{
 "provenance": {
  "task": "Phase 0 impact-theory baseline; 100 m stony asteroid, 18 km/s vertical, Moon",
  "reference_file": "tillotson_reference.json (v6dd33323)",
  "eos": "Tillotson granite, Castro external/Microphysics/EOS/tillotson (_parameters; Reinhardt & Stadel 2017 Table A1)",
  "energy_convention": "e measured from ZERO (P(rho_0,0)=0.00 GPa verified); NOT e=eos_e_0 which gives P=49.68 GPa at rest",
  "citation_status": "Sources read in full this session: Marcus et al. 2009 (arXiv:0907.0234) for both decay-exponent fits; Nakajima et al. 2016 (arXiv:1603.08682) for the Bjorkman & Holsapple 1987 melt-scaling FORM. Cited at second hand, NOT read: Pierazzo et al. 1997 (paywalled, fetch failed) for the decay fit and the 46/56 GPa melt pressures; Holsapple 1993; Pike 1977. Not evaluated for want of a sourced coefficient: the B&H87 melt mass."
 },
 "tillotson_params_cgs": {
  "la": 0.5,
  "lb": 1.3,
  "e_0": 160000000000.0,
  "rho_0": 2.7,
  "A": 180000000000.0,
  "B": 180000000000.0,
  "e_s": 35000000000.0,
  "e_s_prime": 180000000000.0,
  "alpha": 5.0,
  "beta": 5.0,
  "c_v": 7900000.0
 },
 "hugoniot_check": {
  "method": "independent P(rho,e) implementation of all four Tillotson regions + Rankine-Hugoniot solve (brentq), symmetric granite-on-granite so u_p=v/2, e_H=u_p^2/2",
  "peak_state_18kms": {
   "u_p_kms": 9.0,
   "U_s_kms": 16.1069,
   "rho_g_cm3": 6.1192,
   "rho_over_rho0": 2.2664,
   "P_GPa": 391.397,
   "e_erg_g": 405000000000.0
  },
  "verdict": "CONFIRMS reference file exactly",
  "max_relative_deviation_vs_reference_percent": 0.0,
  "checks": {
   "P(rho_0,0)_GPa": 0.0,
   "P(rho_0,e_0)_GPa": 49.68,
   "all_velocities_5_to_30_kms": "P and U_s agree with hugoniot_e_from_zero to <1e-3 %"
  },
  "linear_fit_of_my_solution": {
   "form": "U_s = c0 + c1*u_p (km/s)",
   "c0": 3.043,
   "c1": 1.432,
   "published_granite": "U_s = 3.68 + 1.24 u_p (km/s)",
   "residual_at_up_9kms_percent": 8.54,
   "note": "Tillotson is stiffer than the linear granite fit at high u_p; +6 to +9 % in U_s over u_p=5-15 km/s, -6 % at u_p=2.5. This is an EOS-model limitation, not an arithmetic error."
  },
  "hugoniot_table": [
   {
    "v_imp_kms": 5,
    "u_p_kms": 2.5,
    "U_s_kms": 6.365488262612245,
    "eta": 1.646748827096563,
    "rho": 4.44622183316072,
    "P_GPa": 42.96704577263265,
    "e_erg_g": 31250000000.0
   },
   {
    "v_imp_kms": 10,
    "u_p_kms": 5.0,
    "U_s_kms": 10.225185356184513,
    "eta": 1.9569038530053324,
    "rho": 5.283640403114398,
    "P_GPa": 138.04000230849093,
    "e_erg_g": 125000000000.0
   },
   {
    "v_imp_kms": 15,
    "u_p_kms": 7.5,
    "U_s_kms": 13.951524063672267,
    "eta": 2.162516007997485,
    "rho": 5.83879322159321,
    "P_GPa": 282.51836228936344,
    "e_erg_g": 281250000000.0
   },
   {
    "v_imp_kms": 18,
    "u_p_kms": 9.0,
    "U_s_kms": 16.106872543455854,
    "eta": 2.2663798238913646,
    "rho": 6.119225524506685,
    "P_GPa": 391.39700280597725,
    "e_erg_g": 405000000000.0
   },
   {
    "v_imp_kms": 20,
    "u_p_kms": 10.0,
    "U_s_kms": 17.513764689547983,
    "eta": 2.3308907602483875,
    "rho": 6.293405052670646,
    "P_GPa": 472.87164661779553,
    "e_erg_g": 500000000000.0
   },
   {
    "v_imp_kms": 25,
    "u_p_kms": 12.5,
    "U_s_kms": 20.94421819492513,
    "eta": 2.4803028192133096,
    "rho": 6.696817611875937,
    "P_GPa": 706.8673640787232,
    "e_erg_g": 781250000000.0
   },
   {
    "v_imp_kms": 30,
    "u_p_kms": 15.0,
    "U_s_kms": 24.278655012156552,
    "eta": 2.6166136126785133,
    "rho": 7.064856754231986,
    "P_GPa": 983.2855279923405,
    "e_erg_g": 1125000000000.0
   }
  ]
 },
 "decay_law": {
  "form": "P(r) = P_0 for r <= r_ic ; P(r) = P_0 (r/r_ic)^-n for r > r_ic",
  "P_0_GPa": 391.4,
  "exponent_candidates": {
   "Pierazzo_Vickery_Melosh_1997_fit": {
    "expression": "n = (-1.84 +/- 0.17) + (2.61 +/- 0.14) log10(v_imp[km/s])",
    "n_at_18kms": 1.436,
    "range_at_18kms": [
     1.091,
     1.782
    ],
    "source": "Marcus, Stewart, Sasselov & Hernquist 2009, ApJL 700, L118 (arXiv:0907.0234), Sec. 2.2 'Test One: Shock Pressure Decay', p.2: verbatim 'Pierazzo et al. (1997) found that n = (-1.84 +/- 0.17) + (2.61 +/- 0.14) log(Vi), where Vi is the impact velocity in km s-1.' PDF fetched and read this session (arxiv.org/pdf/0907.0234, 10 pages).",
    "provenance": "secondary quotation: the coefficients are read from Marcus et al. 2009, which attributes them to Pierazzo, Vickery & Melosh 1997 Icarus 127, 408-423. The primary P97 paper is paywalled and could NOT be retrieved this session (fetch_article_fulltext on DOI 10.1006/icar.1997.5713 returned found:false), so P97 is cited at second hand, not read."
   },
   "Marcus_2009_independent_refit": {
    "expression": "n = (-1.70 +/- 0.33) + (2.45 +/- 0.24) log10(v)",
    "n_at_18kms": 1.375,
    "source": "Marcus et al. 2009 same section, verbatim: 'We fit the exponent n with (-1.70 +/- 0.33) + (2.45 +/- 0.24)log(Vi), in excellent agreement with previous work.' Their GADGET reproduction of P97 used a 10 km diameter SiO2 impactor at 10, 20, 30, 40 and 60 km/s. PRIMARY source, read this session."
   },
   "literature_bracket": {
    "range": [
     1.0,
     3.0
    ],
    "source": "Barr & Citron 2011 Icarus (Ahrens & O'Keefe 1977; Pierazzo et al. 1997): 'decay exponent n ... ranges from 1 to 3 for a wide range of nonporous materials'"
   },
   "competent_rock_near_field_typical": {
    "range": [
     1.5,
     2.0
    ],
    "note": "near-field / mid-field regressions; the drop is shallower near the core and steepens outward (Monteux & Arkani-Hamed 2016; Ahrens et al. 1977)"
   },
   "adopted_central": 2.0,
   "adopted_bracket": [
    1.44,
    3.0
   ],
   "adoption_rationale": "The P97 fit gives n=1.44 at 18 km/s. Note 18 km/s is INSIDE the 10-60 km/s range Marcus et al. verified, so this is interpolation, not extrapolation -- the fit itself is not in question. It is rejected as the central value on a self-consistency ground instead: combined with r_ic=1.44a and hemispherical isobar geometry, n=1.44 implies 130 impactor masses of melt, requiring 108 % of the total impact kinetic energy. Something in that combination is wrong, and n, r_ic and the geometric prefactor are all uncertain; n=2 is adopted as the shallowest exponent for which the melt budget closes. If the simulation returns n near 1.4 with a smaller melt volume, the geometry assumption is the culprit, not the exponent."
  },
  "isobaric_core_radius": {
   "adopted_r_ic_over_a": 1.442,
   "basis": "r_ic = 3^(1/3) a = 1.44 a, from the energy-partition argument of Senshu et al. 2002 / Pierazzo et al. 1997 as used by Monteux et al. 2009",
   "alternatives": {
    "Kurosawa_style_R<=2Rp": 2.0,
    "near_field_extent_1_to_3_a": [
     1.0,
     3.0
    ]
   },
   "uncertainty": "factor ~2; r_ic/a is 1-3 in the literature and this directly scales all melt/vapour volumes as r_ic^3"
  },
  "P_vs_r_over_a_table": [
   {
    "r_over_a": 1.0,
    "P_GPa_n1.44": 391.4,
    "P_GPa_n2.0": 391.4,
    "P_GPa_n3.0": 391.4
   },
   {
    "r_over_a": 1.5,
    "P_GPa_n1.44": 369.94,
    "P_GPa_n2.0": 361.84,
    "P_GPa_n3.0": 347.91
   },
   {
    "r_over_a": 2.0,
    "P_GPa_n1.44": 244.73,
    "P_GPa_n2.0": 203.53,
    "P_GPa_n3.0": 146.77
   },
   {
    "r_over_a": 3.0,
    "P_GPa_n1.44": 136.7,
    "P_GPa_n2.0": 90.46,
    "P_GPa_n3.0": 43.49
   },
   {
    "r_over_a": 4.0,
    "P_GPa_n1.44": 90.43,
    "P_GPa_n2.0": 50.88,
    "P_GPa_n3.0": 18.35
   },
   {
    "r_over_a": 5.0,
    "P_GPa_n1.44": 65.64,
    "P_GPa_n2.0": 32.57,
    "P_GPa_n3.0": 9.39
   },
   {
    "r_over_a": 7.0,
    "P_GPa_n1.44": 40.48,
    "P_GPa_n2.0": 16.62,
    "P_GPa_n3.0": 3.42
   },
   {
    "r_over_a": 10.0,
    "P_GPa_n1.44": 24.25,
    "P_GPa_n2.0": 8.14,
    "P_GPa_n3.0": 1.17
   },
   {
    "r_over_a": 15.0,
    "P_GPa_n1.44": 13.55,
    "P_GPa_n2.0": 3.62,
    "P_GPa_n3.0": 0.35
   },
   {
    "r_over_a": 20.0,
    "P_GPa_n1.44": 8.96,
    "P_GPa_n2.0": 2.04,
    "P_GPa_n3.0": 0.15
   },
   {
    "r_over_a": 30.0,
    "P_GPa_n1.44": 5.01,
    "P_GPa_n2.0": 0.9,
    "P_GPa_n3.0": 0.04
   },
   {
    "r_over_a": 50.0,
    "P_GPa_n1.44": 2.4,
    "P_GPa_n2.0": 0.33,
    "P_GPa_n3.0": 0.01
   },
   {
    "r_over_a": 100.0,
    "P_GPa_n1.44": 0.89,
    "P_GPa_n2.0": 0.08,
    "P_GPa_n3.0": 0.0
   }
  ]
 },
 "melt_vapor_thresholds": {
  "primary_pressure_thresholds_granite": {
   "incipient_melt_GPa": 46.0,
   "complete_melt_GPa": 56.0,
   "source": "Pierazzo, Vickery & Melosh 1997, as quoted in Silber et al. 2021 (arXiv:2104.07909): 'peak shock pressures of 46 GPa and 56 GPa ... to partially and fully melt rock (granite)'",
   "confidence": "firm (widely reused hydrocode-calibrated values)"
  },
  "derived_vaporisation_thresholds": {
   "incipient_vaporisation_GPa": 119.2,
   "complete_vaporisation_GPa": 579.0,
   "method": "post-shock waste-heat energy thresholds converted to Hugoniot pressure using the waste-heat fraction f=0.250 implied by anchoring e_wh(incipient melt) to the P97 46 GPa point, then inverted on the Tillotson Hugoniot",
   "confidence": "order-of-magnitude; the release-isentrope calculation these should come from (Ahrens & O'Keefe 1972 entropy method) is not reproduced here"
  },
  "specific_internal_energy_thresholds_postshock_erg_g": {
   "incipient_melt": 8492500000.0,
   "complete_melt": 13495800000.0,
   "incipient_vaporisation": 26372800000.0,
   "complete_vaporisation": 156372800000.0,
   "construction": "c_v(T_sol-T_0) [+L_f + c_v(T_liq-T_sol)] [+c_v(T_boil-T_sol)] [+L_v]",
   "constants": {
    "c_v_erg_g_K": 7900000.0,
    "source_c_v": "Tillotson granite parameter set (Castro _parameters)",
    "T_0_K": 298,
    "T_solidus_K": 1373,
    "T_liquidus_K": 1500,
    "source_T": "dry granite 1-bar solidus/liquidus, standard petrology",
    "L_fusion_erg_g": 4000000000.0,
    "L_vaporisation_erg_g": 130000000000.0,
    "T_boil_K": 3130,
    "source_T_boil": "silica 1-bar boiling point, 3177 K (Kraus et al. 2012 JGR 117, E09009); 3130 K used"
   }
  },
  "specific_internal_energy_thresholds_on_Hugoniot_erg_g": {
   "incipient_melt": 34006134213.6748,
   "complete_melt": 43266499604.9272,
   "incipient_vaporisation": 105603495603.3039,
   "complete_vaporisation": 626156541134.6985
  },
  "full_threshold_table": {
   "incipient_melt": {
    "P_GPa": 46.0,
    "e_Hugoniot_erg_g": 34006134213.674847,
    "u_p_kms": 2.608,
    "e_postshock_wasteheat_erg_g": 8492500000.0,
    "source": "Pierazzo+1997 granite"
   },
   "complete_melt": {
    "P_GPa": 56.0,
    "e_Hugoniot_erg_g": 43266499604.92716,
    "u_p_kms": 2.942,
    "e_postshock_wasteheat_erg_g": 13495800000.0,
    "source": "Pierazzo+1997 granite"
   },
   "incipient_vaporisation": {
    "P_GPa": 119.2,
    "e_Hugoniot_erg_g": 105603495603.30392,
    "u_p_kms": 4.596,
    "e_postshock_wasteheat_erg_g": 26372800000.0,
    "source": "thermodynamic, waste-heat fraction from P97 melt anchor"
   },
   "complete_vaporisation": {
    "P_GPa": 579.0,
    "e_Hugoniot_erg_g": 626156541134.6985,
    "u_p_kms": 11.191,
    "e_postshock_wasteheat_erg_g": 156372800000.0,
    "source": "thermodynamic, ditto"
   }
  },
  "tillotson_internal_thresholds": {
   "e_s_incipient_vap_erg_g": 35000000000.0,
   "e_s_prime_complete_vap_erg_g": 180000000000.0,
   "P_on_Hugoniot_for_e_s_GPa": 47.1,
   "P_on_Hugoniot_for_e_s_prime_GPa": 190.1,
   "u_p_kms_for_e_s": 2.65,
   "u_p_kms_for_e_s_prime": 6.0,
   "note": "e_s=3.5e10 and e_s'=1.8e11 erg/g are the EOS's OWN incipient/complete vaporisation energies (region boundaries). They map to 47 and 190 GPa on this Hugoniot. e_s -> 47 GPa is within 2 % of the P97 46 GPa incipient-MELT pressure, i.e. Tillotson's 'incipient vaporisation' energy coincides with the literature incipient-melt pressure -- a known coarseness of Tillotson, and the single largest systematic in this section."
  }
 },
 "predicted_melt_vapor_mass": {
  "impact_energetics": {
   "m_imp_g": 1413716694115.407,
   "KE_erg": 2.2902210444669592e+24,
   "KE_Mt_TNT": 54.7,
   "a_cm": 5000.0,
   "D_imp_m": 100.0,
   "reference_file_KE_erg": 2.29e+24,
   "agreement": "KE matches reference to 0.4 %"
  },
  "method": "integrate the decay field: material with peak P > P_c occupies a hemisphere of radius r_c = r_ic (P_0/P_c)^(1/n); mass = (2/3) pi r_c^3 rho_t, expressed in impactor masses",
  "target_mass_above_threshold_over_m_impactor": {
   "melt_incipient": {
    "n=1.44": {
     "mass_over_m_imp": 129.81,
     "frac_of_KE": 1.081,
     "energetically_allowed": false,
     "note": "exceeds the energy budget; see decay_law.exponent_candidates.adoption_rationale"
    },
    "n=2.0": {
     "mass_over_m_imp": 37.23,
     "frac_of_KE": 0.31,
     "energetically_allowed": true
    },
    "n=2.5": {
     "mass_over_m_imp": 19.58,
     "frac_of_KE": 0.163,
     "energetically_allowed": true
    },
    "n=3.0": {
     "mass_over_m_imp": 12.76,
     "frac_of_KE": 0.106,
     "energetically_allowed": true
    }
   },
   "melt_complete": {
    "n=1.44": {
     "mass_over_m_imp": 86.16,
     "frac_of_KE": 0.718,
     "energetically_allowed": false,
     "note": "exceeds the energy budget; see decay_law.exponent_candidates.adoption_rationale"
    },
    "n=2.0": {
     "mass_over_m_imp": 27.72,
     "frac_of_KE": 0.231,
     "energetically_allowed": true
    },
    "n=2.5": {
     "mass_over_m_imp": 15.47,
     "frac_of_KE": 0.129,
     "energetically_allowed": true
    },
    "n=3.0": {
     "mass_over_m_imp": 10.48,
     "frac_of_KE": 0.087,
     "energetically_allowed": true
    }
   },
   "vapour_incipient": {
    "n=1.44": {
     "mass_over_m_imp": 17.85,
     "frac_of_KE": 0.291,
     "energetically_allowed": true
    },
    "n=2.0": {
     "mass_over_m_imp": 8.92,
     "frac_of_KE": 0.145,
     "energetically_allowed": true
    },
    "n=2.5": {
     "mass_over_m_imp": 6.25,
     "frac_of_KE": 0.102,
     "energetically_allowed": true
    },
    "n=3.0": {
     "mass_over_m_imp": 4.92,
     "frac_of_KE": 0.08,
     "energetically_allowed": true
    }
   },
   "vapour_complete": {
    "n=1.44": {
     "mass_over_m_imp": 0.0,
     "frac_of_KE": 0.0,
     "energetically_allowed": true
    },
    "n=2.0": {
     "mass_over_m_imp": 0.0,
     "frac_of_KE": 0.0,
     "energetically_allowed": true
    },
    "n=2.5": {
     "mass_over_m_imp": 0.0,
     "frac_of_KE": 0.0,
     "energetically_allowed": true
    },
    "n=3.0": {
     "mass_over_m_imp": 0.0,
     "frac_of_KE": 0.0,
     "energetically_allowed": true
    }
   }
  },
  "energy_cap": {
   "max_melt_mass_over_m_imp_at_50pct_KE": 60.0,
   "note": "a hard bound: melting M requires M*e_CM erg. n=1.44 violates it (108 % of KE into melting alone), which is why n=2 is adopted."
  },
  "adopted_predictions_n2": {
   "melt_mass_over_m_imp": {
    "incipient_and_above": 37.2,
    "complete_melt": 27.7
   },
   "vapour_mass_over_m_imp": {
    "incipient_and_above": 8.9,
    "complete_vaporisation": 0.0
   },
   "plausible_range_over_n_1.44_to_3": {
    "melt_complete": [
     10.5,
     27.7
    ],
    "vapour_incipient": [
     4.9,
     8.9
    ]
   },
   "headline": "expect of order 10-30 impactor masses of melt and 5-10 impactor masses of vapour"
  },
  "cross_check_Bjorkman_Holsapple": {
   "form": "M_melt/m_p = k (v^2/E_m)^(3mu/2)",
   "source": "Bjorkman & Holsapple 1987, as written by Nakajima et al. 2016 (arXiv:1603.08682) eq.1; also Pierazzo et al. 1997, Abramov et al. 2012",
   "status": "NOT evaluated numerically -- the coefficient k for granite is not in any source retrieved this session; quoting a k from memory would be fabrication. The decay-field integral above is the primary estimate.",
   "qualitative_consistency": "P97/Barr & Citron 2011 report melt volume directly proportional to impact energy, consistent with the decay-integral scaling used here"
  },
  "impactor_fate": {
   "peak_P_in_impactor_GPa": 391.4,
   "vs_complete_melt_56_GPa": "exceeded by 7x -> impactor completely melted",
   "vs_incipient_vaporisation_119_GPa": "exceeded by 3.3x -> impactor at least partially vaporised",
   "vs_complete_vaporisation_579_GPa": "NOT reached (391 < 579) -> impactor NOT completely vaporised on release",
   "caveat": "symmetric granite-on-granite, so impactor and target both see 391 GPa at the interface"
  },
  "caveats": [
   "Tillotson has no explicit melt curve, no solid-solid phase transitions and no liquid-vapour dome; it cannot represent latent heat. Melt/vapour masses derived from it are systematically less reliable than ANEOS/M-ANEOS estimates and should be treated as order-of-magnitude.",
   "ANEOS-based melt thresholds for silicates run higher than Tillotson region boundaries (e.g. 106 GPa complete melt for dunite/basalt, Wunnemann et al. 2008 / Quintana et al. 2015, versus 56 GPa for granite in P97). A factor ~2 discrepancy in threshold pressure moves melt mass by (2)^(3/n) ~ 2-3x.",
   "The volume integral assumes a hemispherical isobar geometry. P97 found the melt region is better described as a buried sphere whose depth of burial scales with impactor radius, which changes the geometric prefactor by tens of percent.",
   "Vaporisation thresholds here are thermodynamic estimates, not release-isentrope calculations; treat 119 and 579 GPa as +/- a factor of ~1.5."
  ]
 },
 "crater_scaling": {
  "law": "Holsapple 1993 eq.18 combined form: pi_V = K1 [ pi_2 (rho/delta)^((6nu-2-mu)/3mu) + (K2 pi_3 (rho/delta)^((6nu-2)/3mu))^((2+mu)/2) ]^(-3mu/(2+mu))",
  "source": "Holsapple 1993 Annu. Rev. Earth Planet. Sci. 21, 333-373 (eq.18); parameter set as tabulated by Singer et al. 2020 (arXiv:2008.10132) Table S1 from Holsapple's crater-scaling site; underlying experiments Schmidt & Housen 1987, Holsapple & Schmidt 1982",
  "parameters_hard_rock": {
   "K1": 0.095,
   "K2": 0.257,
   "mu": 0.55,
   "nu": 0.33,
   "note": "reference file used nu=0.4; recomputing with nu=0.4 changes D_tr by <0.3 %"
  },
  "dimensionless_groups": {
   "pi_2_g_a_over_U2": 2.5e-07,
   "pi_3_Y_over_rho_U2": 1.1431184270690442e-05,
   "pi_3_over_pi_2": 45.72,
   "reference_file_value": 45.7,
   "verdict": "pi_3/pi_2 = 45.7 CONFIRMED"
  },
  "regime_determination": {
   "CORRECTION_to_reference_file": "The reference file infers 'strength-dominated' from pi_3/pi_2 = 46. That inference is WRONG: pi_3 and pi_2 are not directly comparable because the strength term enters eq.18 raised to (2+mu)/2 = 1.275 and carries the coefficient K2 = 0.257. The correct comparison is pi_2 versus (K2 pi_3)^1.275.",
   "gravity_term": 2.5e-07,
   "strength_term": 8.845676345706557e-08,
   "strength_over_gravity": 0.354,
   "dominant_regime_at_Y_1e8": "GRAVITY-dominated (marginally; strength contributes 35 % of the gravity term, so the event is transitional and neither term is negligible)",
   "regime_by_Y": {
    "1e+07": "gravity",
    "3e+07": "gravity",
    "1e+08": "gravity",
    "3e+08": "strength",
    "1e+09": "strength"
   },
   "crossover_Y_dyncm2": "between 1e8 and 3e8 (strength/gravity = 0.35 at 1e8, 1.44 at 3e8)"
  },
  "adopted_crater": {
   "V_transient_cm3": 764740827274909.2,
   "D_transient_km_paraboloid": 1.77,
   "d_transient_km": 0.62,
   "D_transient_km_hemisphere": 1.43,
   "D_final_km": 2.21,
   "final_from_transient": "D_final = 1.25 D_tr (standard simple-crater collapse/rim widening factor, Melosh 1989)",
   "geometry_note": "D from V assuming a paraboloid of depth/diameter = 1/(2 sqrt 2) (Holsapple's convention). A hemispherical cavity of the same volume gives D = 1.43 km, i.e. the volume-to-diameter conversion alone is a ~20 % uncertainty."
  },
  "single_regime_limits": {
   "V_gravity_regime_only_cm3": 930343651566617.5,
   "D_gravity_regime_only_km": 1.89,
   "V_strength_regime_only_cm3": 1822225583474052.8,
   "D_strength_regime_only_km": 2.36,
   "note": "the strength-only limit gives a LARGER crater than the gravity-only limit here, which is the arithmetic statement that gravity is the more restrictive (dominant) term"
  },
  "Y_sensitivity": {
   "1e+07": {
    "Y_dyncm2": 10000000.0,
    "D_transient_km": 1.88,
    "D_final_km": 2.35,
    "regime": "gravity",
    "strength_over_gravity": 0.02
   },
   "3e+07": {
    "Y_dyncm2": 30000000.0,
    "D_transient_km": 1.86,
    "D_final_km": 2.32,
    "regime": "gravity",
    "strength_over_gravity": 0.08
   },
   "1e+08": {
    "Y_dyncm2": 100000000.0,
    "D_transient_km": 1.77,
    "D_final_km": 2.21,
    "regime": "gravity",
    "strength_over_gravity": 0.35
   },
   "3e+08": {
    "Y_dyncm2": 300000000.0,
    "D_transient_km": 1.56,
    "D_final_km": 1.95,
    "regime": "strength",
    "strength_over_gravity": 1.44
   },
   "1e+09": {
    "Y_dyncm2": 1000000000.0,
    "D_transient_km": 1.22,
    "D_final_km": 1.52,
    "regime": "strength",
    "strength_over_gravity": 6.66
   }
  },
  "Y_sensitivity_summary": "Over Y = 1e7 (fractured megaregolith) to 1e9 dyn/cm^2 (competent rock), D_transient runs 1.88 -> 1.22 km and D_final 2.35 -> 1.52 km. Two orders of magnitude in Y swings the crater diameter by only a factor 1.55, because gravity carries most of the resistance at this size; the answer is far more robust to Y than the reference file's strength-dominated framing would imply.",
  "regime_transition_impactor_size": {
   "criterion": "pi_2 = (K2 pi_3)^((2+mu)/2) at v=18 km/s, g=162 cm/s^2",
   "Y_1e7_dyncm2": {
    "D_imp_m": 1.9
   },
   "Y_1e8_dyncm2": {
    "D_imp_m": 35.4
   },
   "Y_1e9_dyncm2": {
    "D_imp_m": 666.5
   },
   "interpretation": "At Y=1e8 the transition is at a ~35 m impactor; our 100 m impactor is ~3x above it, hence gravity-dominated. Only for competent rock at Y~1e9 (transition at ~670 m) would a 100 m impactor be strength-dominated. THIS is the real Y-sensitivity: Y decides which regime, more than it decides the diameter."
  },
  "reference_file_discrepancy": {
   "reference_V_tr_cm3": 457000000000000.0,
   "reference_D_tr_km": 1.2,
   "reference_D_final_km": 1.51,
   "my_V_tr_cm3": 764740827274909.2,
   "my_D_tr_km": 1.77,
   "my_D_final_km": 2.21,
   "diagnosis": "The reference file's 4.57e14 cm^3 is reproduced EXACTLY by evaluating eq.18 with the K2=0.257 coefficient OMITTED from the strength term (verified: that variant returns 4.570e14 cm^3 and D_hemisphere = 1.204 km, matching its 1.2 km). Dropping K2 inflates the strength term by 0.257^-1.275 = 5.1x, which is what makes the strength term appear to dominate.",
   "resolution": "Use K2 = 0.257. Corrected values: V_tr = 7.65e14 cm^3, D_tr = 1.77 km (paraboloid), D_final = 2.21 km, gravity-dominated. The reference file's crater is ~30-45 % too small in diameter and its regime label is wrong.",
   "confidence": "high -- the omission is reproduced to 4 significant figures"
  },
  "simple_vs_complex": {
   "lunar_transition_diameter_km": [
    15,
    20
   ],
   "source": "Pike 1977 as reported in Lunar Sourcebook ch.4: 'On the Moon, the transition from simple to complex craters takes place in the 15-20 km diameter range'; Chandnani et al. 2019 and Silber et al. 2017 confirm 15-20 km (mean ~19 km)",
   "this_crater_D_final_km": 2.21,
   "verdict": "SIMPLE crater -- 2.2 km final diameter is a factor ~7-9 below the lunar simple-to-complex transition. Bowl-shaped, no central peak, no terraces. The 1.25 D_tr collapse factor is therefore the appropriate one."
  }
 },
 "figure": "hugoniot_decay.png"
}