{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:MKBQXBUUFWVAXDP6M3RO74ASPZ","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":"229244192978eaf4d73588ed2bc16339902d33df3da9382458026b148bfced3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-07-10T15:31:26Z","title_canon_sha256":"6ae144f04a2aa9d04baf720ef0890c5f8b0da39bb60ca7058709e08adf110447"},"schema_version":"1.0","source":{"id":"0807.1681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1681","created_at":"2026-05-18T04:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1681v2","created_at":"2026-05-18T04:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1681","created_at":"2026-05-18T04:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"MKBQXBUUFWVA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"MKBQXBUUFWVAXDP6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"MKBQXBUU","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:320402243f7082f3124f0849d6dbada9b15153602527a3fbf2cc9a4677b7418a","target":"graph","created_at":"2026-05-18T04:37:11Z","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":"The Eyring-Kramers law describes the mean transition time of an overdamped Brownian particle between local minima in a potential landscape. In the weak-noise limit, the transition time is to leading order exponential in the potential difference to overcome. This exponential is corrected by a prefactor which depends on the principal curvatures of the potential at the starting minimum and at the highest saddle crossed by an optimal transition path. The Eyring-Kramers law, however, does not hold whenever one of these principal curvatures vanishes, since it would predict a vanishing or infinite tr","authors_text":"Barbara Gentz, Nils Berglund (MAPMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-07-10T15:31:26Z","title":"The Eyring-Kramers law for potentials with nonquadratic saddles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1681","kind":"arxiv","version":2},"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:a6162141a955ac05bfd03d807f1ee83153100f27ac5d55124b230f314a51da97","target":"record","created_at":"2026-05-18T04:37:11Z","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":"229244192978eaf4d73588ed2bc16339902d33df3da9382458026b148bfced3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-07-10T15:31:26Z","title_canon_sha256":"6ae144f04a2aa9d04baf720ef0890c5f8b0da39bb60ca7058709e08adf110447"},"schema_version":"1.0","source":{"id":"0807.1681","kind":"arxiv","version":2}},"canonical_sha256":"62830b86942daa0b8dfe66e2eff0127e54243333525b08f241f103aee9970629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62830b86942daa0b8dfe66e2eff0127e54243333525b08f241f103aee9970629","first_computed_at":"2026-05-18T04:37:11.451796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:11.451796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4MloEFsocZD1xjdeOG0A5/f0tKdoFTZT/OinAL5eJOmzpdEHfyVgj3gkj8oId0LzbiPwEgcLQXWeSrr596ZjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:11.452511Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.1681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6162141a955ac05bfd03d807f1ee83153100f27ac5d55124b230f314a51da97","sha256:320402243f7082f3124f0849d6dbada9b15153602527a3fbf2cc9a4677b7418a"],"state_sha256":"7b75d4445e033c66770ba03e174f7d9c45d01daced1764c463425ca63b8b130e"}