     641,
     644,
     647,
     650,
     653,
     656,
     659,
     662,
     665,
     668,
     671,
     674,
     677,
     680,
     683,
     686,
     689,
     692,
     695,
     698,
     701,
     704,
     707,
     710,
     713,
     716,
     719,
     722,
     725,
     728,
     731,
     734,
     737,
     740,
     743,
     746,
     749,
     752,
     755,
     758,
     761,
     764,
     767,
     770,
     773,
     776,
     779,
     782,
     785,
     788,
     791,
     794,
     797,
     800,
     803,
     806,
     809,
     812,
     815,
     818,
     821,
     824,
     827,
     830,
     833,
     836,
     839,
     842,
     845,
     848,
     851,
     854,
     857,
     860,
     863,
     866,
     869,
     872,
     875,
     878
    ],
    "N": [
     1,
     1,
     3,
     5,
     8,
     11,
     13,
     19,
     27,
     35,
     43,
     52,
     65,
     80,
     95,
     118,
     137,
     159,
     185,
     218,
     251,
     291,
     326,
     374,
     426,
     484,
     539,
     612,
     682,
     765,
     846,
     949,
     1049,
     1165,
     1274,
     1418,
     1556,
     1711,
     1865,
     2055,
     2237,
     2449,
     2654,
     2902,
     3145,
     3420,
     3690,
     4015,
     4329,
     4686,
     5035,
     5448,
     5857,
     6309,
     6753,
     7279,
     7791,
     8361,
     8928,
     9580,
     10221,
     10932,
     11634,
     12444,
     13240,
     14111,
     14983,
     15971,
     16943,
     18016,
     19080,
     20275,
     21465,
     22758,
     24048,
     25497,
     26928,
     28482,
     30040,
     31767,
     33485,
     35345,
     37204,
     39261,
     41305,
     43508,
     45725,
     48153,
     50569,
     53174,
     55785,
     58639,
     61489,
     64541,
     67608,
     70947,
     74276,
     77844,
     81428,
     85309,
     89191,
     93332,
     97495,
     102000,
     106493,
     111280,
     116104,
     121288,
     126477,
     131998,
     137548,
     143504,
     149469,
     155793,
     162169,
     168984,
     175809,
     183043,
     190325,
     198092,
     205890,
     214119,
     222412,
     231244,
     240097,
     249440,
     258864,
     268858,
     278892,
     289461,
     300115,
     311406,
     322742,
     334657,
     346682,
     359384,
     372148,
     385560,
     399077,
     413334,
     427676,
     442703,
     457868,
     473841,
     489897,
     506707,
     523671,
     541499,
     559444,
     578201,
     597127,
     616996,
     636986,
     657859,
     678940,
     701017,
     723242,
     746429,
     769829,
     794316,
     818981,
     844669,
     870603,
     897702,
     924996,
     953407,
     982087,
     1012016,
     1042174,
     1073519,
     1105167,
     1138168,
     1171409,
     1205934,
     1240800,
     1277096,
     1313678,
     1351640,
     1389967,
     1429832,
     1470011,
     1511663,
     1553731,
     1597434,
     1641488,
     1687127,
     1733206,
     1781037,
     1829270,
     1879175,
     1929574,
     1981849,
     2034546,
     2089047,
     2144091,
     2201115,
     2258618,
     2318040,
     2378045,
     2440175,
     2502822,
     2567508,
     2632844,
     2700421,
     2768570,
     2838906,
     2909923,
     2983326,
     3057369,
     3133713,
     3210815,
     3290455,
     3370771,
     3453539,
     3537130,
     3623400,
     3710424,
     3800045,
     3890547,
     3983896,
     4078052,
     4174963,
     4272845,
     4373716,
     4475465,
     4580144,
     4685850,
     4794731,
     4904574,
     5017496,
     5131528,
     5248915,
     5367332,
     5489022,
     5611903,
     5738317,
     5865849,
     5996825,
     6129084,
     6265089,
     6402275,
     6543102,
     6685314,
     6831450,
     6978876,
     7130153,
     7282893,
     7439772,
     7598032,
     7760341,
     7924236,
     8092482,
     8262204,
     8436202,
     8611872,
     8792123,
     8973978,
     9160307,
     9348430,
     9541380,
     9736014,
     9935377,
     10136663,
     10342995,
     10551140,
     10764252,
     10979394,
     11199859,
     11422251,
     11649854,
     11879635,
     12114975,
     12352370,
     12595264,
     12840440,
     13091454,
     13344677,
     13603634,
     13865034,
     14132565,
     14402416,
     14678295,
     14956767,
     15241639,
     15529002,
     15822676,
     16119085,
     16422215,
     16727968,
     17040329,
     17355614,
     17677897,
     18002970,
     18334982,
     18670054,
     19012464,
     19357843,
     19710451
    ]
   },
   "17": {
    "A4": [
     -11,
     -8,
     -5,
     -2,
     1,
     4,
     7,
     10,
     13,
     16,
     19,
     22,
     25,
     28,
     31,
     34,
     37,
     40,
     43,
     46,
     49,
     52,
     55,
     58,
     61,
     64,
     67,
     70,
     73,
     76,
     79,
     82,
     85,
     88,
     91,
     94,
     97,
     100,
     103,
     106,
     109,
     112,
     115,
     118,
     121,
     124,
     127,
     130,
     133,
     136,
     139,
     142,
     145,
     148,
     151,
     154,
     157,
     160,
     163,
     166,
     169,
     172,
     175,
     178,
     181,
     184,
     187,
     190,
     193,
     196,
     199,
     202,
     205,
     208,
     211,
     214,
     217,
     220,
     223,
     226,
     229,
     232,
     235,
     238,
     241,
     244,
     247,
     250,
     253,
     256,
     259,
     262,
     265,
     268,
     271,
     274,
     277,
     280,
     283,
     286,
     289,
     292,
     295,
     298,
     301,
     304,
     307,
     310,
     313,
     316,
     319,
     322,
     325,
     328,
     331,
     334,
     337,
     340,
     343,
     346,
     349,
     352,
     355,
     358,
     361,
     364,
     367,
     370,
     373,
     376,
     379,
     382,
     385,
     388,
     391,
     394,
     397,
     400,
     403,
     406,
     409,
     412,
     415,
     418,
     421,
     424,
     427,
     430,
     433,
     436,
     439,
     442,
     445,
     448,
     451,
     454,
     457,
     460,
     463,
     466,
     469,
     472,
     475,
     478,
     481,
     484,
     487,
     490,
     493,
     496,
     499,
     502,
     505,
     508,
     511,
     514,
     517,
     520,
     523,
     526,
     529,
     532,
     535,
     538,
     541,
     544,
     547,
     550,
     553,
     556,
     559,
     562,
     565,
     568,
     571,
     574,
     577,
     580,
     583,
     586,
     589,
     592,
     595,
     598,
     601,
     604,
     607,
     610,
     613,
     616,
     619,
     622,
     625,
     628,
     631,
     634,
     637,
     640,
     643,
     646,
     649,
     652,
     655,
     658,
     661,
     664,
     667,
     670,
     673,
     676,
     679,
     682,
     685,
     688,
     691,
     694,
     697,
     700,
     703,
     706,
     709,
     712,
     715,
     718,
     721,
     724,
     727,
     730,
     733,
     736,
     739,
     742,
     745,
     748,
     751,
     754,
     757,
     760,
     763,
     766,
     769,
     772,
     775,
     778,
     781,
     784,
     787,
     790,
     793,
     796,
     799,
     802,
     805,
     808,
     811,
     814,
     817,
     820,
     823,
     826,
     829,
     832,
     835,
     838,
     841,
     844,
     847,
     850,
     853,
     856,
     859,
     862,
     865,
     868,
     871,
     874,
     877,
     880
    ],
    "N": [
     1,
     3,
     4,
     6,
     8,
     12,
     19,
     25,
     28,
     38,
     49,
     61,
     75,
     90,
     106,
     128,
     149,
     179,
     207,
     238,
     270,
     314,
     358,
     410,
     458,
     520,
     584,
     659,
     730,
     822,
     912,
     1014,
     1114,
     1243,
     1367,
     1509,
     1646,
     1819,
     1986,
     2176,
     2365,
     2592,
     2812,
     3065,
     3311,
     3607,
     3900,
     4226,
     4546,
     4929,
     5300,
     5721,
     6135,
     6617,
     7094,
     7622,
     8141,
     8754,
     9351,
     10008,
     10666,
     11417,
     12156,
     12977,
     13789,
     14711,
     15624,
     16621,
     17619,
     18746,
     19857,
     21072,
     22285,
     23640,
     24991,
     26455,
     27917,
     29548,
     31164,
     32915,
     34674,
     36615,
     38545,
     40629,
     42717,
     45018,
     47307,
     49769,
     52246,
     54951,
     57646,
     60548,
     63455,
     66623,
     69791,
     73175,
     76579,
     80278,
     83964,
     87906,
     91873,
     96154,
     100440,
     105006,
     109595,
     114548,
     119498,
     124758,
     130065,
     135752,
     141444,
     147496,
     153584,
     160100,
     166636,
     173551,
     180518,
     187960,
     195418,
     203307,
     211255,
     219714,
     228205,
     237165,
     246196,
     255796,
     265422,
     275565,
     285798,
     296639,
     307529,
     318987,
     330537,
     342752,
     355025,
     367917,
     380929,
     394653,
     408448,
     422923,
     437519,
     452899,
     468377,
     484571,
     500915,
     518110,
     535399,
     553490,
     571753,
     590916,
     610205,
     630353,
     650686,
     672014,
     693478,
     715865,
     738475,
     762134,
     785956,
     810798,
     835864,
     862064,
     888463,
     915935,
     943674,
     972644,
     1001820,
     1032159,
     1062794,
     1094736,
     1126927,
     1160369,
     1194132,
     1229304,
     1264743,
     1301524,
     1338675,
     1377320,
     1416269,
     1456663,
     1497448,
     1539840,
     1582577,
     1626852,
     1671562,
     1717984,
     1764784,
     1813238,
     1862164,
     1912919,
     1964098,
     2017029,
     2070483,
     2125895,
     2181755,
     2239497,
     2297816,
     2358198,
     2419093,
     2481992,
     2545505,
     2611225,
     2677502,
     2745904,
     2814993,
     2886413,
     2958441,
     3032743,
     3107773,
     3185282,
     3263472,
     3344049,
     3425425,
     3509443,
     3594179,
     3681467,
     3769627,
     3860561,
     3952286,
     4046719,
     4142083,
     4240401,
     4339572,
     4441601,
     4544647,
     4650804,
     4757888,
     4868017,
     4979217,
     5093705,
     5209210,
     5327914,
     5447788,
     5571144,
     5695574,
     5823389,
     5952462,
     6085199,
     6219113,
     6356598,
     6495423,
     6638119,
     6782064,
     6929783,
     7078960,
     7232189,
     7386765,
     7545331,
     7705430,
     7869816,
     8035660,
     8205684,
     8377354,
     8553531,
     8731256,
     8913407,
     9097311,
     9285944,
     9476246,
     9671184,
     9867992,
     10069796,
     10273357,
     10481799,
     10692247,
     10907909,
     11125466,
     11348167,
     11572979,
     11803271,
     12035582,
     12273278,
     12513240,
     12758946,
     13006796,
     13260312,
     13516212,
     13778132,
     14042358,
     14312499,
     14585180,
     14864182,
     15145603,
     15433244,
     15723587,
     16020523,
     16320044,
     16626077,
     16934955,
     17250757,
     17569290,
     17894636,
     18223013,
     18558604,
     18897095,
     19242741,
     19591553,
     19947922
    ]
   },
   "21": {
    "A4": [
     -12,
     -9,
     -6,
     -3,
     0,
     3,
     6,
     9,
     12,
     15,
     18,
     21,
     24,
     27,
     30,
     33,
     36,
     39,
     42,
     45,
     48,
     51,
     54,
     57,
     60,
     63,
     66,
     69,
     72,
     75,
     78,
     81,
     84,
     87,
     90,
     93,
     96,
     99,
     102,
     105,
     108,
     111,
     114,
     117,
     120,
     123,
     126,
     129,
     132,
     135,
     138,
     141,
     144,
     147,
     150,
     153,
     156,
     159,
     162,
     165,
     168,
     171,
     174,
     177,
     180,
     183,
     186,
     189,
     192,
     195,
     198,
     201,
     204,
     207,
     210,
     213,
     216,
     219,
     222,
     225,
     228,
     231,
     234,
     237,
     240,
     243,
     246,
     249,
     252,
     255,
     258,
     261,
     264,
     267,
     270,
     273,
     276,
     279,
     282,
     285,
     288,
     291,
     294,
     297,
     300,
     303,
     306,
     309,
     312,
     315,
     318,
     321,
     324,
     327,
     330,
     333,
     336,
     339,
     342,
     345,
     348,
     351,
     354,
     357,
     360,
     363,
     366,
     369,
     372,
     375,
     378,
     381,
     384,
     387,
     390,
     393,
     396,
     399,
     402,
     405,
     408,
     411,
     414,
     417,
     420,
     423,
     426,
     429,
     432,
     435,
     438,
     441,
     444,
     447,
     450,
     453,
     456,
     459,
     462,
     465,
     468,
     471,
     474,
     477,
     480,
     483,
     486,
     489,
     492,
     495,
     498,
     501,
     504,
     507,
     510,
     513,
     516,
     519,
     522,
     525,
     528,
     531,
     534,
     537,
     540,
     543,
     546,
     549,
     552,
     555,
     558,
     561,
     564,
     567,
     570,
     573,
     576,
     579,
     582,
     585,
     588,
     591,
     594,
     597,
     600,
     603,
     606,
     609,
     612,
     615,
     618,
     621,
     624,
     627,
     630,
     633,
     636,
     639,
     642,
     645,
     648,
     651,
     654,
     657,
     660,
     663,
     666,
     669,
     672,
     675,
     678,
     681,
     684,
     687,
     690,
     693,
     696,
     699,
     702,
     705,
     708,
     711,
     714,
     717,
     720,
     723,
     726,
     729,
     732,
     735,
     738,
     741,
     744,
     747,
     750,
     753,
     756,
     759,
     762,
     765,
     768,
     771,
     774,
     777,
     780,
     783,
     786,
     789,
     792,
     795,
     798,
     801,
     804,
     807,
     810,
     813,
     816,
     819,
     822,
     825,
     828,
     831,
     834,
     837,
     840,
     843,
     846,
     849,
     852,
     855,
     858,
     861,
     864,
     867,
     870,
     873,
     876,
     879
    ],
    "N": [
     1,
     1,
     3,
     5,
     8,
     11,
     15,
     19,
     27,
     37,
     46,
     52,
     68,
     83,
     101,
     121,
     142,
     164,
     195,
     223,
     262,
     300,
     341,
     383,
     442,
     498,
     564,
     626,
     705,
     787,
     882,
     970,
     1084,
     1196,
     1322,
     1448,
     1607,
     1756,
     1929,
     2098,
     2306,
     2509,
     2739,
     2964,
     3235,
     3500,
     3803,
     4097,
     4447,
     4792,
     5177,
     5557,
     6008,
     6445,
     6935,
     7419,
     7981,
     8538,
     9152,
     9757,
     10462,
     11152,
     11910,
     12673,
     13535,
     14383,
     15322,
     16253,
     17305,
     18352,
     19489,
     20624,
     21903,
     23166,
     24543,
     25922,
     27453,
     28977,
     30630,
     32281,
     34117,
     35938,
     37903,
     39879,
     42053,
     44216,
     46550,
     48890,
     51453,
     54009,
     56753,
     59515,
     62523,
     65523,
     68742,
     71974,
     75484,
     78998,
     82743,
     86512,
     90596,
     94670,
     99019,
     103401,
     108115,
     112835,
     117858,
     122910,
     128348,
     133788,
     139558,
     145380,
     151610,
     157849,
     164474,
     171137,
     178253,
     185398,
     192947,
     200556,
     208672,
     216804,
     225391,
     234052,
     243253,
     252493,
     262232,
     272047,
     282461,
     292916,
     303917,
     315022,
     326763,
     338558,
     350958,
     363463,
     376669,
     389949,
     403876,
     417928,
     432738,
     447632,
     463242,
     478989,
     495556,
     512228,
     529664,
     547264,
     565761,
     584362,
     603802,
     623430,
     644007,
     664727,
     686355,
     708181,
     731041,
     754057,
     778048,
     802280,
     827613,
     853125,
     879701,
     906524,
     934538,
     962773,
     992129,
     1021771,
     1052701,
     1083855,
     1116234,
     1148936,
     1183000,
     1217329,
     1252970,
     1288956,
     1326418,
     1364171,
     1403326,
     1442874,
     1483985,
     1525423,
     1568379,
     1611747,
     1656790,
     1702208,
     1749230,
     1796718,
     1846000,
     1895681,
     1947083,
     1998995,
     2052811,
     2107081,
     2163183,
     2219838,
     2278529,
     2337707,
     2398842,
     2460594,
     2524490,
     2588929,
     2655460,
     2722644,
     2792123,
     2862201,
     2934486,
     3007490,
     3082927,
     3159012,
     3237459,
     3316678,
     3398472,
     3480982,
     3565985,
     3651830,
     3740420,
     3829765,
     3921760,
     4014676,
     4110476,
     4207115,
     4306570,
     4406999,
     4510484,
     4614878,
     4722244,
     4830679,
     4942339,
     5054975,
     5170764,
     5287688,
     5408022,
     5529430,
     5654147,
     5780089,
     5909640,
     6040324,
     6174523,
     6310047,
     6449355,
     6589890,
     6734132,
     6879782,
     7029441,
     7180413,
     7335289,
     7491683,
     7652277,
     7814285,
     7980431,
     8148172,
     8320341,
     8494039,
     8672064,
     8851814,
     9036232,
     9222261,
     9412857,
     9605290,
     9802611,
     10001680,
     10205547,
     10411361,
     10622327,
     10835136,
     11052987,
     11272939,
     11498268,
     11725570,
     11958188,
     12193006,
     12433481,
     12676075,
     12924221,
     13174715,
     13431143,
     13689807,
     13954317,
     14221316,
     14494520,
     14770119,
     15051830,
     15336177,
     15627046,
     15920431,
     16220226,
     16522832,
     16832235,
     17144327,
     17463141,
     17784905,
     18113790,
     18445525,
     18784284,
     19126185,
     19475520,
     19827869
    ]
   }
  },
  "recurrence": {
   "step": 6,
   "tested": 4694,
   "failures": 0,
   "ratio_7_over_1": {
    "74": 0.9974059662775616,
    "140": 0.9998165810711666,
    "212": 0.9999607873892243
   }
  },
  "fibre": {
   "A4": 86,
   "k8D": 1,
   "n": 81,
   "qrs": [
    "86",
    "0",
    "349/2"
   ],
   "G": 58.2124836589562,
   "n_2W": 1,
   "the_2W": [
    "17"
   ],
   "size_min": 19,
   "size_max": 198,
   "n_classes": 27,
   "n_rung": 1169
  },
  "budget": [
   {
    "k8D": 9,
    "A4": 600,
    "N": 2792133
   },
   {
    "k8D": 13,
    "A4": 800,
    "N": 12114975
   },
   {
    "k8D": 17,
    "A4": 400,
    "N": 394653
   },
   {
    "k8D": 17,
    "A4": 850,
    "N": 16626077
   },
   {
    "k8D": 21,
    "A4": 600,
    "N": 2792123
   }
  ],
  "quasipolynomial": [
   {
    "period": 1,
    "points": 77,
    "degree": null
   },
   {
    "period": 2,
    "points": 39,
    "degree": null
   },
   {
    "period": 3,
    "points": 26,
    "degree": null
   },
   {
    "period": 6,
    "points": 13,
    "degree": null
   },
   {
    "period": 12,
    "points": 7,
    "degree": null,
    "note": "muy pocos puntos"
   }
  ],
  "brute_force_points": 37,
  "source": "research/smeft_formalization/part_viii/outputs/rung_census.json",
  "note": "N(A_4, 8D) counted by a dynamic programme over the two partial moments, not by enumeration. The four rung totals -- 69 million contents -- are the strongest falsification the enumerator has, because the two algorithms share nothing. The quasi-polynomial structure a vector partition function must have is NOT claimed: the period comes from the 2x2 determinants of the generators and is too large to measure on the 77 legal A_4 of rung one. Measured, then not claimed."
 }
}