{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FQIEQZJZQN7ORVR7DKDF73N45C","short_pith_number":"pith:FQIEQZJZ","canonical_record":{"source":{"id":"1601.00512","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-04T14:15:44Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2b38c50c309fe32a0ef562a4f0f231ed769098915df8dc02ff56fbd7f34cca61","abstract_canon_sha256":"06ed428f52c14229eaaae35ac988a5c43b57fc1651263da32f1b375beded863c"},"schema_version":"1.0"},"canonical_sha256":"2c10486539837ee8d63f1a865fedbce89fc15911301b16f7051016778f44b558","source":{"kind":"arxiv","id":"1601.00512","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00512","created_at":"2026-05-18T01:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00512v3","created_at":"2026-05-18T01:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00512","created_at":"2026-05-18T01:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"FQIEQZJZQN7O","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FQIEQZJZQN7ORVR7","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FQIEQZJZ","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FQIEQZJZQN7ORVR7DKDF73N45C","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00512","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-04T14:15:44Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"2b38c50c309fe32a0ef562a4f0f231ed769098915df8dc02ff56fbd7f34cca61","abstract_canon_sha256":"06ed428f52c14229eaaae35ac988a5c43b57fc1651263da32f1b375beded863c"},"schema_version":"1.0"},"canonical_sha256":"2c10486539837ee8d63f1a865fedbce89fc15911301b16f7051016778f44b558","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:44.197704Z","signature_b64":"Jqb5+3tLnbaFZvXQVhSL4R9EmLqnekgh2+nUtKHcr8AKwAaOYV5b5WhCrKoh3NUUi9dM+QP8+qWWY8N65WaAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c10486539837ee8d63f1a865fedbce89fc15911301b16f7051016778f44b558","last_reissued_at":"2026-05-18T01:05:44.197284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:44.197284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00512","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IXlUFTYJuCc7X3j76o8MNDFW/eaFihjNjiFkr3h86awHjQj0UVZQ470jw8zZ2PmBahfhppJjfUNfYU+1zZgECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:54:55.389062Z"},"content_sha256":"035283d41719d32ef0483f8963b9b8b8b14439cc66e1baf62f377b87e53a2045","schema_version":"1.0","event_id":"sha256:035283d41719d32ef0483f8963b9b8b8b14439cc66e1baf62f377b87e53a2045"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FQIEQZJZQN7ORVR7DKDF73N45C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodicity and Mixing in Quantum Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Biao Wu, Dongliang Zhang, H.T. Quan","submitted_at":"2016-01-04T14:15:44Z","abstract_excerpt":"After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00512","kind":"arxiv","version":3},"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":"2026-05-18T01:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNp/N0aHAasx/tH8qAh6ORoxqnJy9SvH1Y4m0XGWkyzZiZhKK4Y9lyvTH6JWUPhXnx6cimLs4/J3dK37zSEYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:54:55.389410Z"},"content_sha256":"dc11eada2ef53a2c3624d36db70f140cbd74146aa9ba5034be43c43d1bd4c0ed","schema_version":"1.0","event_id":"sha256:dc11eada2ef53a2c3624d36db70f140cbd74146aa9ba5034be43c43d1bd4c0ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQIEQZJZQN7ORVR7DKDF73N45C/bundle.json","state_url":"https://pith.science/pith/FQIEQZJZQN7ORVR7DKDF73N45C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQIEQZJZQN7ORVR7DKDF73N45C/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":"2026-06-01T15:54:55Z","links":{"resolver":"https://pith.science/pith/FQIEQZJZQN7ORVR7DKDF73N45C","bundle":"https://pith.science/pith/FQIEQZJZQN7ORVR7DKDF73N45C/bundle.json","state":"https://pith.science/pith/FQIEQZJZQN7ORVR7DKDF73N45C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQIEQZJZQN7ORVR7DKDF73N45C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FQIEQZJZQN7ORVR7DKDF73N45C","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":"06ed428f52c14229eaaae35ac988a5c43b57fc1651263da32f1b375beded863c","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-04T14:15:44Z","title_canon_sha256":"2b38c50c309fe32a0ef562a4f0f231ed769098915df8dc02ff56fbd7f34cca61"},"schema_version":"1.0","source":{"id":"1601.00512","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00512","created_at":"2026-05-18T01:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00512v3","created_at":"2026-05-18T01:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00512","created_at":"2026-05-18T01:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"FQIEQZJZQN7O","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FQIEQZJZQN7ORVR7","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FQIEQZJZ","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:dc11eada2ef53a2c3624d36db70f140cbd74146aa9ba5034be43c43d1bd4c0ed","target":"graph","created_at":"2026-05-18T01:05:44Z","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":"After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our definitions are consistent with usual understanding of ergodicity and mixing. Two parameters concerning the degeneracy in energy levels and spacings are introduced. They are computed for right triangular billiards and the results indicate a very close relation between quantum ergodicity (mixing) and quantum chaos. At the end, we argue that, besides ergodicity and mixi","authors_text":"Biao Wu, Dongliang Zhang, H.T. Quan","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-04T14:15:44Z","title":"Ergodicity and Mixing in Quantum Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00512","kind":"arxiv","version":3},"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":"sha256:035283d41719d32ef0483f8963b9b8b8b14439cc66e1baf62f377b87e53a2045","target":"record","created_at":"2026-05-18T01:05:44Z","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":"06ed428f52c14229eaaae35ac988a5c43b57fc1651263da32f1b375beded863c","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-01-04T14:15:44Z","title_canon_sha256":"2b38c50c309fe32a0ef562a4f0f231ed769098915df8dc02ff56fbd7f34cca61"},"schema_version":"1.0","source":{"id":"1601.00512","kind":"arxiv","version":3}},"canonical_sha256":"2c10486539837ee8d63f1a865fedbce89fc15911301b16f7051016778f44b558","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c10486539837ee8d63f1a865fedbce89fc15911301b16f7051016778f44b558","first_computed_at":"2026-05-18T01:05:44.197284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:44.197284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jqb5+3tLnbaFZvXQVhSL4R9EmLqnekgh2+nUtKHcr8AKwAaOYV5b5WhCrKoh3NUUi9dM+QP8+qWWY8N65WaAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:44.197704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00512","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:035283d41719d32ef0483f8963b9b8b8b14439cc66e1baf62f377b87e53a2045","sha256:dc11eada2ef53a2c3624d36db70f140cbd74146aa9ba5034be43c43d1bd4c0ed"],"state_sha256":"916574f513a652a06af220f704e99aed15aee8b833ed5c35d88dd937857e4bc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMEEHJAgPWzgwQOrwXfNVab/8bBT20zVzCtMFk1e7s4o1bv0QIxMCqDxYKTb478Bhz05RTZf0xSWgiMfPLwhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:54:55.391435Z","bundle_sha256":"ad31993f976e9b9c9e7028868060772ddb5ad4da328a33ee17f5973cd38ae2d3"}}