{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WDM2YS23BATOBHYYXSQQHC4Q5T","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":"2a10b98efd229c9fc79a1e20b1b5e63bd13ab32f7a0e3147018573ea9c7aa8d7","cross_cats_sorted":["physics.bio-ph","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-06T22:31:13Z","title_canon_sha256":"e5f1658727db385390dd3ab36f960e57d4734174111ee8272359c3bb9154d1d2"},"schema_version":"1.0","source":{"id":"2607.05672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.05672","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.05672v1","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.05672","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"WDM2YS23BATO","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_16","alias_value":"WDM2YS23BATOBHYY","created_at":"2026-07-08T01:18:41Z"},{"alias_kind":"pith_short_8","alias_value":"WDM2YS23","created_at":"2026-07-08T01:18:41Z"}],"graph_snapshots":[{"event_id":"sha256:9b0a9f99f20d8969749b24cde727fcddc45091990e888ad0f7b68e1e124daf51","target":"graph","created_at":"2026-07-08T01:18:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.05672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"More than 80 years ago Kramers published a paper calculating how fast a Brownian particle escapes from a potential well over an activation barrier. Since then Kramers' model has been widely adopted by nuclear physics, biophysics and chemical physics communities as a description of activated barrier crossing. From a chemical kinetics perspective, Kramers' theory provides a mapping from continuous dynamics to discrete-state chemical kinetics. Motivated by recent developments, this Perspective provides a rigorous way of performing such a mapping, explaining why and how Kramers' theory works from ","authors_text":"Alexander M. Berezhkovskii, Dmitrii E. Makarov, Kevin Song","cross_cats":["physics.bio-ph","physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-06T22:31:13Z","title":"Modern view of activated rate processes: unidirectional fluxes at equilibrium, correlation functions, and splitting probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05672","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":"sha256:5248efeb331df9883fe7eba485bb14ab0eb403ceb0144b7aa71283dab6058e9c","target":"record","created_at":"2026-07-08T01:18:41Z","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":"2a10b98efd229c9fc79a1e20b1b5e63bd13ab32f7a0e3147018573ea9c7aa8d7","cross_cats_sorted":["physics.bio-ph","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-07-06T22:31:13Z","title_canon_sha256":"e5f1658727db385390dd3ab36f960e57d4734174111ee8272359c3bb9154d1d2"},"schema_version":"1.0","source":{"id":"2607.05672","kind":"arxiv","version":1}},"canonical_sha256":"b0d9ac4b5b0826e09f18bca1038b90ecf60ba414ea8f7089932d0a9fdf0e8857","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0d9ac4b5b0826e09f18bca1038b90ecf60ba414ea8f7089932d0a9fdf0e8857","first_computed_at":"2026-07-08T01:18:41.236840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:18:41.236840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"veX7HmaHddqDYfFb0jzO0B53sv4sYqKkfAmj+32jEmtv5pNk2Ddw0NgiS7SQdr5QkrTRCciL8aFJw9Tpt/28AA==","signature_status":"signed_v1","signed_at":"2026-07-08T01:18:41.237251Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.05672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5248efeb331df9883fe7eba485bb14ab0eb403ceb0144b7aa71283dab6058e9c","sha256:9b0a9f99f20d8969749b24cde727fcddc45091990e888ad0f7b68e1e124daf51"],"state_sha256":"0e5f80f4b952b5fbe7203d2c6082151053155763120ec44e80b4b262c6780ef8"}