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    Inverse View

    It is not the case that Zambella's characterization presupposes a fixed encoding of finite objects into binary strings, but Cook and Nguyen's 'Logical Foundations of Proof Complexity' (2010) acknowledges that Σ^B_1-definability is encoding-sensitive.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Cook-Nguyen's acknowledgment of encoding-sensitivity doesn't entail that Zambella's specific definitions require a *fixed* encoding assumption.
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    • 2.Many encoding schemes are polynomially equivalent; variations may be theoretically noted yet practically irrelevant for Zambella's central claims.
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    • 3.Identifying a presupposition doesn't refute it—Zambella may have justified reasons for standardizing encoding that the criticism doesn't address.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Zambella's framework treats encoding as transparent, but polynomial-time definability genuinely varies across binary encodings of the same objects.
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    • 2.Cook-Nguyen explicitly document encoding-sensitivity for Σ^B_1 formulas, making Zambella's presupposition of fixed encoding empirically problematic.
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    • 3.Without addressing encoding choice, foundational claims about what is provably polynomial-time definable remain incomplete and potentially misleading.
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