{
 "pulsars": [
  {
   "letter": "H",
   "theta_arcmin": 0.56,
   "b_pc": 0.8845328649107262,
   "DM": 98.1716,
   "DM_err": 0.0005,
   "DM_where": "TRAPUM2026 Table D.2 (DM0)",
   "timing_solution": true,
   "DM1": -0.0015,
   "DM1_err": 0.0004
  },
  {
   "letter": "B",
   "theta_arcmin": 0.76,
   "b_pc": 1.2004374595217,
   "DM": 100.2806,
   "DM_err": 0.0008,
   "DM_where": "TRAPUM2026 Table D.2 (DM0)",
   "timing_solution": true,
   "DM1": 0.00068,
   "DM1_err": 0.00054
  },
  {
   "letter": "F",
   "theta_arcmin": 1.0,
   "b_pc": 1.579522973054868,
   "DM": 98.29,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table 1",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "P",
   "theta_arcmin": 1.0,
   "b_pc": 1.579522973054868,
   "DM": 102.17,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table 1",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "O",
   "theta_arcmin": 1.5,
   "b_pc": 2.3692844595823024,
   "DM": 94.305,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table 1",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "E",
   "theta_arcmin": 1.58,
   "b_pc": 2.4956462974266915,
   "DM": 94.33967,
   "DM_err": 5e-05,
   "DM_where": "TRAPUM2026 Table D.1 (DM0)",
   "timing_solution": true,
   "DM1": 0.0059,
   "DM1_err": 0.0035
  },
  {
   "letter": "J",
   "theta_arcmin": 1.8,
   "b_pc": 2.8431413514987627,
   "DM": 97.28,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table 1",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "K",
   "theta_arcmin": 1.89,
   "b_pc": 2.985298419073701,
   "DM": 94.7836,
   "DM_err": 0.0007,
   "DM_where": "TRAPUM2026 Table D.2 (DM0)",
   "timing_solution": true,
   "DM1": -0.00058,
   "DM1_err": 0.00044
  },
  {
   "letter": "A",
   "theta_arcmin": 1.93,
   "b_pc": 3.048479337995895,
   "DM": 100.3267,
   "DM_err": 0.0004,
   "DM_where": "TRAPUM2026 Table D.1 (DM0)",
   "timing_solution": true,
   "DM1": 0.0023,
   "DM1_err": 0.0003
  },
  {
   "letter": "G",
   "theta_arcmin": 1.96,
   "b_pc": 3.0958650271875414,
   "DM": 99.7445,
   "DM_err": 0.001,
   "DM_where": "TRAPUM2026 Table D.2 (DM0)",
   "timing_solution": true,
   "DM1": -0.00087,
   "DM1_err": 0.00064
  },
  {
   "letter": "C",
   "theta_arcmin": 1.98,
   "b_pc": 3.127455486648639,
   "DM": 100.6643,
   "DM_err": 0.0013,
   "DM_where": "TRAPUM2026 Table D.1 (DM0)",
   "timing_solution": true,
   "DM1": 1.7e-05,
   "DM1_err": 8e-06
  },
  {
   "letter": "Q",
   "theta_arcmin": 2.3,
   "b_pc": 3.6329028380261965,
   "DM": 95.923,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table D.3 (DM0); note Table 1 rounds this to 95.955",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "S",
   "theta_arcmin": 2.32,
   "b_pc": 3.6644932974872937,
   "DM": 96.24,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Sec. 3.3",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "M",
   "theta_arcmin": 2.4,
   "b_pc": 3.7908551353316837,
   "DM": 101.47,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table 1",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "D",
   "theta_arcmin": 2.5,
   "b_pc": 3.9488074326371696,
   "DM": 96.5462,
   "DM_err": 0.0009,
   "DM_where": "TRAPUM2026 Table D.1 (DM0)",
   "timing_solution": true,
   "DM1": 0.0002,
   "DM1_err": 0.00056
  },
  {
   "letter": "N",
   "theta_arcmin": 2.66,
   "b_pc": 4.201531108325949,
   "DM": 102.1,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table D.3 (DM0)",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "L",
   "theta_arcmin": 3.32,
   "b_pc": 5.244016270542162,
   "DM": 101.4759,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table D.3 (DM0)",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "I",
   "theta_arcmin": 3.53,
   "b_pc": 5.575716094883684,
   "DM": 102.555,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table D.3 (DM0)",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  },
  {
   "letter": "R",
   "theta_arcmin": 3.9,
   "b_pc": 6.1601395949139865,
   "DM": 102.2,
   "DM_err": null,
   "DM_where": "TRAPUM2026 Table 1",
   "timing_solution": false,
   "DM1": null,
   "DM1_err": null
  }
 ],
 "n_pulsars": 19,
 "n_with_timing_DM": 8,
 "n_with_DM1": 8,
 "timing_DM_precision_pc_cm3": {
  "min": 5e-05,
  "max": 0.0013,
  "median": 0.00075
 },
 "DM_range_pc_cm3": [
  94.305,
  102.555
 ],
 "DM_scatter_rms_pc_cm3": 2.8872095649809593,
 "geometry": {
  "D_kpc": 5.43,
  "R_core_pc": 3.74,
  "R_infl_pc": 0.4,
  "b_range_pc": [
   0.8845328649107262,
   6.1601395949139865
  ]
 },
 "signals": {
  "core": {
   "R_pc": 3.74,
   "by_density": {
    "ne_0.01": {
     "full_chord_centre_pc_cm3": 0.0748,
     "per_pulsar": {
      "H": 0.07267792405096014,
      "B": 0.07084221878449909,
      "F": 0.06780179106068486,
      "P": 0.06780179106068486,
      "O": 0.057876043920025495,
      "E": 0.05571121810960679,
      "J": 0.048596902186858755,
      "K": 0.045058155084628425,
      "A": 0.04333300693841641,
      "G": 0.04196770059670692,
      "C": 0.04102010326184626,
      "Q": 0.017772078881900213,
      "S": 0.01495444913957987,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 13
    },
    "ne_0.05": {
     "full_chord_centre_pc_cm3": 0.37400000000000005,
     "per_pulsar": {
      "H": 0.3633896202548007,
      "B": 0.35421109392249545,
      "F": 0.33900895530342434,
      "P": 0.33900895530342434,
      "O": 0.2893802196001275,
      "E": 0.27855609054803393,
      "J": 0.24298451093429377,
      "K": 0.22529077542314213,
      "A": 0.21666503469208204,
      "G": 0.20983850298353457,
      "C": 0.20510051630923132,
      "Q": 0.08886039440950107,
      "S": 0.07477224569789935,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 13
    },
    "ne_0.1": {
     "full_chord_centre_pc_cm3": 0.7480000000000001,
     "per_pulsar": {
      "H": 0.7267792405096014,
      "B": 0.7084221878449909,
      "F": 0.6780179106068487,
      "P": 0.6780179106068487,
      "O": 0.578760439200255,
      "E": 0.5571121810960679,
      "J": 0.48596902186858754,
      "K": 0.45058155084628426,
      "A": 0.4333300693841641,
      "G": 0.41967700596706914,
      "C": 0.41020103261846264,
      "Q": 0.17772078881900213,
      "S": 0.1495444913957987,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 13
    },
    "ne_0.2": {
     "full_chord_centre_pc_cm3": 1.4960000000000002,
     "per_pulsar": {
      "H": 1.4535584810192028,
      "B": 1.4168443756899818,
      "F": 1.3560358212136974,
      "P": 1.3560358212136974,
      "O": 1.15752087840051,
      "E": 1.1142243621921357,
      "J": 0.9719380437371751,
      "K": 0.9011631016925685,
      "A": 0.8666601387683281,
      "G": 0.8393540119341383,
      "C": 0.8204020652369253,
      "Q": 0.35544157763800427,
      "S": 0.2990889827915974,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 13
    }
   }
  },
  "infl": {
   "R_pc": 0.4,
   "by_density": {
    "ne_0.01": {
     "full_chord_centre_pc_cm3": 0.008,
     "per_pulsar": {
      "H": 0.0,
      "B": 0.0,
      "F": 0.0,
      "P": 0.0,
      "O": 0.0,
      "E": 0.0,
      "J": 0.0,
      "K": 0.0,
      "A": 0.0,
      "G": 0.0,
      "C": 0.0,
      "Q": 0.0,
      "S": 0.0,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 0
    },
    "ne_0.05": {
     "full_chord_centre_pc_cm3": 0.04000000000000001,
     "per_pulsar": {
      "H": 0.0,
      "B": 0.0,
      "F": 0.0,
      "P": 0.0,
      "O": 0.0,
      "E": 0.0,
      "J": 0.0,
      "K": 0.0,
      "A": 0.0,
      "G": 0.0,
      "C": 0.0,
      "Q": 0.0,
      "S": 0.0,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 0
    },
    "ne_0.1": {
     "full_chord_centre_pc_cm3": 0.08000000000000002,
     "per_pulsar": {
      "H": 0.0,
      "B": 0.0,
      "F": 0.0,
      "P": 0.0,
      "O": 0.0,
      "E": 0.0,
      "J": 0.0,
      "K": 0.0,
      "A": 0.0,
      "G": 0.0,
      "C": 0.0,
      "Q": 0.0,
      "S": 0.0,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 0
    },
    "ne_0.2": {
     "full_chord_centre_pc_cm3": 0.16000000000000003,
     "per_pulsar": {
      "H": 0.0,
      "B": 0.0,
      "F": 0.0,
      "P": 0.0,
      "O": 0.0,
      "E": 0.0,
      "J": 0.0,
      "K": 0.0,
      "A": 0.0,
      "G": 0.0,
      "C": 0.0,
      "Q": 0.0,
      "S": 0.0,
      "M": 0.0,
      "D": 0.0,
      "N": 0.0,
      "L": 0.0,
      "I": 0.0,
      "R": 0.0
     },
     "n_pulsars_inside": 0
    }
   }
  }
 },
 "present_constraint": {
  "model": "DM_i = DM_0 + n_e * chord(b_i; R_core), uniform sphere, free foreground constant, ordinary least squares on the 19 published DMs",
  "ne_hat_cm3": -0.3320618269167108,
  "ne_err_cm3": 0.23523407635969115,
  "ne_95_upper_cm3": 0.05489822869498112,
  "residual_rms_pc_cm3": 2.810744965248348,
  "note": "The sight-line-to-sight-line DM scatter, not the timing precision, sets this. It exceeds the per-pulsar DM uncertainty by three orders of magnitude, so the requirement is on modelling or averaging down that scatter, not on measuring DM better."
 },
 "precision_required": {
  "basis": "Scaled from the fit above, whose amplitude error is sigma(n_e) = 0.235 cm^-3 on 19 sight lines. Under the same per-sight-line scatter the error falls as N^-1/2, so N_required = 19 * (sigma / target)^2.",
  "core": {
   "sigma_ne_now_cm3": 0.23523407635969115,
   "n_needed_1sigma_at_0.1": 105.1366342935143,
   "n_needed_3sigma_at_0.1": 946.2297086416289,
   "scatter_reduction_needed_for_3sigma_at_0.1": 7.0570222907907345,
   "signal_central_chord_at_0.1_pc_cm3": 0.7480000000000001
  },
  "influence_radius": {
   "signal_central_chord_at_0.1_pc_cm3": 0.08000000000000002,
   "n_sight_lines_intersecting": 0,
   "note": "No published pulsar sight line passes within the influence radius, so this geometry is not constrained at any timing precision; the innermost sight line is at 0.88 pc."
  }
 }
}