"""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 acc(r,u,b):return r*u+(1-r)*b
rs=[i/10 for i in range(11)]
fixed=[acc(r,.85,.2)for r in rs]
fall=[acc(r,.9-.65*r,.2)for r in rs]
check(all(a<=b for a,b in zip(fixed,fixed[1:])),'fixed utilization above baseline gives monotone gain')
check(fall[-1]<max(fall),'declining utilization can reverse recall gains')
for r in rs:
 for u in [.2,.5,.9]:
  outcomes=[r*u,r*(1-u),(1-r)*.2,(1-r)*.8]
  check(abs(sum(outcomes)-1)<1e-12,'branch probabilities normalize')
  check(abs(outcomes[0]+outcomes[2]-acc(r,u,.2))<1e-12,'branch enumeration matches accuracy')
def loglike(a,g1,g2):
 p=1/(1+math.exp(-a));return math.log(p*g1+(1-p)*g2)
ps=[.05,.1,.2,.35,.5,.65,.8,.9,.95]
def grad(p,g1,g2):return p*(1-p)*(g1-g2)/(p*g1+(1-p)*g2)
for p in ps:
 a=math.log(p/(1-p))
 for g1,g2 in [(.8,.2),(.2,.8),(.4,.4)]:
  fd=(loglike(a+1e-5,g1,g2)-loglike(a-1e-5,g1,g2))/2e-5
  check(abs(fd-grad(p,g1,g2))<1e-9,'logit gradient matches finite difference')
figures=[fig('recall-utilization','Recall and conditional utilization jointly determine accuracy','Evidence recall r','Constructed answer accuracy',rs,[('Fixed u=0.85',fixed),('u=0.9-0.65r',fall)],'Author-constructed probability tree with absent-evidence success b=0.2. Declining utilization is a chosen counterexample, not measured RAG performance.'),
fig('retrieval-gradient','Likelihood rewards predictive utility','Retriever probability pi','d log likelihood / d retrieval logit',ps,[('g1=0.8, g2=0.2',[grad(p,.8,.2)for p in ps]),('g1=0.2, g2=0.8',[grad(p,.2,.8)for p in ps])],'Exact two-document mixture for one target answer. g1 and g2 are chosen conditional likelihoods; usefulness does not certify source truth.')]
out={'article_slug':'retrieval-training-exposure','figures':figures}
(ROOT/'figures').mkdir(exist_ok=True)
(ROOT/'figures/retrieval-training-exposure.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/retrieval-training-exposure.json').read_bytes()).hexdigest()}
(ROOT/'analysis/retrieval-training-exposure.receipt.json').write_text(json.dumps(receipt,indent=2)+'\n',encoding='utf-8')
print(json.dumps(receipt))