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    Reidemeister move preservation holds for Fox n-colourings... — Carmelics
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    Challenges→Colourability is preserved under Reidemeister moves

    Reidemeister move preservation holds for Fox n-colourings only when n is fixed throughout; mixed or unspecified moduli can yield failures of preservation under type II moves.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Fox n-colorings depend algebraically on fixed modular arithmetic; changing n mid-invariant computation breaks the underlying group structure.
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    • 2.Type II Reidemeister moves involve crossing changes that alter arc labels; fixed moduli ensure these label updates remain self-consistent.
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    • 3.Known counterexamples exist where mixed-moduli colorings assign contradictory values to the same arc under type II move equivalence.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Invariance under Reidemeister moves is a topological property independent of how we represent or parameterize the coloring scheme.
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    • 2.If mixed moduli genuinely break type II preservation, this would violate functoriality of knot invariants—a foundational theorem in the field.
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    • 3.The claim conflates computational convenience with mathematical necessity; fixed n may simplify proofs without being strictly required.
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    Related

    Colourability is preserved under Reidemeister movesFox n-colorings depend algebraically on fixed modular arithmetic; changing n mid...If mixed moduli genuinely break type II preservation, this would violate functor...Invariance under Reidemeister moves is a topological property independent of how...
    +3 moreShow less
    Known counterexamples exist where mixed-moduli colorings assign contradictory va...The claim conflates computational convenience with mathematical necessity; fixed...Type II Reidemeister moves involve crossing changes that alter arc labels; fixed...

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    claim
    Perspectives
    2 (1 for, 1 against)
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