{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LUJCK3KGYKMMQWYAFSUNRBUH3Y","short_pith_number":"pith:LUJCK3KG","schema_version":"1.0","canonical_sha256":"5d12256d46c298c85b002ca8d88687de0393ed79980ae975287382de9d761c22","source":{"kind":"arxiv","id":"2607.08986","version":1},"attestation_state":"computed","paper":{"title":"A Formalization of the Mean-Field Derivation of the Vlasov Equation: AI-Assisted Lean Formalization as a Strategy Game","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math-ph","math.AP","math.MP"],"primary_cat":"cs.AI","authors_text":"Joseph K. Miller","submitted_at":"2026-07-09T23:17:54Z","abstract_excerpt":"We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game. The objective is to turn a LaTeX document into Lean. The game is won when the development compiles, contains no sorry, and a machine check shows the target theorems rest on Lean's foundational axioms alone. Reuse is a second check, by a definition we introduce: whether the development yields a self-contained layer of general mathematics the wider library could absorb. The case study is a complete, axiom-clean formalization of well-posedness"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.08986","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-09T23:17:54Z","cross_cats_sorted":["cs.LO","math-ph","math.AP","math.MP"],"title_canon_sha256":"ab027c140ce3b6f982558abc651a054fae0c728223040f2c95d197456bcef8ca","abstract_canon_sha256":"841f3b1dee9de4441dfc0aab9b813e6c199cb3d3824378b6eabbd36eefb5d655"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T00:17:32.133937Z","signature_b64":"lChIqd/nJxgrlfZvEc73wJC1P7/R4o4do8WWhzyOEJUrhZAmh/psFIh3iGcSmNbaMcanEaF8d/WvzuPToMrDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d12256d46c298c85b002ca8d88687de0393ed79980ae975287382de9d761c22","last_reissued_at":"2026-07-13T00:17:32.132859Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T00:17:32.132859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Formalization of the Mean-Field Derivation of the Vlasov Equation: AI-Assisted Lean Formalization as a Strategy Game","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO","math-ph","math.AP","math.MP"],"primary_cat":"cs.AI","authors_text":"Joseph K. Miller","submitted_at":"2026-07-09T23:17:54Z","abstract_excerpt":"We formalize a research result in the Lean 4 proof assistant by having a mathematician direct an AI system, and frame the activity as a formalization game. The objective is to turn a LaTeX document into Lean. The game is won when the development compiles, contains no sorry, and a machine check shows the target theorems rest on Lean's foundational axioms alone. Reuse is a second check, by a definition we introduce: whether the development yields a self-contained layer of general mathematics the wider library could absorb. The case study is a complete, axiom-clean formalization of well-posedness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08986","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08986/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.08986","created_at":"2026-07-13T00:17:32.133375+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.08986v1","created_at":"2026-07-13T00:17:32.133375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08986","created_at":"2026-07-13T00:17:32.133375+00:00"},{"alias_kind":"pith_short_12","alias_value":"LUJCK3KGYKMM","created_at":"2026-07-13T00:17:32.133375+00:00"},{"alias_kind":"pith_short_16","alias_value":"LUJCK3KGYKMMQWYA","created_at":"2026-07-13T00:17:32.133375+00:00"},{"alias_kind":"pith_short_8","alias_value":"LUJCK3KG","created_at":"2026-07-13T00:17:32.133375+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y","json":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y.json","graph_json":"https://pith.science/api/pith-number/LUJCK3KGYKMMQWYAFSUNRBUH3Y/graph.json","events_json":"https://pith.science/api/pith-number/LUJCK3KGYKMMQWYAFSUNRBUH3Y/events.json","paper":"https://pith.science/paper/LUJCK3KG"},"agent_actions":{"view_html":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y","download_json":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y.json","view_paper":"https://pith.science/paper/LUJCK3KG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.08986&json=true","fetch_graph":"https://pith.science/api/pith-number/LUJCK3KGYKMMQWYAFSUNRBUH3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/LUJCK3KGYKMMQWYAFSUNRBUH3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y/action/storage_attestation","attest_author":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y/action/author_attestation","sign_citation":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y/action/citation_signature","submit_replication":"https://pith.science/pith/LUJCK3KGYKMMQWYAFSUNRBUH3Y/action/replication_record"}},"created_at":"2026-07-13T00:17:32.133375+00:00","updated_at":"2026-07-13T00:17:32.133375+00:00"}