Four-paper collection · revised 6 September 2026

Attractive Centers

Invariant means of Euclidean point configurations, the geometry of chests and hearts, radial response, and analytic triangle-center constructions. The papers are available as PDF downloads.

Interactive geometry explorer

Move the vertices of a triangle, compare four planar chest constructions, or rotate a tetrahedron and inspect its three-dimensional chest. Brief theory, live area and volume percentages, and freely reusable JavaScript and Julia source.

Open the explorer

Attractive Centers I

Chests, Hearts, and Symmetry–Displacement Geometry · Revised submission · 25 pages

Introduces attractive centers, symmetry-displacement certificates, the standard triangle chest, and higher-point outer constructions.

Download PDF

Attractive Centers II

Isosceles Geometry, Local Admissibility, and Global Extension · Revised submission · 21 pages

Studies the exact isosceles stratum, local positive-semidefinite admissibility, and the obstruction posed by global analytic continuation.

Download PDF

Attractive Centers III

Radial Location Functionals, Mechanical Response, and an Exact Elasticity Classification · Revised submission · 23 pages

Derives the exact elasticity interval for attractive radial location functionals and gives finite counterexamples outside it.

Download PDF

Attractive Centers IV

Analytic Triangle Hearts, Centroidal Rays, and Nonlocal Constraints · Revised submission · 20 pages

Develops certified inner families, centroidal-ray criteria, equivariant jets, and nonlocal constraints for the analytic triangle Heart.

Download PDF