{
 "experiment": "secp256k1_parameter_verification",
 "timestamp_utc": "2026-11-01T05:40:39+00:00",
 "command": "experiments/baselines/secp256k1_facts.py",
 "cwd": "/Users/simon-pierreboucher/Desktop/UQO/Recherche/Recherche-UQO/mathematiques/beyond-square-root-barrier",
 "seed": null,
 "host": {
  "hostname": "MacBookPro-de-simon-pierre-2.local",
  "os": "Darwin 27.0.0 (27.0)",
  "machine": "arm64",
  "python": "3.12.13",
  "cpu": "Apple M5 Max",
  "cores": 18,
  "ram_gb": 48.0
 },
 "software": {
  "numpy": "2.5.4",
  "scipy": "1.18.1",
  "sympy": "1.14.0",
  "gmpy2": "2.3.2",
  "z3": "5.3.3",
  "pysat": "1.9.dev17",
  "ecdsa": "0.19.2",
  "coincurve": "21.0.0"
 },
 "params": {
  "gp_version": "2.19.0"
 },
 "measurements": {
  "python": {
   "p_is_prime": true,
   "p_equals_2^256-2^32-977": true,
   "p_mod_3": 1,
   "p_mod_4": 3,
   "n_is_prime": true,
   "G_on_curve": true,
   "nG_is_infinity": true,
   "cofactor": 1,
   "discriminant_nonzero": true,
   "j_invariant": 0,
   "trace_t": "432420386565659656852420866390673177327",
   "hasse_bound_ok": true,
   "hasse_exact": true,
   "anomalous": false,
   "frobenius_discriminant": "-276180966231670251052810340486134462307742726569900724701098994184861751821723",
   "disc_is_minus3_times_square": true,
   "conductor_f": "303414439467246543595250775667605759171",
   "beta_cubed_is_1_mod_p": true,
   "lambda_cubed_is_1_mod_n": true,
   "beta^2+beta+1=0 mod p": true,
   "lambda^2+lambda+1=0 mod n": true,
   "phi_G_on_curve": true,
   "phi_G_equals_lambda_G": true,
   "phi2_G_equals_lambda2_G": true,
   "beta_lambda2_mismatch": true,
   "glv_basis_v1": true,
   "glv_basis_v2": true,
   "glv_basis_det_is_n": true,
   "x0_points_exist": false,
   "embedding_degree_le_100": null,
   "twist_order": "115792089237316195423570985008687907853702405052206223696310004874299507848991",
   "twist_small_factors": {
    "3": 2,
    "13": 2,
    "3319": 1,
    "22639": 1
   },
   "twist_cofactor_bits": 220,
   "twist_cofactor_is_prime": true,
   "n_minus_1_small_factors": {
    "2": 6,
    "3": 1,
    "149": 1,
    "631": 1
   },
   "p_minus_1_small_factors": {
    "2": 1,
    "3": 1,
    "7": 1,
    "13441": 1
   },
   "glv_basis_rederived_from_euclid": true,
   "glv_euclid_candidates": [
    [
     "367917413016453100223835821029139468248",
     "64502973549206556628585045361533709077"
    ],
    [
     "64502973549206556628585045361533709077",
     "-303414439467246543595250775667605759171"
    ],
    [
     "45402545270420317080910594221470922863",
     "1581575170885439274604838923699562504932"
    ]
   ]
  },
  "pari_gp": {
   "p_is_prime": true,
   "n_is_prime": true,
   "ellcard": "115792089237316195423570985008687907852837564279074904382605163141518161494337",
   "G_on_curve": true,
   "nG_is_infinity": true,
   "trace_t": "432420386565659656852420866390673177327",
   "j_invariant": 0,
   "beta_cubed_is_1_mod_p": true,
   "lambda_cubed_is_1_mod_n": true,
   "phi_G_equals_lambda_G": true,
   "twist_small_primes": "[3, 13, 3319, 22639, 1013176677300131846900870239606035638738100997248092069256697437031]",
   "twist_small_exponents": "[2, 2, 1, 1, 1]",
   "twist_cofactor_is_prime": true,
   "twist_cofactor_bits": 220,
   "embedding_degree": "19298681539552699237261830834781317975472927379845817397100860523586360249056",
   "n_minus_1_small_primes": "[2, 3, 149, 631, 6414488540731361226607730496888035255996436684289152125202372832747357]",
   "p_minus_1_small_primes": "[2, 3, 7, 13441, 205115282021455665897114700593932402728804164701536103180137503955397371]",
   "frobenius_discriminant": "-276180966231670251052810340486134462307742726569900724701098994184861751821723",
   "disc_is_minus3_times_square": true,
   "cube_roots_unity_mod_p": [
    55594575648329892869085402983802832744385952214688224221778511981742606582254,
    60197513588986302554485582024885075108884032450952339817679072026166228089408
   ],
   "cube_roots_unity_mod_n": [
    78074008874160198520644763525212887401909906723592317393988542598630163514318,
    37718080363155996902926221483475020450927657555482586988616620542887997980018
   ],
   "kronecker_7_p": -1,
   "num_roots_x3_plus_7": 0
  },
  "agreement": {
   "p_prime": true,
   "n_prime": true,
   "order_equals_n": true,
   "trace": true,
   "j": true,
   "phi_lambda": true,
   "twist_cofactor_prime": true,
   "twist_cofactor_bits": true,
   "embedding_degree_gt_100": true,
   "beta_in_gp_roots": true,
   "lambda_in_gp_roots": true,
   "x0_points": true,
   "cm_discriminant": true,
   "frobenius_discriminant": true
  },
  "all_agree": true
 },
 "elapsed_s": 4.495
}