[
 {
  "local_id": "C1",
  "type": "empirical",
  "core": true,
  "statement": "In 94,747 TESS 2-minute light curves of 32,908 stars of 5000 to 6500 K with absolute G magnitudes of 4 to 6 and RUWE below 1.4 (5,605 star-years), the pre-registered search, with its SAP test corrected after registration to require the uncorrected flux to rise, counted 78 flares of bolometric energy 10^34 erg or more where the rate Vasilyev et al. (2024) measured with Kepler predicts 23.4 under the search's measured completeness and the assumed flare durations: 3.33 times that rate (95% CI 2.63 to 4.15), about once per 33 years per star; the registered code counted 79 (3.37 times, 2.67 to 4.20).",
  "evidence": [
   {
    "result": "R1.stars",
    "produced_by": "code/run"
   },
   {
    "result": "R1.light_curves",
    "produced_by": "code/run"
   },
   {
    "result": "R1.star_years",
    "produced_by": "code/run",
    "tolerance": 1
   },
   {
    "result": "R1.observed",
    "produced_by": "code/run"
   },
   {
    "result": "R1.expected_kepler",
    "produced_by": "code/run",
    "tolerance": 0.1
   },
   {
    "result": "R1.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R1.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R1.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R1.years_per_superflare",
    "produced_by": "code/run",
    "tolerance": 1
   },
   {
    "result": "R0.observed",
    "produced_by": "code/run"
   },
   {
    "result": "R0.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R17.flares_opposite_sign",
    "produced_by": "code/run"
   },
   {
    "result": "R17.injections_changed_by_sign",
    "produced_by": "code/run"
   }
  ],
  "depends_on": [],
  "falsified_if": "Re-running code/run gives a corrected ratio outside 3.32 to 3.34, an interval that includes 1, or a sign correction that changes recovered injections.",
  "confidence": 0.85
 },
 {
  "local_id": "C2",
  "type": "empirical",
  "core": true,
  "statement": "The same TESS data are incompatible with the earlier Kepler rate of one superflare of 10^34 erg or more per 2,500 years on Sun-like stars, which under the same completeness predicts 1.04 counted flares where 78 were found (Poisson probability below 10^-100).",
  "evidence": [
   {
    "result": "R1.observed",
    "produced_by": "code/run"
   },
   {
    "result": "R1.expected_earlier",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R1.log10_p_at_least_observed_if_earlier",
    "produced_by": "code/run",
    "tolerance": 0.2
   }
  ],
  "depends_on": [
   "C1"
  ],
  "falsified_if": "Re-running code/run gives more than 2 expected flares under the earlier rate, or a decimal logarithm of the probability above -100.",
  "confidence": 0.9
 },
 {
  "local_id": "C3",
  "type": "empirical",
  "core": true,
  "statement": "Among the 18,203 stars of 5500 to 6000 K whose median TESS variability range is below 0.3%, the 50 counted superflares are 3.63 times (95% CI 2.70 to 4.79) the 13.8 that the rate Vasilyev et al. (2024) give for their Sun-like stars predicts.",
  "evidence": [
   {
    "result": "R2.stars",
    "produced_by": "code/run"
   },
   {
    "result": "R2.observed",
    "produced_by": "code/run"
   },
   {
    "result": "R2.expected_kepler",
    "produced_by": "code/run",
    "tolerance": 0.1
   },
   {
    "result": "R2.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R2.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R2.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   }
  ],
  "depends_on": [
   "C1"
  ],
  "falsified_if": "Re-running code/run gives a ratio outside 3.62 to 3.64, or an interval that includes 1.",
  "confidence": 0.8
 },
 {
  "local_id": "C4",
  "type": "empirical",
  "core": false,
  "statement": "Every planned subset and sensitivity analysis gives a ratio above 1, with intervals excluding 1 in all but two: 2.94 (2.29 to 3.72) for the 69 flares that pass the difference-image offset test, 2.62 (1.43 to 4.39) above 10^34.5 erg, 3.28 (2.56 to 4.13) for stars with no Gaia DR3 sign of binarity, 2.61 to 3.51 for flare temperatures of 8000 to 10,000 K, and 2.24 (1.77 to 2.80) and 10.86 (8.58 to 13.55) for injected flares half and two and a half times as long; the brightest stars (2.05, 0.89 to 4.04) and flares above 10^35 erg (2.90, 0.35 to 10.48) leave the question open.",
  "evidence": [
   {
    "result": "R9.observed",
    "produced_by": "code/run"
   },
   {
    "result": "R9.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R9.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R9.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R5.above_e34_5.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R5.above_e34_5.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R5.above_e34_5.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R10.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R10.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R10.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R8.t8000.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R8.t10000.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R7.short.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R7.short.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R7.short.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R7.long.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R7.long.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R7.long.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R4.bright.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R4.bright.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R4.bright.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R5.above_e35.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R5.above_e35.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R5.above_e35.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   }
  ],
  "depends_on": [
   "C1"
  ],
  "falsified_if": "Re-running code/run gives any of these ratios below 1, or an interval including 1 for any analysis other than the brightest stars and flares above 10^35 erg.",
  "confidence": 0.8
 },
 {
  "local_id": "C5",
  "type": "empirical",
  "core": false,
  "statement": "Split at the median Gaia DR3 Ca II activity index, stars below it show 4.35 times the Kepler rate (95% CI 3.18 to 5.80) and stars at or above it 2.55 times (1.70 to 3.69).",
  "evidence": [
   {
    "result": "R3.low.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R3.low.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R3.low.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R3.high.ratio",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R3.high.ratio_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R3.high.ratio_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   }
  ],
  "depends_on": [
   "C1"
  ],
  "falsified_if": "Re-running code/run gives either ratio outside 0.01 of these values.",
  "confidence": 0.75
 },
 {
  "local_id": "C6",
  "type": "empirical",
  "core": false,
  "statement": "The superflares are concentrated on few stars (exploratory): 12 stars have two or more where one rate shared by all stars, passed through the search's measured detection, predicts 0.36 (probability about 10^-14), and they hold 40 of the 78; as a descriptive check, 50 stars have a counted flare where the Kepler rate predicts 23.4, as many as a shared rate 2.14 times the Kepler rate would give (approximate 95% range 1.62 to 2.82).",
  "evidence": [
   {
    "result": "R14.stars_with_two_or_more",
    "produced_by": "code/run"
   },
   {
    "result": "R14.expected_two_or_more_if_one_rate",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R14.log10_p_two_or_more_if_one_rate",
    "produced_by": "code/run",
    "tolerance": 0.2
   },
   {
    "result": "R14.flares_on_stars_with_two_or_more",
    "produced_by": "code/run"
   },
   {
    "result": "R14.stars_with_flares",
    "produced_by": "code/run"
   },
   {
    "result": "R14.expected_stars_with_flares_kepler",
    "produced_by": "code/run",
    "tolerance": 0.1
   },
   {
    "result": "R14.occupancy_rate_multiple",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R14.occupancy_rate_multiple_low",
    "produced_by": "code/run",
    "tolerance": 0.01
   },
   {
    "result": "R14.occupancy_rate_multiple_high",
    "produced_by": "code/run",
    "tolerance": 0.01
   }
  ],
  "depends_on": [
   "C1"
  ],
  "falsified_if": "Re-running code/run gives fewer than 10 stars with two or more counted flares, or a shared-rate prediction above 1.",
  "confidence": 0.8
 },
 {
  "local_id": "C7",
  "type": "methodological",
  "core": false,
  "statement": "Searching again, with the same seeds, the 254 audited light curves (every one with a vetted event of 10^34 erg or more on the stars not set aside as fast rotators, and 150 others chosen by the hash of their names) reproduces every column of their rows of the search's tables, 243,234 fields, within a relative 1e-6, except template-fit parameters of candidates that fail vetting, which differ across platforms by at most 1%; and selecting the sample again from the catalogs gives the same 39,937 confirmatory stars and 121,190 light curves.",
  "evidence": [
   {
    "result": "R12.light_curves",
    "produced_by": "code/run"
   },
   {
    "result": "R12.fields_compared",
    "produced_by": "code/run"
   },
   {
    "result": "R12.all_but_fits_agree",
    "produced_by": "code/run"
   },
   {
    "result": "R12.fit_differences_on_vetted",
    "produced_by": "code/run"
   },
   {
    "result": "R12.fits_within_one_percent",
    "produced_by": "code/run"
   },
   {
    "result": "R11.stars_selected",
    "produced_by": "code/run"
   },
   {
    "result": "R11.light_curves_selected",
    "produced_by": "code/run"
   },
   {
    "result": "R11.selection_reproduced",
    "produced_by": "code/run"
   }
  ],
  "depends_on": [],
  "falsified_if": "Re-running code/run finds a field other than a fitted template parameter that differs, a fitted parameter of a vetted candidate that differs, or a different sample.",
  "confidence": 0.95
 },
 {
  "local_id": "C8",
  "type": "empirical",
  "core": false,
  "statement": "Exploratory: an emulation of the Kepler search of Vasilyev et al. (2024), calibrated so that it detects the profile they injected as often as the completeness their correction applied to their full sample (root mean square difference 0.017 over 17 energy bins), recovers that profile's rate (true over estimated rate 0.98 between 10^34 and 10^35 erg and 1.01 above) but understates the rate of flares of the Davenport shape and the widths this study assumes by a factor of 1.79 between 10^34 and 10^35 erg (1.83 and 2.21 for flares half and two and a half times as long, 1.85 for a cumulative energy distribution of slope 1.66 instead of 1.36), and by none above 10^35 erg (0.98). The completeness their correction applied exceeds that of their detectability figure at every temperature from 10^34.68 erg up, and their corrected frequency integrates to 0.0121 per star per year between 10^34 and 10^35 erg and 0.000288 above, against their Table 1's 0.00863 and 0.00039, so these factors are not applied to the published rates.",
  "evidence": [
   {
    "result": "R18.energy_bins",
    "produced_by": "code/run"
   },
   {
    "result": "R18.fit_rms",
    "produced_by": "code/run",
    "tolerance": 0.005
   },
   {
    "result": "R18.two_point.factor_low_bin",
    "produced_by": "code/run",
    "tolerance": 0.03
   },
   {
    "result": "R18.two_point.factor_high_bin",
    "produced_by": "code/run",
    "tolerance": 0.03
   },
   {
    "result": "R18.base.factor_low_bin",
    "produced_by": "code/run",
    "tolerance": 0.05
   },
   {
    "result": "R18.base.factor_high_bin",
    "produced_by": "code/run",
    "tolerance": 0.03
   },
   {
    "result": "R18.short.factor_low_bin",
    "produced_by": "code/run",
    "tolerance": 0.05
   },
   {
    "result": "R18.long.factor_low_bin",
    "produced_by": "code/run",
    "tolerance": 0.05
   },
   {
    "result": "R18.base_steeper.factor_low_bin",
    "produced_by": "code/run",
    "tolerance": 0.05
   },
   {
    "result": "R18.applied_exceeds_figure_from_log_e",
    "produced_by": "code/run",
    "tolerance": 0.15
   },
   {
    "result": "R18.figure_rate_low_bin",
    "produced_by": "code/run",
    "tolerance": 0.0002
   },
   {
    "result": "R18.figure_rate_high_bin",
    "produced_by": "code/run",
    "tolerance": 1e-05
   }
  ],
  "depends_on": [],
  "falsified_if": "Re-running code/run gives a calibration whose root mean square difference exceeds 0.03, a factor for their profile outside 0.95 to 1.05 in either energy bin, or a factor between 10^34 and 10^35 erg for flares of the assumed widths outside 1.7 to 1.9.",
  "confidence": 0.6
 }
]