Four-paper collection · Version 2 · 1 October 2026
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.
The triangle explorer now shows the enlarged certified heart by default: B46, the constant and shape-dependent families, the repaired continuous conic bridge, R1–R10, and P1–P3. Compare the earlier hearts with checkboxes, drag the vertices, and read the formulas and proof status in the guide. Four planar points and tetrahedra retain their power hearts and geometric chest methods. Light plots, equal coordinate scales, and live area and volume percentages support comparison.
Open the explorer59 slides with 51 embedded animations demonstrate symmetry predecessors, vertex motions, intermediate network chests, and successive geometric bounds for triangles, four planar points, and tetrahedra. Conditional methods are explicitly labelled. Open the presentation in desktop PowerPoint and start Slide Show (F5). Alternatively, extract the offline gallery and open index.html in a browser.
Download animated presentation Download offline animation galleryIntroduces attractive centers, symmetry-displacement certificates, the standard triangle chest, and higher-point outer constructions. Version 2 adds the certified B46 inner comparison without changing the outer axioms or asserting the OSC conjecture.
Download Version 2 PDF Earlier version (unchanged)Studies the isosceles stratum, local positive-semidefinite admissibility, and global extension. Version 2 separates historical numerical experiments from the current proved inventory; the extension problem remains open.
Download Version 2 PDF Earlier version (unchanged)Derives the universal elasticity and power-exponent intervals. Version 2 adds rigorous power-endpoint separation witnesses and certified root-error bounds, showing why both endpoints are needed in the present finite reference.
Download Version 2 PDF Earlier version (unchanged)Includes the complete B46 base, exact fixed-reference sufficiency, all-1,142 native ETC containment, independent replay architecture, and the updated heart–chest figure. B46 is not asserted minimal or maximal; numerical candidates and regularity classes are distinguished.
Download Version 2 PDF Earlier version (unchanged)