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    If NP-completeness proofs rely on unresolved foundational... — Carmelics
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    Challenges→BHP is NP-complete

    If NP-completeness proofs rely on unresolved foundational assumptions about computational complexity classes, the claim 'BHP is NP-complete' is conditionally established at best, not categorically so.

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    Key Terms

    Categorically(as used in logic and philosophy)
    In a complete, absolute, and unconditional way—without any 'ifs,' 'ands,' or 'buts.'
    Computational complexity classes(as used in computer science and mathematical logic)
    Categories that organize computer problems based on how much time or resources a computer needs to solve them; think of them like difficulty ratings for math problems.
    Conditionally established(as used in epistemology (the study of knowledge))
    Something that is proven true only *if* certain conditions or assumptions are true, rather than being true no matter what.
    Foundational assumptions(the core beliefs the ameliorative project depends on)
    Basic beliefs or starting points that a theory relies on; if these turn out to be wrong, the whole theory falls apart.

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    NP-completeness(as used in computational complexity theory)
    A classification in computer science for problems that are extremely difficult to solve quickly, even though verifying a correct answer is easy. Think of it like a jigsaw puzzle: hard to assemble, but easy to check if someone else did it right.

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    BHP is NP-complete

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    BHP is NP-complete

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