"""Independent finite construction checks. Standard library only; no model training.
Run: python this_file.py. Stdout contains the two figure datasets.
"""
import json, math
from itertools import product, combinations
from fractions import Fraction as F
figures=[]
def mul(a,b):return[[sum(a[i][k]*b[k][j]for k in range(len(b)))for j in range(len(b[0]))]for i in range(len(a))]
def mask(a):return[[a,0,1-a],[0,a,1-a],[0,0,1]]
def repl(a):return[[a+(1-a)/2,(1-a)/2],[(1-a)/2,a+(1-a)/2]]
for a,b in [(F(4,5),F(1,2)),(F(0),F(1,2)),(F(1),F(1))]:assert mul(mask(a),mask(b))==mask(a*b)and mul(repl(a),repl(b))==repl(a*b)
t=list(range(7));r=[F(4,5)**i for i in t]
figures.append(dict(id="kernel-observation",x=t,series=[dict(name="Absorbing mask",y=list(map(float,r))),dict(name="Uniform replacement K=2",y=[float((1+v)/2)for v in r])]))
cs=[F(0),F(1,4),F(1,2),F(3,4),F(1)];tvs=[]
for c in cs:
 p=[(1+c)/4,(1-c)/4,(1-c)/4,(1+c)/4];assert sum(p)==1 and p[0]+p[1]==F(1,2)and p[0]+p[2]==F(1,2)
 tv=sum(abs(v-F(1,4))for v in p)/2;assert tv==c/2;tvs.append(float(tv))
 assert [F(1,2)*(2*v)for v in p]==p
figures.append(dict(id="joint-dependence",x=list(map(float,cs)),series=[dict(name="Independent uniform marginals",y=tvs),dict(name="Exact conditional sampling",y=[0]*5)]))
assert len(figures)==2
print(json.dumps({"status":"PASS","scope":"Constructed analytic examples only; not neural training, a benchmark, or measured hardware performance.","figures":figures},indent=2))