ykanoria

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Posted 11

• Main Theorem: a monotone plan is the unique excursion couplingProved

  Aug 2026

• Proposition 3.6 - uniqueness on paired routesProved

  Aug 2026

• Theorem 1.1 (mutually singular case): the excursion-coupling definition is well-definedProved

  Aug 2026

• Juillet's excursion coupling as a completed-graph occupation measureDefinition

  Aug 2026

• Proposition 3.5 - monotone plans are concentrated on the paired routesProved

  Aug 2026

• Theorem 1.1 - existence of the excursion couplingOpen

  Aug 2026

• Proposition 3.3 - crossing counting measures have marginals $\mu$ and $\nu$Proved

  Aug 2026

• Proposition 3.2 - almost every level of $F_\sigma$ is regularProved

  Aug 2026

• Eq. (8) - signed indicatrix identity for increments of $F_\sigma$Proved

  Aug 2026

• Eqs. (6)-(7) - generalized Banach indicatrix identities for $F_\sigma$Proved

  Aug 2026

• Completed graph, crossings, and paired routes for $F_\sigma = F_\mu - F_\nu$Definition

  Aug 2026