"""Original cohort/visibility model, not live monitoring or a recommended universal SLA."""
def status(expected,completed,input_fresh=True,completion_fresh=True,worker_fresh=True,oldest_minutes=0,budget_minutes=15):
    if not input_fresh or not completion_fresh:return 'visibility unknown'
    missing=expected-completed
    if missing and oldest_minutes>budget_minutes:return 'overdue work: '+','.join(sorted(missing))
    if not worker_fresh:return 'worker heartbeat gap'
    if not expected:return 'known quiet'
    if not missing:return 'cohort complete'
    return 'work within budget'
alljobs={f'J{i:02}' for i in range(1,13)}
cases=[
 ('Quiet',set(),set(),{},'known quiet'),
 ('Overdue',alljobs,{f'J{i:02}' for i in range(1,8)},{'oldest_minutes':18},'overdue work: J08,J09,J10,J11,J12'),
 ('Blind source',set(),set(),{'input_fresh':False},'visibility unknown'),
 ('Heartbeat gap',set(),set(),{'worker_fresh':False},'worker heartbeat gap'),
 ('Complete',alljobs,alljobs,{},'cohort complete'),
 ('Pending',alljobs,{'J01'},{'oldest_minutes':5},'work within budget'),
]
for label,expected,completed,options,want in cases:
    actual=status(expected,completed,**options);assert actual==want
    print(label,':',actual)
print('6/6 synthetic state assertions passed. Missing IDs belong to the declared cohort; counts are not arbitrary time-window totals.')