{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:OVD3BAKTZHWPZILFWNGE35FBTN","short_pith_number":"pith:OVD3BAKT","schema_version":"1.0","canonical_sha256":"7547b08153c9ecfca165b34c4df4a19b492603906f0d30758f7be1b10ebe84af","source":{"kind":"arxiv","id":"1106.5799","version":2},"attestation_state":"computed","paper":{"title":"Kramers' law: Validity, derivations and generalisations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.HO","math.MP"],"primary_cat":"math.PR","authors_text":"Nils Berglund","submitted_at":"2011-06-28T20:45:19Z","abstract_excerpt":"Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to obtain a mathematically rigorous proof of this formula. We also discuss some generalisations, and a case in which Kramers' law is not valid. This review is written for both mathematicians and theoretical physicists, and endeavours to link concepts and terminology from both fields."},"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":"1106.5799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-28T20:45:19Z","cross_cats_sorted":["math-ph","math.HO","math.MP"],"title_canon_sha256":"60af260285d1d6cfbca9fae1aad31a656b2e19a04c7d178e95d3b01b79b017a1","abstract_canon_sha256":"d6adb27ccd1de8629096d98d343ca1a17ff58c2065937fbabadd3939d675edd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:24.668956Z","signature_b64":"d92+/yjgsbChMiVjfYRqHW6jVAMyPRChCfOdjXRqi/g1zN/3vIIcSjRVooioccSbhUave3L6Was35OYq10bbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7547b08153c9ecfca165b34c4df4a19b492603906f0d30758f7be1b10ebe84af","last_reissued_at":"2026-05-18T03:10:24.668100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:24.668100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kramers' law: Validity, derivations and generalisations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.HO","math.MP"],"primary_cat":"math.PR","authors_text":"Nils Berglund","submitted_at":"2011-06-28T20:45:19Z","abstract_excerpt":"Kramers' law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. We review different approaches that have been followed to obtain a mathematically rigorous proof of this formula. We also discuss some generalisations, and a case in which Kramers' law is not valid. This review is written for both mathematicians and theoretical physicists, and endeavours to link concepts and terminology from both fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5799","kind":"arxiv","version":2},"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":"1106.5799","created_at":"2026-05-18T03:10:24.668224+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.5799v2","created_at":"2026-05-18T03:10:24.668224+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5799","created_at":"2026-05-18T03:10:24.668224+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVD3BAKTZHWP","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVD3BAKTZHWPZILF","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVD3BAKT","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.17815","citing_title":"Global Optimization via Softmin Energy Minimization","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN","json":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN.json","graph_json":"https://pith.science/api/pith-number/OVD3BAKTZHWPZILFWNGE35FBTN/graph.json","events_json":"https://pith.science/api/pith-number/OVD3BAKTZHWPZILFWNGE35FBTN/events.json","paper":"https://pith.science/paper/OVD3BAKT"},"agent_actions":{"view_html":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN","download_json":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN.json","view_paper":"https://pith.science/paper/OVD3BAKT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.5799&json=true","fetch_graph":"https://pith.science/api/pith-number/OVD3BAKTZHWPZILFWNGE35FBTN/graph.json","fetch_events":"https://pith.science/api/pith-number/OVD3BAKTZHWPZILFWNGE35FBTN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN/action/storage_attestation","attest_author":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN/action/author_attestation","sign_citation":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN/action/citation_signature","submit_replication":"https://pith.science/pith/OVD3BAKTZHWPZILFWNGE35FBTN/action/replication_record"}},"created_at":"2026-05-18T03:10:24.668224+00:00","updated_at":"2026-05-18T03:10:24.668224+00:00"}