"""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 var(r,k):
 return k if r==1 else (1-r**(2*k))/(1-r*r)
for r in [.5,.9,.99,1.]:
 for k in [1,2,4,16,64]:
  signal=1.
  for _ in range(k):signal*=r
  check(abs(signal-r**k)<1e-12,'impulse recurrence')
  check(abs(sum(r**(2*j)for j in range(k))-var(r,k))<1e-10,'variance finite geometric sum')
  for p in [0,.1,.5,1]:
   # Enumerate a single gated Rademacher write; independence adds variances.
   mean=(1-p)*0+p*.5*(-1)+p*.5*1
   second=p*.5+p*.5
   check(abs(second-mean*mean-p)<1e-12,'Bernoulli-gated zero-mean variance')
   check(abs(sum(p*r**(2*j)for j in range(k))-p*var(r,k))<1e-10,'independent write variances add')
check(var(1,20)==20,'unit-retention variance is linear')
ks=[1,2,4,8,16,32,64];ps=[0,.01,.05,.1,.25,.5,.75,1]
figures=[fig('memory-snr','Retention competes with accumulated interference','Later writes k','Signal energy / noise variance',ks,[(f'rho={r}',[r**(2*k)/var(r,k)for k in ks])for r in [.5,.9,.99,1]],'Unit initial signal and independent mean-zero unit-variance distractors. k=0 excluded because noise variance is zero. Not learned recall accuracy.'),
fig('selective-interference','Idealized selection reduces interference','Distractor admission probability p','Expected noise variance',ps,[('rho=0.95, k=32',[p*var(.95,32)for p in ps])],'Independent Bernoulli gate; original signal always admitted. Selection quality is assumed, not learned; distractors are mean-zero and independent.')]
out={'article_slug':'state-space-memory-capacity','figures':figures}
(ROOT/'figures').mkdir(exist_ok=True)
(ROOT/'figures/state-space-memory-capacity.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/state-space-memory-capacity.json').read_bytes()).hexdigest()}
(ROOT/'analysis/state-space-memory-capacity.receipt.json').write_text(json.dumps(receipt,indent=2)+'\n',encoding='utf-8')
print(json.dumps(receipt))