Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    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 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.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Invariance under Reidemeister moves is a topological property independent of how we represent or parameterize the coloring scheme.
      ?

      Think about whether this reason is strong or weak

    • 2.If mixed moduli genuinely break type II preservation, this would violate functoriality of knot invariants—a foundational theorem in the field.
      ?

      Think about whether this reason is strong or weak

    • 3.The claim conflates computational convenience with mathematical necessity; fixed n may simplify proofs without being strictly required.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Fox n-colorings depend algebraically on fixed modular arithmetic; changing n mid-invariant computation breaks the underlying group structure.
      ?

      Think about whether this reason is strong or weak

    • 2.Type II Reidemeister moves involve crossing changes that alter arc labels; fixed moduli ensure these label updates remain self-consistent.
      ?

      Think about whether this reason is strong or weak

    • 3.Known counterexamples exist where mixed-moduli colorings assign contradictory values to the same arc under type II move equivalence.
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.