{
 "seeds": 3,
 "paper_prior": "smooth_1e-3",
 "controls": {
  "C1_stateless": {
   "feature_rms_gap": 2.5552325258184276,
   "gap_over_seed_sd": 7.144815284357369,
   "verdict": "stateless data give a different X (differential exists)"
  },
  "C2_nonsolution": {
   "fit_ratio_nonsolution_over_real": 0.7767660651788036,
   "family_distance_real": 0.5385066202505622,
   "family_distance_nonsolution": 0.7449135821341182,
   "violation_reproduced": false,
   "verdict": "non-solution data fit as well \u2014 the pipeline does not forbid the alternative"
  },
  "C3_prior_swap": {
   "priors": {
    "einstein_1e-4": {
     "fit": 0.003459992834497787,
     "equal_fit": true,
     "feature_rms_shift": 0.41488044718204775,
     "shift_over_seed_sd": 1.1600682639470876,
     "family_distance": 0.08308317849957374,
     "family_distance_ratio_vs_paper_prior": 0.15428441429543782,
     "generator_distance": 0.7894275864268588,
     "generator_distance_paper_prior": 1.150458592469584,
     "nonsolution_family_distance_under_this_prior": 0.1712755493452827
    }
   },
   "verdict": "X moves under a prior swap at equal fit \u2014 the moved part is the prior's, not the data's: einstein_1e-4"
  },
  "C4_family_conditioning": {
   "family_distance_real": [
    0.5385066202505622,
    0.1844414169346635
   ],
   "generator_distance_real": [
    1.150458592469584,
    0.20008251975757135
   ],
   "condition_number": 3426811.1525600734,
   "verdict": "output is closer to ANOTHER member of the family than to its generator; ill-conditioned parametrisation (cond 3426811): function-space fit hides parameter error"
  }
 },
 "overall": "EMERGENCE CLAIM NOT SUPPORTED by these controls: C2_nonsolution, C3_prior_swap, C4_family_conditioning"
}