{"paper":{"title":"Progress in Formalizing Sphere Packing in Dimension 8","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The sphere packing problem in eight dimensions has been formally verified in Lean with AI assistance.","cross_cats":["cs.AI","cs.LO","math.NT"],"primary_cat":"math.MG","authors_text":"Auguste Poiroux, Bhavik Mehta, Christopher Birkbeck, Ho Kiu Gareth Ma, Maryna Viazovska, Seewoo Lee, Sidharth Hariharan","submitted_at":"2026-04-25T23:27:10Z","abstract_excerpt":"In 2016, Viazovska famously solved the sphere packing problem in dimension $8$, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 2003. In March 2024, Hariharan and Viazovska launched a project to formalize this solution and related mathematical facts in the Lean Theorem Prover. A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'. We discuss the techniques used to achieve this milestone, reflect o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the combination of human-written Lean code and the Gauss AI model correctly captured every detail of Viazovska's original proof without introducing or overlooking logical gaps.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The sphere packing problem in dimension 8 has been formally verified in the Lean theorem prover, with the final stages completed by the AI model Gauss.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The sphere packing problem in eight dimensions has been formally verified in Lean with AI assistance.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5bdb6106aa3be70f9bd2213922fd5a280388d23cf536097b6439e8982b4d62b3"},"source":{"id":"2604.23468","kind":"arxiv","version":3},"verdict":{"id":"a84d2e89-42db-440c-997d-96bc02b1994e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T06:39:19.849384Z","strongest_claim":"A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'.","one_line_summary":"The sphere packing problem in dimension 8 has been formally verified in the Lean theorem prover, with the final stages completed by the AI model Gauss.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the combination of human-written Lean code and the Gauss AI model correctly captured every detail of Viazovska's original proof without introducing or overlooking logical gaps.","pith_extraction_headline":"The sphere packing problem in eight dimensions has been formally verified in Lean with AI assistance."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.23468/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T08:40:02.063528Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:04:52.872207Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"86e552cc3b07a782c4f3a82ccaa3b409219f20eed776b10a17bb7020c5f265c3"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}