#!/usr/bin/env python3
"""Standard-library verifier for every recipe in exact_results.json.

This independently verifies the exhibited constructions.  It separately checks
that archived solver metadata is internally consistent; it does not replay or
certify an optimizer's lower-bound proof.
"""
import json,sys
from itertools import combinations
from collections import Counter

def shift(block,v,kind):
 if kind=="cyclic": return tuple(sorted((x+1)%v for x in block))
 f=v-1; return tuple(sorted(f if x==f else (x+1)%(v-1) for x in block))
def develop(base,v,kind):
 n=v if kind=="cyclic" else v-1; out=set(); cur=tuple(sorted(base))
 for _ in range(n): out.add(cur); cur=shift(cur,v,kind)
 return out
def near(x,n,tol=1e-7): return abs(float(x)-n)<=tol

def main(path="exact_results.json"):
 d=json.load(open(path,encoding="utf-8")); failures=0
 for e in d["entries"]:
  v,k,t=e["cell"]; bases=[tuple(b) for b in e["base_blocks"]]
  bases_ok=all(len(b)==k and len(set(b))==k and tuple(sorted(b))==b and min(b)>=0 and max(b)<v for b in bases)
  orbit_sets=[develop(b,v,e["kind"]) for b in bases]
  canonical_ok=all(b==min(o) for b,o in zip(bases,orbit_sets))
  distinct_orbits=len(set().union(*orbit_sets))==sum(map(len,orbit_sets))
  blocks=set().union(*orbit_sets)
  malformed=[b for b in blocks if len(b)!=k or len(set(b))!=k or min(b)<0 or max(b)>=v]
  mult=Counter(q for b in blocks for q in combinations(b,t))
  all_t=list(combinations(range(v),t)); unc=[q for q in all_t if mult[q]==0]
  expected=e["exact_minimum_blocks"]
  construction_ok=(bases_ok and canonical_ok and distinct_orbits and not malformed and len(blocks)==expected and not unc)
  cp=e["cp_sat"]; sc=e["scip"]
  metadata_ok=(cp["status"]=="OPTIMAL" and sc["status"]=="OPTIMAL" and near(cp["objective"],expected) and near(cp["best_bound"],expected) and near(sc["objective"],expected) and near(sc["best_bound"],expected))
  prof=Counter(mult[q] for q in all_t)
  print(f"{e['cell']} {e['group']}: blocks={len(blocks)} expected={expected} uncovered={len(unc)} multiplicity={dict(sorted(prof.items()))} construction={'PASS' if construction_ok else 'FAIL'} recorded_metadata={'CONSISTENT' if metadata_ok else 'INCONSISTENT'}")
  failures += not (construction_ok and metadata_ok)
 return 1 if failures else 0
if __name__=="__main__":sys.exit(main(sys.argv[1] if len(sys.argv)>1 else "exact_results.json"))