Ball-Lens: Order and Counting on Discrete Substrates

Ball-Lens is the public mathematical artifact of a research program by Adam Bishop, founder of XOps360 LLC. The program asks which physical structures emerge from minimal primitives: a set carrying a graph metric and a counting measure. Results that are self-contained mathematics are published in a public repository, independent of whether the physical program succeeds. The current public state is v2.0.0-rc1, a release candidate dated 3 August 2026, gated by a pre-release verification pass conducted by a reviewer with no access to the authoring context and instructions to attack rather than confirm. That pass found a geometric misdescription in one theorem, which was corrected before release; the review is published unedited. Four problems are published as open, including uniform diluted winding rigidity, which is posed formally to outside mathematicians. This page carries framing, status, and links only. Every claim lives in the repository, where it is versioned and can be checked.