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    NP-hardness is established via polynomial-time many-one r... — Carmelics
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    Challenges→BHP is NP-complete

    NP-hardness is established via polynomial-time many-one reductions, which themselves presuppose P ≠ NP is not provably false—a claim independent of ZFC under some interpretations.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Polynomial reductions define NP-hardness relative to computational models; this definition doesn't logically require P≠NP's truth.
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    • 2.Some proof systems cannot decide P vs NP (Razborov-Rudich barrier); independence from ZFC is technically consistent with known results.
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    • 3.NP-hardness classifications remain structurally valid even if P=NP holds, making the reduction framework independent of that outcome.
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    Reasons Against

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    Reason against
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    • 1.NP-hardness definitions presuppose only that NP is well-defined; they make no assumption about P≠NP being unprovable in ZFC.
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    • 2.No consensus model of computation suggests P vs NP is actually independent of ZFC; believed independence is speculative, not established.
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    • 3.Reductions work identically under both P=NP and P≠NP; the practical notion of hardness doesn't depend on any metatheoretic claim.
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    BHP is NP-complete

    Related

    BHP is NP-completeNP-hardness classifications remain structurally valid even if P=NP holds, making...NP-hardness definitions presuppose only that NP is well-defined; they make no as...No consensus model of computation suggests P vs NP is actually independent of ZF...
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    Polynomial reductions define NP-hardness relative to computational models; this ...Reductions work identically under both P=NP and P≠NP; the practical notion of ha...Some proof systems cannot decide P vs NP (Razborov-Rudich barrier); independence...

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    2 (1 for, 1 against)
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