{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:4AQVLU7ACFP226D3BWNBGKZ36Y","short_pith_number":"pith:4AQVLU7A","canonical_record":{"source":{"id":"0811.2164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-11-13T16:20:26Z","cross_cats_sorted":[],"title_canon_sha256":"3dc1e655e7850300432d5c96a774d81b4208cd9d19b927031b37ca3aec56a34b","abstract_canon_sha256":"111969b6caa4ccf72227e00ff6ea1ba9c28443a41c594661ec187e401b10b762"},"schema_version":"1.0"},"canonical_sha256":"e02155d3e0115fad787b0d9a132b3bf63b0617cc096e3eacdf6cecd9cec9ad53","source":{"kind":"arxiv","id":"0811.2164","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.2164","created_at":"2026-05-18T02:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"0811.2164v2","created_at":"2026-05-18T02:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.2164","created_at":"2026-05-18T02:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"4AQVLU7ACFP2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4AQVLU7ACFP226D3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4AQVLU7A","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:4AQVLU7ACFP226D3BWNBGKZ36Y","target":"record","payload":{"canonical_record":{"source":{"id":"0811.2164","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-11-13T16:20:26Z","cross_cats_sorted":[],"title_canon_sha256":"3dc1e655e7850300432d5c96a774d81b4208cd9d19b927031b37ca3aec56a34b","abstract_canon_sha256":"111969b6caa4ccf72227e00ff6ea1ba9c28443a41c594661ec187e401b10b762"},"schema_version":"1.0"},"canonical_sha256":"e02155d3e0115fad787b0d9a132b3bf63b0617cc096e3eacdf6cecd9cec9ad53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:21.226360Z","signature_b64":"mOAx4A5E+1hjwyEYeET0gfGJkWz5Sx3LY2cpTm0rYI59IW/LBwY36JT6hNEF9dAXiCNsdxLgjwXxp0Xc6GfIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e02155d3e0115fad787b0d9a132b3bf63b0617cc096e3eacdf6cecd9cec9ad53","last_reissued_at":"2026-05-18T02:15:21.225691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:21.225691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.2164","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"361E114hBavXYupt9xPyWhLJqyRbCxHCkhxKWfPL3fQlz8zj9TGxDuVd6TjPRTSowpBQe0BdPl90cSeC5tHaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T14:36:37.737936Z"},"content_sha256":"433642cf325f89c32d1889539e947c33f3bffd40f62eab48b85790d152c45a61","schema_version":"1.0","event_id":"sha256:433642cf325f89c32d1889539e947c33f3bffd40f62eab48b85790d152c45a61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:4AQVLU7ACFP226D3BWNBGKZ36Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The semiclassical continuity equation for open chaotic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Daniel Waltner, Jack Kuipers, Klaus Richter, Martha Gutierrez","submitted_at":"2008-11-13T16:20:26Z","abstract_excerpt":"We consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical trajectories. The current density is related to the survival probability via the continuity equation, and we show that this relation is satisfied within the semiclassical approximation to all orders. For this we develop recursion relation arguments which connect the trajectory structures involved for the survival probability, which travel from one point in the bulk to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2164","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nMCO9ylpcGIW70j+kV0x/HbFsM3zIpj0RTZ2JmIMeD3g+DBF+dKFPL/gNKa32d0YfQhpVrfoe1CKoN6psds/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T14:36:37.738646Z"},"content_sha256":"0980dcf0f1bdbef8d468811bf1b7cdd1a59cfb8bf7175576b45fdfec3df00d83","schema_version":"1.0","event_id":"sha256:0980dcf0f1bdbef8d468811bf1b7cdd1a59cfb8bf7175576b45fdfec3df00d83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4AQVLU7ACFP226D3BWNBGKZ36Y/bundle.json","state_url":"https://pith.science/pith/4AQVLU7ACFP226D3BWNBGKZ36Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4AQVLU7ACFP226D3BWNBGKZ36Y/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":"2026-05-24T14:36:37Z","links":{"resolver":"https://pith.science/pith/4AQVLU7ACFP226D3BWNBGKZ36Y","bundle":"https://pith.science/pith/4AQVLU7ACFP226D3BWNBGKZ36Y/bundle.json","state":"https://pith.science/pith/4AQVLU7ACFP226D3BWNBGKZ36Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4AQVLU7ACFP226D3BWNBGKZ36Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4AQVLU7ACFP226D3BWNBGKZ36Y","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":"111969b6caa4ccf72227e00ff6ea1ba9c28443a41c594661ec187e401b10b762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-11-13T16:20:26Z","title_canon_sha256":"3dc1e655e7850300432d5c96a774d81b4208cd9d19b927031b37ca3aec56a34b"},"schema_version":"1.0","source":{"id":"0811.2164","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.2164","created_at":"2026-05-18T02:15:21Z"},{"alias_kind":"arxiv_version","alias_value":"0811.2164v2","created_at":"2026-05-18T02:15:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.2164","created_at":"2026-05-18T02:15:21Z"},{"alias_kind":"pith_short_12","alias_value":"4AQVLU7ACFP2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4AQVLU7ACFP226D3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4AQVLU7A","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:0980dcf0f1bdbef8d468811bf1b7cdd1a59cfb8bf7175576b45fdfec3df00d83","target":"graph","created_at":"2026-05-18T02:15:21Z","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 consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical trajectories. The current density is related to the survival probability via the continuity equation, and we show that this relation is satisfied within the semiclassical approximation to all orders. For this we develop recursion relation arguments which connect the trajectory structures involved for the survival probability, which travel from one point in the bulk to a","authors_text":"Daniel Waltner, Jack Kuipers, Klaus Richter, Martha Gutierrez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-11-13T16:20:26Z","title":"The semiclassical continuity equation for open chaotic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2164","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":"sha256:433642cf325f89c32d1889539e947c33f3bffd40f62eab48b85790d152c45a61","target":"record","created_at":"2026-05-18T02:15:21Z","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":"111969b6caa4ccf72227e00ff6ea1ba9c28443a41c594661ec187e401b10b762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-11-13T16:20:26Z","title_canon_sha256":"3dc1e655e7850300432d5c96a774d81b4208cd9d19b927031b37ca3aec56a34b"},"schema_version":"1.0","source":{"id":"0811.2164","kind":"arxiv","version":2}},"canonical_sha256":"e02155d3e0115fad787b0d9a132b3bf63b0617cc096e3eacdf6cecd9cec9ad53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e02155d3e0115fad787b0d9a132b3bf63b0617cc096e3eacdf6cecd9cec9ad53","first_computed_at":"2026-05-18T02:15:21.225691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:21.225691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mOAx4A5E+1hjwyEYeET0gfGJkWz5Sx3LY2cpTm0rYI59IW/LBwY36JT6hNEF9dAXiCNsdxLgjwXxp0Xc6GfIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:21.226360Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.2164","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:433642cf325f89c32d1889539e947c33f3bffd40f62eab48b85790d152c45a61","sha256:0980dcf0f1bdbef8d468811bf1b7cdd1a59cfb8bf7175576b45fdfec3df00d83"],"state_sha256":"a258d5a7836d6cff2316b582202d36c88d7c77e56b69c12d05e38d005fcb182d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AO1Kr1IxvQpwJHPDkBsYNioCbqwQCbkHReBH7h7l7vkjs1bWfuklSX6vfbVuSEWATZxrFe7+488/6AR7udVQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T14:36:37.745661Z","bundle_sha256":"4e568e007ac3c0c250a54499eb8e410735b4c7e9bae69f36ab52cf1c84f50ce5"}}