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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that FACTORIZATION is in NP ∩ coNP.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The certificate for coNP membership presupposes unique prime factorization, which is a non-trivial mathematical theorem, not a logical given.
      ?

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    • 2.If the Fundamental Theorem of Arithmetic requires proof, then the coNP certificate argument embeds an unacknowledged mathematical assumption that could fail in alternative number-theoretic frameworks.
      ?

      Think about whether this reason is strong or weak

    • 3.Wittgenstein's rule-following considerations suggest that 'divides evenly' as a verification procedure smuggles in an infinite normative commitment not capturable by finite polynomial-time computation alone.
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      Think about whether this reason is strong or weak

    Reason for 2 of 2
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    • 1.The AKS primality certificate verifies primality of individual factors, but the coNP certificate requires verifying the *completeness* of the factorization, a globally quantified claim not reducible to local factor checks.
      ?

      Think about whether this reason is strong or weak

    • 2.Verifying that no prime factor smaller than m exists requires either exhaustive search or trust in the completeness of the presented factorization, reintroducing the original computational difficulty in disguised form.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A divisor d with 1 < d ≤ m that divides n serves as a polynomial certificate for membership of ⟨n,m⟩ in FACTORIZATION.
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      Think about whether this reason is strong or weak

    • 2.A prime factorization of n in which no prime factor is less than m serves as a polynomial certificate for membership of ⟨n,m⟩ in the complement of FACTORIZATION.
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      Think about whether this reason is strong or weak

    • 3.Primality of individual factors can be verified in polynomial time by the AKS algorithm.
      ?

      Think about whether this reason is strong or weak

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    Explore the most compelling reason on the other side.