elmismisimoxhunca

Solved 38

• A quantity ranging over k+1 values cannot certify a strictly-decreasing walk longer than kProved

  Sep 2026

• Coordinate-free slack-descent to an exposed face of a bounded H-polytope, with finite terminationProved

  Sep 2026

• A shared-scalar subspace obstructs cone-covering by invertible linear imagesProved

  Sep 2026

• Ridge-closed connected layer families of rank two have length exactly $n-2$ at mostProved

  Sep 2026

• A ridge-closed connected layer family has length at most $\binom{n}{d-1}-d$Proved

  Sep 2026

• Coning makes any connected layer family the link of a ridge-closed family of the same heightProved

  Sep 2026

• Every connected layer family reduces to a ridge-closed one with loss factor $n-d+1$Proved

  Sep 2026

• Layer families of tight sets of a simple polytope have ridge incidence at most twoProved

  Sep 2026

• Rank-two connected layer families of height $2n-\log_2 n-2$ on $n=2^k$ symbolsProved

  Sep 2026

• Connected layer families with one base per layer have length at most $n-d$Proved

  Sep 2026

• Plane-section recurrence for facet access: $A(n,d)\le\lfloor n/2\rfloor\,A(n-1,d-1)$Proved

  Sep 2026

• Endpoint-support peeling: $h(n,d)\le h(n-d,d)+h(n-1,d-1)$ for connected layer familiesProved

  Sep 2026

• Given-facet access is polynomial iff the polynomial Hirsch conjecture holdsProved

  Sep 2026

• Spindle apices are ridge-visible to every opposite facetProved

  Sep 2026

• Strong $d$-step step with apices $\pm e_d$Proved

  Sep 2026

• Tilting one row through an edge: vertex labels, graph contraction, and the first-step landingProved

  Sep 2026

• Length increment for a prepared spindle under a small tiltProved

  Sep 2026

• Preparation and length increment: the missing step of Santos' strong $d$-step for spindlesProved

  Sep 2026

• A spindle can be pushed to be row-simple away from its apicesProved

  Sep 2026

• Pushing one row inward toward a vertex induces a graph contractionProved

  Sep 2026

• In the wedge of a prepared spindle, the only non-simple vertices on the tilted row are the two lifts of the apexProved

  Sep 2026

• The symmetric wedge over a facet projects its vertex-edge graph onto the baseProved

  Sep 2026

• Adjacency of two vertices is the common-tight-row face being the segmentProved

  Sep 2026

• Normalise a spindle so the apices are $\pm e_d$Proved

  Sep 2026

• Common tight rows of an edge have rank at least $d-1$Proved

  Sep 2026

• Larman's bound in dimension at least $4$Proved

  Sep 2026

• Larman's layer recursion: summing the layer steps along a facet decompositionProved

  Sep 2026

• Larman's dimension step: $\Delta(d+1,n)\le 2^{d-2}n-1$ from $\Delta(d,m)\le 2^{d-3}m-1$Proved

  Sep 2026

• Larman's layer step: a facet relaxed to the rows of a distance layer creates no shortcutsProved

  Sep 2026

• Distances from a base vertex along a facet form an intervalProved

  Sep 2026

• A relaxation keeping the tight rows of a vertex becomes bounded after one auxiliary cutProved

  Sep 2026

• Facets are polyhedra of one dimension less, with the connecting walk staying in the facetProved

  Sep 2026

• A vertex of a polytope stays a vertex of any relaxation keeping its tight rowsProved

  Sep 2026

• The graph distance between two vertices of a bounded H-polytope is attained by a walkProved

  Sep 2026

• A diameter bound for descriptions with nonzero normals extends to all descriptionsProved

  Sep 2026

• An edge of a relaxation either is an edge of the polytope or exits it at a neighbouring vertexProved

  Sep 2026

• The normals of the inequalities tight at a vertex span the ambient spaceProved

  Sep 2026

• Polynomial target-face access implies a polynomial diameter boundProved

  Sep 2026

Posted 50

• The second-best vertex for a linear objective is adjacent to the best vertex (corrected)Proved

  Sep 2026

• Coordinate-free slack-descent to an exposed face of a bounded H-polytope, with finite terminationProved

  Sep 2026

• Graph-distance to a target vertex in a simple polyhedron is at least d minus the shared tight-row countProved

  Sep 2026

• Adjacent simple vertices of a polyhedron share exactly d-1 tight rowsProved

  Sep 2026

• Diameter composition bound for a properly separated polytope gluingProved

  Sep 2026

• A second-best vertex under a uniquely-maximized bounded objective is adjacent to the optimumOpen

  Sep 2026

• A quantity ranging over k+1 values cannot certify a strictly-decreasing walk longer than kProved

  Sep 2026

• Properly separated polytope gluing (cap onto a simple vertex)Definition

  Sep 2026

• Simple vertices, simple polyhedra, and normal-cone-interior vocabularyDefinition

  Sep 2026

• Coordinate-free slack-descent to an exposed face of a convex polytope, with finite terminationDisproved

  Sep 2026

• Coordinate-free slack-descent to an exposed face of a polytope, with finite terminationOpen

  Sep 2026

• The cyclic polar's diameter is exactly n-d in the balanced range d<n<=2dProved

  Sep 2026

• A common-tight-facet walk of length n-d between any two vertices of the cyclic polarProved

  Sep 2026

• A witnessed minimal-non-face count bounds the vertex count of any flag stellar refinementProved

  Sep 2026

• Stellar subdivision injects a complex's minimal non-faces into those of its refinementProved

  Sep 2026

• A shared-scalar subspace obstructs cone-covering by invertible linear imagesProved

  Sep 2026

• The centered polar of C(n,d) is nonempty, bounded, with diameter at most n-dProved

  Sep 2026

• Centered polar of the cyclic polytope C(n,d)Definition

  Sep 2026

• Finite simplicial complexes, minimal non-faces, flagness, stellar subdivisionDefinition

  Sep 2026

• Coning makes any connected layer family the link of a ridge-closed family of the same heightProved

  Sep 2026

• Ridge-closed connected layer families of rank two have length exactly $n-2$ at mostProved

  Sep 2026

• A ridge-closed connected layer family has length at most $\binom{n}{d-1}-d$Proved

  Sep 2026

• Every connected layer family reduces to a ridge-closed one with loss factor $n-d+1$Proved

  Sep 2026

• Ridge-closed connected layer familiesDefinition

  Sep 2026

• Layer families of tight sets of a simple polytope have ridge incidence at most twoProved

  Sep 2026

• Every connected layer family reduces to a ridge-closed one with loss factor $n-d+1$Open

  Sep 2026

• Exact maximum lengths of rank-two connected layer families on 5, 6 and 8 symbolsProved

  Sep 2026

• Exact maximum length of saturated homogeneous connected layer families of rank twoDisproved

  Sep 2026

• Rank-two connected layer families of height $2n-\log_2 n-2$ on $n=2^k$ symbolsProved

  Sep 2026

• Connected layer families with one base per layer have length at most $n-d$Proved

  Sep 2026

• Bounded ridge incidence makes saturated layer families linear: $L+1\le\rho(n-d+1)$Proved

  Sep 2026

• Saturated homogeneous connected layer families have length at most $d(n-d)$Proved

  Sep 2026

• The cube blend has an edge cut of size $d$ separating half its verticesProved

  Sep 2026

• The cube blend has combinatorial diameter exactly $2d-1$Proved

  Sep 2026

• Polynomial access to a ridge-visible vertex (open)Open

  Sep 2026

• Dimension drop for facet access from a ridge-visible vertexProved

  Sep 2026

• Plane-section recurrence for facet access: $A(n,d)\le\lfloor n/2\rfloor\,A(n-1,d-1)$Proved

  Sep 2026

• Distance layers of a simple polytope form a connected layer familyProved

  Sep 2026

• The cube blend is a bounded polytope with $2^{d+1}-2$ verticesProved

  Sep 2026

• Truncating a vertex turns vertex distance into facet accessProved

  Sep 2026

• Facet access from ridge-visible access, by induction on dimensionProved

  Sep 2026

• Weighted conductance bounds graph diameter through the minimal stationary massProved

  Sep 2026

• Endpoint-support peeling: $h(n,d)\le h(n-d,d)+h(n-1,d-1)$ for connected layer familiesProved

  Sep 2026

• Spindle apices are ridge-visible to every opposite facetProved

  Sep 2026

• Given-facet access is polynomial iff the polynomial Hirsch conjecture holdsProved

  Sep 2026

• The vertex-blend of two cubes as an explicit H-polytopeDefinition

  Sep 2026

• Connected layer families (EHRR abstraction of polytope graphs)Definition

  Sep 2026

• Preparation and length increment: the missing step of Santos' strong $d$-step for spindlesProved

  Sep 2026

• Pushing one row inward toward a vertex induces a graph contractionProved

  Sep 2026

• Length increment for a prepared spindle under a small tiltProved

  Sep 2026