{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TMOFMM6FZIZPEGSDON4NLELRTU","short_pith_number":"pith:TMOFMM6F","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"},"canonical_sha256":"9b1c5633c5ca32f21a437378d591719d118ec341501eada81bd9e20bbf55c424","source":{"kind":"arxiv","id":"1711.02250","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02250","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02250v1","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02250","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"TMOFMM6FZIZP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TMOFMM6FZIZPEGSD","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TMOFMM6F","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TMOFMM6FZIZPEGSDON4NLELRTU","target":"record","payload":{"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"},"canonical_sha256":"9b1c5633c5ca32f21a437378d591719d118ec341501eada81bd9e20bbf55c424","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"},"source_kind":"arxiv","source_id":"1711.02250","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYWonRcXPQn27JcZY08vgIPLhJk1zmpyf/Gb18Oxad9kN2XoluqLzhI3LwGUaL2a54ypg83kyZd2Ac/g+UWpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:17:06.333934Z"},"content_sha256":"08acdfc974ffff56581522a52d57dc99e730a546fe2fd16751b08d1c5414b337","schema_version":"1.0","event_id":"sha256:08acdfc974ffff56581522a52d57dc99e730a546fe2fd16751b08d1c5414b337"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TMOFMM6FZIZPEGSDON4NLELRTU","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gvsYC1icZzBhnsvnssyjC/0GRo9Y3pV9nFtiMPXl9gThgU2bwKrthC85n9IS1dhN0QdzwvoKX3Uukqt7TeqmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:17:06.334785Z"},"content_sha256":"5bf73913dfaca506d8656a4d4cf55c56c39d892f44a5d17b1c566353bf2ebb4a","schema_version":"1.0","event_id":"sha256:5bf73913dfaca506d8656a4d4cf55c56c39d892f44a5d17b1c566353bf2ebb4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/bundle.json","state_url":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TMOFMM6FZIZPEGSDON4NLELRTU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T07:17:06Z","links":{"resolver":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU","bundle":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/bundle.json","state":"https://pith.science/pith/TMOFMM6FZIZPEGSDON4NLELRTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TMOFMM6FZIZPEGSDON4NLELRTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TMOFMM6FZIZPEGSDON4NLELRTU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a18f77a418c90b1ceb17efc6dc8d835e9763fe6f74ded7a6eb3bbeefa20bd6de","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T01:42:13Z","title_canon_sha256":"05cc0d903f4d5e554a6457a40c5c6d4d6172ae41e6cee06dd6ade1526a02432a"},"schema_version":"1.0","source":{"id":"1711.02250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02250","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02250v1","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02250","created_at":"2026-05-18T00:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"TMOFMM6FZIZP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TMOFMM6FZIZPEGSD","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TMOFMM6F","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:5bf73913dfaca506d8656a4d4cf55c56c39d892f44a5d17b1c566353bf2ebb4a","target":"graph","created_at":"2026-05-18T00:31:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"David P. Herzog, Jonathan C. Mattingly","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T01:42:13Z","title":"Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02250","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:08acdfc974ffff56581522a52d57dc99e730a546fe2fd16751b08d1c5414b337","target":"record","created_at":"2026-05-18T00:31:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a18f77a418c90b1ceb17efc6dc8d835e9763fe6f74ded7a6eb3bbeefa20bd6de","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-07T01:42:13Z","title_canon_sha256":"05cc0d903f4d5e554a6457a40c5c6d4d6172ae41e6cee06dd6ade1526a02432a"},"schema_version":"1.0","source":{"id":"1711.02250","kind":"arxiv","version":1}},"canonical_sha256":"9b1c5633c5ca32f21a437378d591719d118ec341501eada81bd9e20bbf55c424","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b1c5633c5ca32f21a437378d591719d118ec341501eada81bd9e20bbf55c424","first_computed_at":"2026-05-18T00:31:08.433596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:08.433596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XNO62bU+WFab+LYiao2jhrw4x8wZQkp9z5ax18pMpbF4U3Ayllvkfwx3OQ7xZ+G+j6N431/ekID98BtVhy1CAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:08.434224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08acdfc974ffff56581522a52d57dc99e730a546fe2fd16751b08d1c5414b337","sha256:5bf73913dfaca506d8656a4d4cf55c56c39d892f44a5d17b1c566353bf2ebb4a"],"state_sha256":"92d280c430a1c2882929e827f0f12a11fa8a7c6a7aefa17e757f906f48540519"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IAClxuS8qUtsNK9Nwc4L9UL001XZqvHiDY94Sx+ehfZoXYEPtka5DWpMM9JoeBWZINPYE+x0HZ0zPalCBYTyAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:17:06.339014Z","bundle_sha256":"e404586052af065dc1b58645451a92c6c7d939557945a826060f8369db0c745b"}}