{
  "kind": "symbolic checks and illustrative scale estimate",
  "vacuum_scalar_mass_squared": "2*Lambda**4/f**2",
  "hilltop_slow_roll_eta": "-16*Mpl**2/f**2",
  "ordinary_scalar_coupling": "-2*Mpl/f",
  "inputs": {
    "density_kg_m3": 1000.0,
    "illustrative_dark_energy_J_m3": 6e-10
  },
  "derived": {
    "matter_rest_energy_J_m3": 8.987551787368176e+19,
    "Lambda4_if_hilltop_is_dark_energy_J_m3": 9.6e-09,
    "Lambda4_lower_bound_for_cold_ordinary_branch_J_m3": 7.190041429894541e+20,
    "scale_ratio": 7.48962648947348e+28,
    "r_at_dark_energy_choice": 9.36203311184185e+27
  },
  "scope": "The density contradiction applies to the same universal mass function, homogeneous cold matter, no extra supports or screening; it is not a theorem excluding all theories."
}