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      lex: "Measured: 32 counterexamples across the rule formulas, the 8-step histories, and the Diophantine gadgets (n = 65536, exact). Interpretation: The claim (NKS p. 785-786 and the note on universal Diophantine equations) says an exponential Diophantine equation can be built whose solutions emulate rule 110, and that because rule 110 is universal the axioms of arithmetic support universality, which implies there are arithmetic statements that cannot be proved true or false. The computation tests the emulation gadgets the note actually writes down: the rule 30 and rule 110 integer formulas, the relations a^2+b^2=0, ab=0, a<b, mod, quotient, the binomial equation for C(b,c), Lucas parity for BitAnd/BitOr, and an 8-step rule 110 history. It does not replay Cook\'s proof that rule 110 is universal and does not exhibit an unprovable arithmetic sentence. Those two implications remain outside the measured verdict and are stated as caveats. Wolfram\'s note says the exponential equation can be rewritten as a polynomial in 2154 variables; that expansion is quoted from the note and is not recomputed here."
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      lex: "Pre-registered. All integer ranges below are inclusive. Bit convention, frozen: bit k of a formula output equals the elementary rule on (left, center, right) = (bit k, bit k-1, bit k-2), negative bits read as 0, Wolfram neighborhood index 4*left+2*center+right. Formula 30 is BitXor[a, 2*BitOr[a, 2*a]]. Formula 110 is BitXor[BitAnd[a, 2*a, 4*a], BitOr[2*a, 4*a]]. Part F: both formulas equal an independent truth-table scan for every a from 0 through 65535 (integer equality). Part H: for every a from 0 through 255, iterating formula 110 for 8 steps equals iterating the truth-table scan for 8 steps. Part G, every pair or triple in range, zero counterexamples: for a,b in 0..40, a^2+b^2=0 iff a=b=0; a*b=0 iff a=0 or b=0; a+b=0 iff a=b=0; for a,b in 0..40 there exists an integer c with 0 <= c <= 40 and b = a+c+1 iff a < b. For a in 0..40, b in 0..40, c in 1..40, there exists d >= 0 with b = a + c*d and a < c iff a = b mod c; there exists d >= 0 with b = a*c + d and d < c iff a = floor(b/c). Part B: for b,c in 0..8 and a >= 0, with n = 2*b+1, a equals C(b,c) iff a < n and there exist integers d,e >= 0 with e < n^c and (n+1)^b = n^c * (a + d*n) + e. Part L: for x,y in 0..128, C(x,y) is odd iff every bit set in y is set in x (math.comb exact). Part A: for c,d in 0..64, writing sigma(x,y) for \'C(x,y) is odd\', sigma(c, a) and sigma(d, a) and sigma(b, c) and sigma(b, d) and a+b = c+d hold for a = c AND d and b = c OR d, and for no other a,b in 0..64. SUPPORTS if every counterexample count is 0. Confidence if supports: 0.88."
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  prefix {
    id: 14
    value: "https://w3id.org/delphi/resource/assessment/"
  }
}
rows {
  quad {
    p_iri {
      prefix_id: 9
      name_id: 59
    }
    o_iri {
      prefix_id: 14
      name_id: 12
    }
  }
}
rows {
  quad {
    p_iri {
      prefix_id: 11
      name_id: 16
    }
    o_literal {
      lex: "Claim test of wolfram2002-ch12-34 (pr-130): mixed, confidence 0.74"
    }
  }
}
rows {
  name {
    value: "domain"
  }
}
rows {
  prefix {
    id: 16
    value: "https://w3id.org/delphi/resource/domain/"
  }
}
rows {
  name {
    value: "wolfram-nks-2002"
  }
}
rows {
  quad {
    p_iri {
      prefix_id: 10
      name_id: 60
    }
    o_iri {
      prefix_id: 16
    }
  }
}
rows {
  name {
    value: "sig"
  }
}
rows {
  name {
    value: "hasAlgorithm"
  }
}
rows {
  quad {
    s_iri {
      prefix_id: 2
    }
    p_iri {
      prefix_id: 9
    }
    o_literal {
      lex: "RSA"
    }
  }
}
rows {
  name {
    value: "hasPublicKey"
  }
}
rows {
  quad {
    p_iri {
    }
    o_literal {
      lex: "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB"
    }
  }
}
rows {
  name {
    value: "hasSignature"
  }
}
rows {
  quad {
    p_iri {
    }
    o_literal {
      lex: "cO3r7kKc2Nb21zHpY8IWXCjp9txKC5Ri4G4sK2qqXth7LsVr8KuhLiUSaWnAY2d60UeR47O+i+epmOh1mExe6+xkOX19D+r/SR1m2eGj/gFHoVlYMkHwPCRfgA6Lbqt4q/xRGUze2S1Imc7NP3/eBSu85xPRu21BhWRPoiP+cCIFVfJRUJcfZhjHmqHe1H/CcbY7pgnE3GvoZYFC9v4BvaHZjgbO1k9sQfpg7dXErvk8UdBX31bvjshOSRq66rWLREkkFjL4+EokEn2yIiXytniRBcWxkAhm5FcLDNGIzQNYE7VwmuRWgoq3wiNAXFMLUICn/vF/Uql5SSdJDjqcYQ=="
    }
  }
}
rows {
  name {
    value: "hasSignatureTarget"
  }
}
rows {
  quad {
    p_iri {
    }
    o_iri {
      prefix_id: 3
      name_id: 1
    }
  }
}
rows {
  name {
    value: "signedBy"
  }
}
rows {
  quad {
    p_iri {
      prefix_id: 9
      name_id: 67
    }
    o_iri {
      prefix_id: 6
      name_id: 43
    }
  }
}