{
  "computed_at": "2026-11-01T02:56:15Z",
  "constants": {
    "rho_kg_m3": 1.225,
    "g_m_s2": 9.81
  },
  "inputs": {
    "glide_rows": 27,
    "comparison_rows": 9
  },
  "coverage": {
    "rows": 27,
    "distinct_species_or_groups": [
      "Cheilopogon heterurus doederleini",
      "Cypselurus californicus",
      "Cypselurus hiraii",
      "Exocoetidae (adults)",
      "Exocoetidae (four-wingers)",
      "Exocoetidae (several genera)"
    ],
    "n_species_or_groups": 6,
    "rows_measured_first_hand": 19,
    "rows_secondary_or_theory": 8,
    "species_with_first_hand_measurements": [
      "Cheilopogon heterurus doederleini",
      "Cypselurus hiraii"
    ],
    "sources": [
      "davenport-1994",
      "deng-2019",
      "makiguchi-2013",
      "park-choi-2010"
    ],
    "per_column": {
      "glide_distance_m": {
        "rows_with_value": 4,
        "species": [
          "Cheilopogon heterurus doederleini",
          "Cypselurus californicus",
          "Exocoetidae (several genera)"
        ],
        "by_value_kind": {
          "secondary": 2,
          "theory-secondary": 2
        }
      },
      "glide_duration_s": {
        "rows_with_value": 1,
        "species": [
          "Exocoetidae (several genera)"
        ],
        "by_value_kind": {
          "secondary": 1
        }
      },
      "airspeed_m_s": {
        "rows_with_value": 3,
        "species": [
          "Cypselurus californicus",
          "Exocoetidae (several genera)"
        ],
        "by_value_kind": {
          "secondary": 2,
          "theory-secondary": 1
        }
      },
      "launch_speed_m_s": {
        "rows_with_value": 3,
        "species": [
          "Cheilopogon heterurus doederleini",
          "Exocoetidae (four-wingers)",
          "Exocoetidae (several genera)"
        ],
        "by_value_kind": {
          "secondary": 2,
          "measured (length and mass); estimated (speed)": 1
        }
      },
      "height_m": {
        "rows_with_value": 2,
        "species": [
          "Cypselurus californicus",
          "Exocoetidae (several genera)"
        ],
        "by_value_kind": {
          "secondary": 1,
          "theory-secondary": 1
        }
      },
      "body_mass_kg": {
        "rows_with_value": 21,
        "species": [
          "Cheilopogon heterurus doederleini",
          "Cypselurus californicus",
          "Cypselurus hiraii"
        ],
        "by_value_kind": {
          "measured": 18,
          "theory-secondary": 2,
          "measured (length and mass); estimated (speed)": 1
        }
      },
      "body_length_m": {
        "rows_with_value": 20,
        "species": [
          "Cheilopogon heterurus doederleini",
          "Cypselurus hiraii",
          "Exocoetidae (adults)"
        ],
        "by_value_kind": {
          "measured": 18,
          "measured (length and mass); estimated (speed)": 1,
          "secondary": 1
        }
      },
      "pectoral_fin_span_m": {
        "rows_with_value": 4,
        "species": [
          "Cypselurus hiraii"
        ],
        "by_value_kind": {
          "measured": 4
        }
      },
      "pectoral_fin_area_m2": {
        "rows_with_value": 6,
        "species": [
          "Cheilopogon heterurus doederleini",
          "Cypselurus hiraii"
        ],
        "by_value_kind": {
          "measured": 5,
          "theory-secondary": 1
        }
      },
      "pelvic_fin_area_m2": {
        "rows_with_value": 5,
        "species": [
          "Cypselurus hiraii"
        ],
        "by_value_kind": {
          "measured": 5
        }
      },
      "CL_max": {
        "rows_with_value": 2,
        "species": [
          "Cypselurus californicus",
          "Cypselurus hiraii"
        ],
        "by_value_kind": {
          "measured": 1,
          "theory-secondary": 1
        }
      },
      "LD_max": {
        "rows_with_value": 2,
        "species": [
          "Cheilopogon heterurus doederleini",
          "Cypselurus hiraii"
        ],
        "by_value_kind": {
          "measured": 1,
          "theory-secondary": 1
        }
      }
    },
    "what_is_missing": [
      "No first-hand measurement of airspeed or glide distance for any identified species: every speed and distance is a second-hand quote of Hertel 1966, Fish 1990, Davenport 1990/1994 or Edgerton and Breder 1941, none of which could be fetched in full.",
      "No species has body mass, fin area and a measured airspeed in the same source; Park and Choi 2010 gives mass and areas for 0.04-0.06 kg specimens, the speeds come from other, larger fish.",
      "Pectoral-fin span and area exist for one species (Cypselurus hiraii, five specimens).",
      "Wing loading for the north-east Atlantic species measured by Davenport 1992 is behind a paywall; only its allometric exponents are in the abstract (physics/allometry.json)."
    ]
  },
  "derived_wing_loading": [
    {
      "species": "Cypselurus hiraii",
      "source_id": "park-choi-2010",
      "locator": "Table 1 model L1",
      "mass_kg": 0.06,
      "wing_loading_total_ref_area_N_m2": 45.106904743658525,
      "wing_loading_fins_only_N_m2": 67.87361623616236,
      "reference_area_m2": 0.013048999999999998
    },
    {
      "species": "Cypselurus hiraii",
      "source_id": "park-choi-2010",
      "locator": "Table 1 model L2",
      "mass_kg": 0.05,
      "wing_loading_total_ref_area_N_m2": 37.03843539983388,
      "wing_loading_fins_only_N_m2": 56.10844200411806,
      "reference_area_m2": 0.013243
    },
    {
      "species": "Cypselurus hiraii",
      "source_id": "park-choi-2010",
      "locator": "Table 1 model L3; Table 2",
      "mass_kg": 0.06,
      "wing_loading_total_ref_area_N_m2": 46.39029003783103,
      "wing_loading_fins_only_N_m2": 71.65814463111761,
      "reference_area_m2": 0.012687999999999998
    },
    {
      "species": "Cypselurus hiraii",
      "source_id": "park-choi-2010",
      "locator": "Table 1 model M",
      "mass_kg": 0.04,
      "wing_loading_total_ref_area_N_m2": 40.22140221402214,
      "wing_loading_fins_only_N_m2": 71.37140778464897,
      "reference_area_m2": 0.009756
    },
    {
      "species": "Cypselurus hiraii",
      "source_id": "park-choi-2010",
      "locator": "Table 1 model N",
      "mass_kg": 0.04,
      "wing_loading_total_ref_area_N_m2": 84.56896551724138,
      "wing_loading_fins_only_N_m2": null,
      "reference_area_m2": 0.00464
    },
    {
      "species": "Cheilopogon heterurus doederleini",
      "source_id": "deng-2019",
      "locator": "Introduction citing Kawachi et al. 1993",
      "mass_kg": 0.226,
      "wing_loading_stated_wing_area_N_m2": 98.536,
      "reference_area_m2": 0.0225
    }
  ],
  "interpretation_B": {
    "specimen": "Cypselurus hiraii model L3 (Park and Choi 2010 Table 1 and Table 2)",
    "W_N": 0.5886,
    "reference_area_m2": 0.012687999999999998,
    "C_Lmax": 0.78,
    "LD_max": 4.37,
    "v_min_m_s": 9.854014478123766,
    "three_v_min_m_s": 29.562043434371297,
    "airspeed_range_m_s": [
      10.0,
      20.0
    ],
    "airspeed_sources": [
      "park-choi-2010: Introduction citing Hertel 1966; Fish 1990; Davenport 1994",
      "makiguchi-2013: Introduction citing Edgerton and Breder 1941 and Davenport 1990"
    ],
    "verdict": "inside",
    "caveat": "W, S and C_Lmax are from 0.04-0.06 kg stuffed specimens of one species; the airspeed range is a second-hand field figure for larger flying fish of several genera. The pre-registration allowed same species or genus; the field figure is at family level, so this verdict rests on an assumption the pre-registration did not foresee and is reported with that weakness.",
    "second_specimen": {
      "specimen": "Cheilopogon heterurus doederleini as quoted by Deng 2019 from Kawachi 1993 (0.226 kg, 0.0225 m2)",
      "wing_loading_N_m2": 98.536,
      "v_min_with_Park_Choi_CLmax_m_s": 14.36141117096643,
      "airspeed_quoted_for_this_species_m_s": [
        15.0,
        20.0
      ],
      "note": "C_Lmax borrowed from another species; wing area is a second-hand figure; descriptive only, no verdict"
    }
  },
  "interpretation_C": {
    "P_req_W_at_v_min": 1.3272478081976313,
    "P_req_per_kg_body_W_kg": 22.120796803293857,
    "formula": "P_req = W v_min / (L/D)_max, the power to fly level at the minimum lift-supported speed with the best measured glide ratio",
    "P_avail": null,
    "verdict": "cannot-tell",
    "why": "No fetched source gives a muscle mass fraction or a mass-specific muscle power for a flying fish; Davenport 1992 (abstract) says only that red axial muscle is no more than in mackerel. Without a sourced P_avail the pre-registered verdict is cannot-tell.",
    "what_would_decide_it": "A sourced pectoral-plus-axial muscle mass fraction f and specific power p (W per kg muscle): INSIDE if f * p >= 22.1 W per kg body mass."
  },
  "interpretation_A": {
    "points": [
      {
        "lineage": "Exocoetidae",
        "species": "Cypselurus hiraii (W/S) with family-level field airspeed",
        "mode": "glider",
        "WS": 46.39029003783103,
        "v": 15.0,
        "v_lo": 10.0,
        "v_hi": 20.0,
        "provenance": "W/S measured (Park and Choi 2010); airspeed second-hand field range 10-20 m/s"
      },
      {
        "lineage": "Pteromyini",
        "species": "Glaucomys sabrinus",
        "mode": "glider",
        "WS": 59.0,
        "v": 7.2,
        "provenance": "measured (speed); published population values (mass and wing loading) (bahlman-2013)"
      },
      {
        "lineage": "Chiroptera",
        "species": "Glossophaga soricina",
        "mode": "powered",
        "WS": 11.05,
        "v": 4.3,
        "provenance": "secondary-compilation (span-efficiency-2026)"
      },
      {
        "lineage": "Chiroptera",
        "species": "Leptonycteris yerbabuenae",
        "mode": "powered",
        "WS": 14.25,
        "v": 3.27,
        "provenance": "secondary-compilation (span-efficiency-2026)"
      },
      {
        "lineage": "Chiroptera",
        "species": "Plecotus auritus",
        "mode": "powered",
        "WS": 6.5,
        "v": 3.0,
        "provenance": "secondary-compilation (span-efficiency-2026)"
      },
      {
        "lineage": "Diptera",
        "species": "Episyrphus balteatus",
        "mode": "powered",
        "WS": 1.97,
        "v": 1.8,
        "provenance": "secondary-compilation (span-efficiency-2026)"
      },
      {
        "lineage": "Diptera",
        "species": "Eristalis pertinax",
        "mode": "powered",
        "WS": 2.73,
        "v": 1.4,
        "provenance": "secondary-compilation (span-efficiency-2026)"
      },
      {
        "lineage": "Diptera",
        "species": "Syrphus ribesii",
        "mode": "powered",
        "WS": 1.67,
        "v": 1.8,
        "provenance": "secondary-compilation (span-efficiency-2026)"
      }
    ],
    "gliders": {
      "n": 2,
      "taxa": [
        "Cypselurus hiraii (W/S) with family-level field airspeed",
        "Glaucomys sabrinus"
      ],
      "decades_of_WS": 0.10442492385208069,
      "verdict": "inconclusive",
      "reason": "underpowered",
      "why": "n = 2 < 5; W/S spans 0.10 decades < 1"
    },
    "powered": {
      "n": 6,
      "taxa": [
        "Glossophaga soricina",
        "Leptonycteris yerbabuenae",
        "Plecotus auritus",
        "Episyrphus balteatus",
        "Eristalis pertinax",
        "Syrphus ribesii"
      ],
      "slope": 0.41937638662824034,
      "intercept": 0.10327318437064453,
      "slope_se": 0.11087035662827174,
      "r2": 0.7815155404354466,
      "slope_ci95": [
        0.11155092765614155,
        0.7272018456003391
      ],
      "decades_of_WS": 0.9310983931969457,
      "verdict": "inconclusive",
      "reason": "underpowered",
      "why": "W/S spans 0.93 decades < 1"
    },
    "pooled_descriptive_only": {
      "n": 8,
      "slope": 0.5353398309898791,
      "slope_se": 0.09247969436083754,
      "r2": 0.8481373138570998,
      "note": "mixes two physical regimes; decides nothing (hub ruling 2026-10-31)"
    },
    "thompson_prediction": "slope 0.5 of log v on log (W/S); from v_min = sqrt(2 (W/S) / (rho C_L)) with constant rho and C_L"
  },
  "interpretation_D": {
    "status": "provable; sent to the Lean thread via physics/FORMAL-STATEMENTS.md",
    "statements": [
      "W = k L^3 (cube law; already formalised as thompson1917-ch03-07)",
      "S = c L^2 (area law)",
      "v_min = sqrt(2 W / (rho S C_L)) ~ L^0.5",
      "P_req = W v / (L/D) ~ L^3.5",
      "P_avail = f M p ~ L^3 (constant specific power assumed)",
      "F_break = sigma A_cs ~ L^2 (strength law; the one the open-problems ledger needs)"
    ]
  },
  "verdicts": {
    "A_gliders": "inconclusive",
    "A_powered": "inconclusive",
    "B": "inside",
    "C": "cannot-tell"
  },
  "overall": {
    "verdict": "inconclusive",
    "sentence": "The scaling test is underpowered in both regimes (too few taxa with measured W/S and speed, and the powered set spans under one decade of wing loading); the flying fish itself sits inside the envelope (its quoted glide speeds of 10-20 m/s are at or above the 9.9 m/s minimum lift-supported speed computed from the measured wing loading and lift coefficient of the one 0.060 kg Park & Choi specimen; at the population length-weight mass for its length, 0.100-0.132 kg, that minimum is 12.7-14.6 m/s, still inside the quoted range); whether its muscles could power level flight cannot be told because no source gives the muscle numbers."
  }
}