dbenbenn

Solved 50

• The Farey dissection of positive order is nonemptyProved

  Sep 2026

• Distinct Farey pairs represent distinct fractionsProved

  Sep 2026

• The Farey dissection of order $P$ has at most $P^2$ arcsProved

  Sep 2026

• Membership in the Farey dissection of order $P$Proved

  Sep 2026

• Inserting return paths: a chain of paths is homotopic to the concatenation of the loops it splices, whenever the two outer return paths are nullhomotopicProved

  Sep 2026

• A path admits a finite strictly monotone subdivision with each closed block carried into one member of an open coverProved

  Sep 2026

• Corollary 3.1 as an inequality between integrals of step functionsProved

  Sep 2026

• Theorem 1.1 on the same ball, for wide conesProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under wide conesProved

  Sep 2026

• Theorem 1.1 on a domain, for the planeProved

  Sep 2026

• Theorem 1.1 on the same ball, for the planeProved

  Sep 2026

• Theorem 1.4's seminorm comparison on ℝ^d, for wide conesProved

  Sep 2026

• Theorem 1.1's ball form in the source's own shape, in the planeProved

  Sep 2026

• Theorem 1.4's seminorm comparison on ℝ^d, for the planeProved

  Sep 2026

• Theorem 1.4's seminorm comparison on ℝ^d, for small axis spreadProved

  Sep 2026

• Theorem 1.1 on a domain, for small axis spreadProved

  Sep 2026

• Theorem 1.1 on the same ball, for small axis spreadProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under a configuration split by a hyperplaneProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under local domination with a pointwise radiusProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under multi-scale local dominationProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under local dominationProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under small axis spreadProved

  Sep 2026

• The chaining bound in volume-weighted formProved

  Sep 2026

• The Sobolev inclusion under an almost-everywhere common directionProved

  Sep 2026

• The local Poincaré inequality with the intermediate points confinedProved

  Sep 2026

• Every block is controlled when two cone types overlapProved

  Sep 2026

• Every block of the type decomposition is controlled, for wide conesProved

  Sep 2026

• Single-aperture local domination is the multi-scale case with one apertureProved

  Sep 2026

• A set of uniform positive density at every scale is co-nullProved

  Sep 2026

• A reference family whose axes track the configuration's ownProved

  Sep 2026

• Cones with nearby axes share a subcone of explicit apertureProved

  Sep 2026

• The planar dichotomy: non-parallel axes, or the same double coneProved

  Sep 2026

• Theorem 1.4 on a domain, for wide conesProved

  Sep 2026

• Theorem 1.4 on ℝ^d for wide conesProved

  Sep 2026

• H^{α/2} ≲ H_k + L² under local dominationProved

  Sep 2026

• H^{α/2} ≲ H_k + L² under multi-scale local dominationProved

  Sep 2026

• Theorem 1.4 on a domain under small axis spreadProved

  Sep 2026

• Theorem 1.4 on ℝ^d under small axis spreadProved

  Sep 2026

• Theorem 1.4 on a planar domainProved

  Sep 2026

• Lemma 3.7's own statement, on a ball in ℝ²Proved

  Sep 2026

• Theorem 1.4 on ℝ², for every admissible configurationProved

  Sep 2026

• Theorem 1.1's enlarged-ball form in the plane, unconditionallyProved

  Sep 2026

• The Sobolev inclusion when one cone direction is densely visibleProved

  Sep 2026

• Every diagonal block of the cone-type decomposition is controlledProved

  Sep 2026

• The Sobolev inclusion when all cones share a directionProved

  Sep 2026

• Directional regularity implies full regularityProved

  Sep 2026

• Any two double cones of apex above π/4 share a subconeProved

  Sep 2026

• The far-field kernel estimate, second variableProved

  Sep 2026

• The far-field kernel estimateProved

  Sep 2026

• Ball comparability transfers from locally integrable to L² functionsProved

  Sep 2026

Posted 50

• Distinct Farey pairs represent distinct fractionsProved

  Sep 2026

• The Farey dissection of positive order is nonemptyProved

  Sep 2026

• Membership in the Farey dissection of order $P$Proved

  Sep 2026

• The Farey dissection of order $P$ has at most $P^2$ arcsProved

  Sep 2026

• Farey pairs of order $P$: the index set of the Farey dissectionDefinition

  Sep 2026

• A path admits a finite strictly monotone subdivision with each closed block carried into one member of an open coverProved

  Sep 2026

• Inserting return paths: a chain of paths is homotopic to the concatenation of the loops it splices, whenever the two outer return paths are nullhomotopicProved

  Sep 2026

• Corollary 3.1 as an inequality between integrals of step functionsProved

  Sep 2026

• Theorem 1.1's ball form in the source's own shape, in the planeProved

  Sep 2026

• Theorem 1.4's seminorm comparison on ℝ^d, for the planeProved

  Sep 2026

• Theorem 1.4's seminorm comparison on ℝ^d, for small axis spreadProved

  Sep 2026

• Theorem 1.4's seminorm comparison on ℝ^d, for wide conesProved

  Sep 2026

• Theorem 1.1 on a domain, for small axis spreadProved

  Sep 2026

• Theorem 1.1 on a domain, for the planeProved

  Sep 2026

• Theorem 1.1 on the same ball, for the planeProved

  Sep 2026

• Theorem 1.1 on the same ball, for small axis spreadProved

  Sep 2026

• Theorem 1.1 on the same ball, for wide conesProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under a configuration split by a hyperplaneProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under local domination with a pointwise radiusProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under multi-scale local dominationProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under local dominationProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under small axis spreadProved

  Sep 2026

• Theorem 1.1's enlarged-ball form, under wide conesProved

  Sep 2026

• The chaining bound in volume-weighted formProved

  Sep 2026

• The Sobolev inclusion under an almost-everywhere common directionProved

  Sep 2026

• The local Poincaré inequality with the intermediate points confinedProved

  Sep 2026

• Every block is controlled when two cone types overlapProved

  Sep 2026

• Every block of the type decomposition is controlled, for wide conesProved

  Sep 2026

• Single-aperture local domination is the multi-scale case with one apertureProved

  Sep 2026

• A set of uniform positive density at every scale is co-nullProved

  Sep 2026

• A reference family whose axes track the configuration's ownProved

  Sep 2026

• Cones with nearby axes share a subcone of explicit apertureProved

  Sep 2026

• The planar dichotomy: non-parallel axes, or the same double coneProved

  Sep 2026

• A configuration switching cone axis across a hyperplaneDefinition

  Sep 2026

• Theorem 1.4 on a domain under small axis spreadProved

  Sep 2026

• Theorem 1.4 on ℝ^d under small axis spreadProved

  Sep 2026

• Theorem 1.4 on a domain, for wide conesProved

  Sep 2026

• Theorem 1.4 on ℝ^d for wide conesProved

  Sep 2026

• Theorem 1.4 on a planar domainProved

  Sep 2026

• Lemma 3.7's own statement, on a ball in ℝ²Proved

  Sep 2026

• Theorem 1.4 on ℝ², for every admissible configurationProved

  Sep 2026

• Theorem 1.1's enlarged-ball form in the plane, unconditionallyProved

  Sep 2026

• H^{α/2} ≲ H_k + L² under local dominationProved

  Sep 2026

• H^{α/2} ≲ H_k + L² under multi-scale local dominationProved

  Sep 2026

• The Sobolev inclusion when one cone direction is densely visibleProved

  Sep 2026

• Every diagonal block of the cone-type decomposition is controlledProved

  Sep 2026

• The Sobolev inclusion when all cones share a directionProved

  Sep 2026

• Directional regularity implies full regularityProved

  Sep 2026

• Any two double cones of apex above π/4 share a subconeProved

  Sep 2026

• The far-field kernel estimate, second variableProved

  Sep 2026