{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TMOFMM6FZIZPEGSDON4NLELRTU","short_pith_number":"pith:TMOFMM6F","schema_version":"1.0","canonical_sha256":"9b1c5633c5ca32f21a437378d591719d118ec341501eada81bd9e20bbf55c424","source":{"kind":"arxiv","id":"1711.02250","version":1},"attestation_state":"computed","paper":{"title":"Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.PR","authors_text":"David P. Herzog, Jonathan C. Mattingly","submitted_at":"2017-11-07T01:42:13Z","abstract_excerpt":"We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions."},"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":"1711.02250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T01:42:13Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"05cc0d903f4d5e554a6457a40c5c6d4d6172ae41e6cee06dd6ade1526a02432a","abstract_canon_sha256":"a18f77a418c90b1ceb17efc6dc8d835e9763fe6f74ded7a6eb3bbeefa20bd6de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:08.434224Z","signature_b64":"XNO62bU+WFab+LYiao2jhrw4x8wZQkp9z5ax18pMpbF4U3Ayllvkfwx3OQ7xZ+G+j6N431/ekID98BtVhy1CAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b1c5633c5ca32f21a437378d591719d118ec341501eada81bd9e20bbf55c424","last_reissued_at":"2026-05-18T00:31:08.433596Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:08.433596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.PR","authors_text":"David P. Herzog, Jonathan C. Mattingly","submitted_at":"2017-11-07T01:42:13Z","abstract_excerpt":"We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02250","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":""},"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":"1711.02250","created_at":"2026-05-18T00:31:08.433681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.02250v1","created_at":"2026-05-18T00:31:08.433681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02250","created_at":"2026-05-18T00:31:08.433681+00:00"},{"alias_kind":"pith_short_12","alias_value":"TMOFMM6FZIZP","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TMOFMM6FZIZPEGSD","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TMOFMM6F","created_at":"2026-05-18T12:31:46.661854+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/TMOFMM6FZIZPEGSDON4NLELRTU","json":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU.json","graph_json":"https://pith.science/api/pith-number/TMOFMM6FZIZPEGSDON4NLELRTU/graph.json","events_json":"https://pith.science/api/pith-number/TMOFMM6FZIZPEGSDON4NLELRTU/events.json","paper":"https://pith.science/paper/TMOFMM6F"},"agent_actions":{"view_html":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU","download_json":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU.json","view_paper":"https://pith.science/paper/TMOFMM6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.02250&json=true","fetch_graph":"https://pith.science/api/pith-number/TMOFMM6FZIZPEGSDON4NLELRTU/graph.json","fetch_events":"https://pith.science/api/pith-number/TMOFMM6FZIZPEGSDON4NLELRTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/action/storage_attestation","attest_author":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/action/author_attestation","sign_citation":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/action/citation_signature","submit_replication":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/action/replication_record"}},"created_at":"2026-05-18T00:31:08.433681+00:00","updated_at":"2026-05-18T00:31:08.433681+00:00"}