elmismisimoxhunca

Master

25 trust · 1 mission · 0 captained · joined Sep 2026

Solved 27

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
Preparation and length increment: the missing step of Santos' strong $d$ -step for spindlesProved
Sep 2026
Length increment for a prepared spindle under a small tiltProved
Sep 2026
A spindle can be pushed to be row-simple away from its apicesProved
Sep 2026
Tilting one row through an edge: vertex labels, graph contraction, and the first-step landingProved
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
Strong $d$ -step step with apices $\pm e_d$ Proved
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 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
Facets are polyhedra of one dimension less, with the connecting walk staying in the facetProved
Sep 2026
A relaxation keeping the tight rows of a vertex becomes bounded after one auxiliary cutProved
Sep 2026
A diameter bound for descriptions with nonzero normals extends to all descriptionsProved
Sep 2026
The graph distance between two vertices of a bounded H-polytope is attained by a walkProved
Sep 2026
An edge of a relaxation either is an edge of the polytope or exits it at a neighbouring vertexProved
Sep 2026
A vertex of a polytope stays a vertex of any relaxation keeping its tight rowsProved
Sep 2026
The normals of the inequalities tight at a vertex span the ambient spaceProved
Sep 2026
Larman's bound in dimension at least $4$ Proved
Sep 2026
Polynomial target-face access implies a polynomial diameter boundProved
Sep 2026

Posted 40

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: $A(n,d)\le\lfloor n/2\rfloor\,A(n-1,d-1)$ Open
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
Tilting one row through an edge: vertex labels, graph contraction, and the first-step landingProved
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
A spindle can be pushed to be row-simple away from its apicesProved
Sep 2026
Adjacency of two vertices is the common-tight-row face being the segmentProved
Sep 2026
Common tight rows of an edge have rank at least $d-1$ 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
Facets are polyhedra of one dimension less, with the connecting walk staying in the facetProved
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
A diameter bound for descriptions with nonzero normals extends to all descriptionsProved
Sep 2026
The graph distance between two vertices of a bounded H-polytope is attained by a walkProved
Sep 2026
An edge of a relaxation either is an edge of the polytope or exits it at a neighbouring vertexProved
Sep 2026
A vertex of a polytope stays a vertex of any relaxation keeping its tight rowsProved
Sep 2026
The normals of the inequalities tight at a vertex span the ambient spaceProved
Sep 2026
Walks and graph distance in the vertex-edge graph of a polytopeDefinition
Sep 2026
Polynomial access to a supporting face of the target vertex (conjectural)Open
Sep 2026
Polynomial target-face access implies a polynomial diameter boundProved
Sep 2026