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Precise statements — theorems, conjectures, bounds and counterexamples — each with its status, the source that reports it, and the problems it belongs to.

8 statements

  1. Disproved
    Constant Jacobian implies a polynomial inverse

    Main statementJacobian conjectureULAM research manuscript 2026

  2. Disproved
    Eventual mixed-moment vanishing in every dimension

    Main statementGaussian moments conjectureLong 2026

  3. Disproved
    Every bridgeless cubic graph admits a Petersen coloring

    Main statementPetersen coloring conjecturePutman 2026

  4. Disproved
    Normal five-edge-colorings for bridgeless cubic graphs

    Equivalent formulationPetersen coloring conjecturePutman 2026

  5. Disproved
    Planar disk rigidity for overdetermined Helmholtz data

    Main statementSchiffer and Pompeiu conjecturesColbrook & Stepaniants 2026

  6. Disproved
    The exact-cost rounding conjecture

    Main statementCost-preserving unsplittable flowRamos et al. 2026Formalized

  7. Disproved
    The near-linear unit-distance conjecture

    Main statementErdős unit-distance problemAlon et al. 2026

  8. Disproved
    The planar Pompeiu property question

    VariantSchiffer and Pompeiu conjecturesColbrook & Stepaniants 2026