primeknots

Arithmetic topology and elliptic-curve murmurations, made executable — named theorems of number theory verified in from-scratch C++, with visualizations rendered from emitted JSON. "Verified" means numerically, over a stated range, twinned or oracle-refereed; no proofs are claimed.

Data note (research track, M5)

• A pre-registered replication of the Sawin–Sutherland height-ordered murmuration — the headline write-up (PDF).
• What it took: methods, failures, and costs of an AI-driven replication — the methods companion, on how the work was done, what it cost, and what caught the failures (PDF).

Explainer deck

• Project explainer deck

Interactive viewers

Murmurations (M-ladder):

• Murmurations (the discovery)
• Dirichlet characters
• Zubrilina density
• Sawin–Sutherland height-ordered density
• Sawin–Sutherland analytic-rank split

Arithmetic topology (stages 0–6):

• Borromean rings / Rédei symbol
• Linking & quadratic reciprocity
• Class groups & 4-rank
• Arithmetic Chern–Simons
• Weil explicit formula
• Dijkgraaf–Witten / S₃ counting

Source

• Repository on GitHub (build, tests, and the errata ledger docs/ERRATA.md).

Author: Derek Marshall (ORCID 0009-0001-8101-3908). MIT-licensed.