"""Declared finite analytical controls; no neural training or source benchmark reproduction."""
import json,math,itertools,hashlib
from pathlib import Path
ROOT=Path(__file__).resolve().parents[1]
checks=[]
cases=0
def check(ok,label):
 global cases
 assert ok,label
 cases+=1
 if label not in checks: checks.append(label)
def fig(fid,title,xlabel,ylabel,x,series,caption):
 return dict(id=fid,title=title,kind='analytical_curve',x_label=xlabel,y_label=ylabel,x={'name':xlabel,'values':x},series=[{'name':n,'values':v}for n,v in series],caption=caption)
def posterior(pi,k,eps=.2):
 a=pi*(1-eps)**k;b=(1-pi)*eps**k;return a/(a+b)
for pi in [.1,.5,.9]:
 for k in range(9):
  # Ambiguous zero-input labels have equal likelihood under both hypotheses.
  l=.8**k
  check(abs(pi*l/(pi*l+(1-pi)*l)-pi)<1e-12,'ambiguous examples preserve prior')
  odds=pi/(1-pi)*4**k
  check(abs(posterior(pi,k)-odds/(1+odds))<1e-12,'posterior odds agree with normalization')
for pi in [.1,.5,.9]:
 for k in range(9):
  p=posterior(pi,k)
  noisy=.8*p+.2*(1-p)
  check(abs(noisy-(.2+.6*p))<1e-12,'future noisy-label predictive mixture')
  check(.2<=noisy<=.8,'future noisy-label probability bounds')
check(posterior(.5,0)==.5,'equal-prior zero-evidence symmetry')
for lam in [0,.5,2]:
 for eta in [.1/(1+lam),1/(1+lam)]:
  w=0.;yb=.8;q=1-eta*(1+lam)
  for k in range(21):
   check(abs(w-yb/(1+lam)*(1-q**k))<1e-12,'regression recurrence matches closed form')
   w=q*w+eta*yb
  check(abs((1/(1+lam))*.8-.8/(1+lam))<1e-12,'reciprocal-curvature one-step solution')
ks=list(range(9));steps=list(range(21))
figures=[fig('bayesian-ambiguity','Informative examples and ambiguous repetitions','Number of demonstrations k','Posterior P(H0 | D)',ks,[('Ambiguous, prior 0.1',[.1]*len(ks)),('Discriminating, prior 0.1',[posterior(.1,k)for k in ks]),('Discriminating, prior 0.5',[posterior(.5,k)for k in ks]),('Discriminating, prior 0.9',[posterior(.9,k)for k in ks])],'Two hypotheses: identity and constant zero. Discriminating examples are independent x=1,y=1 with error epsilon=0.2. Ambiguous x=0,y=0 examples preserve the prior. Curves show latent-function hypothesis probability; future noisy-label prediction is 0.2+0.6*posterior.'),
fig('iterative-equivalence','Iterative and closed-form regression predictions','Gradient steps k','Scalar prediction w',steps,[('Gradient descent',[.8/1.5*(1-.7**k)for k in steps]),('Ridge minimizer',[.8/1.5]*len(steps))],'Unit inputs, mean target0.8, lambda0.5, eta0.2, initial w0=0. No Transformer is trained or claimed to implement this recurrence.')]
out={'article_slug':'in-context-bayesian-ambiguity','figures':figures}
(ROOT/'figures').mkdir(exist_ok=True)
(ROOT/'figures/in-context-bayesian-ambiguity.json').write_text(json.dumps(out,indent=2)+'\n',encoding='utf-8')
receipt={'status':'PASS','checks':checks,'cases':cases,'empirical_benchmark':False,'source_proofs_verified':False,'figure_sha256':hashlib.sha256((ROOT/'figures/in-context-bayesian-ambiguity.json').read_bytes()).hexdigest()}
(ROOT/'analysis/in-context-bayesian-ambiguity.receipt.json').write_text(json.dumps(receipt,indent=2)+'\n',encoding='utf-8')
print(json.dumps(receipt))