{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:J7OG7ZQ45M5GDIYCIUS2PHQRKA","short_pith_number":"pith:J7OG7ZQ4","canonical_record":{"source":{"id":"2411.18436","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-11-27T15:20:24Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"008db328f24477d293133ac6be981875b19e4c5fbd303e430900f724bd1b6136","abstract_canon_sha256":"8ef4e6fb6c012dfba7d3c83f2ab650a179653bd03b1c706f3f3e491ffd66cce1"},"schema_version":"1.0"},"canonical_sha256":"4fdc6fe61ceb3a61a3024525a79e11502415712e465b44743b3d62c273395488","source":{"kind":"arxiv","id":"2411.18436","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18436","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18436v3","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18436","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"J7OG7ZQ45M5G","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"pith_short_16","alias_value":"J7OG7ZQ45M5GDIYC","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"pith_short_8","alias_value":"J7OG7ZQ4","created_at":"2026-07-05T10:34:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:J7OG7ZQ45M5GDIYCIUS2PHQRKA","target":"record","payload":{"canonical_record":{"source":{"id":"2411.18436","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-11-27T15:20:24Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"008db328f24477d293133ac6be981875b19e4c5fbd303e430900f724bd1b6136","abstract_canon_sha256":"8ef4e6fb6c012dfba7d3c83f2ab650a179653bd03b1c706f3f3e491ffd66cce1"},"schema_version":"1.0"},"canonical_sha256":"4fdc6fe61ceb3a61a3024525a79e11502415712e465b44743b3d62c273395488","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:34:41.429503Z","signature_b64":"+lt3pgkYf2UGcJcIEybh4Hhs+PVC92uaxIfcsNLJn1wY+IHBtYWAdOH1VctV2nIya+34P7lcymxIGYXrPTrSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fdc6fe61ceb3a61a3024525a79e11502415712e465b44743b3d62c273395488","last_reissued_at":"2026-07-05T10:34:41.428931Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:34:41.428931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.18436","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":"2026-07-05T10:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clvaBDZpxpvU5RJNzGpOR+8qc5IsOiGIDSBm5FQSvxY6HsqlIZ1hOGAqBkskIGcxiu7/6tjuE89YCvkBias/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:16:34.487767Z"},"content_sha256":"04003c841e6c8aa9808308cc8d0f79702a59e8f7d4187bf779007be64b085858","schema_version":"1.0","event_id":"sha256:04003c841e6c8aa9808308cc8d0f79702a59e8f7d4187bf779007be64b085858"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:J7OG7ZQ45M5GDIYCIUS2PHQRKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical features of quantum chaos using the Krylov operator complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Wei Fan, Zhuoran Li","submitted_at":"2024-11-27T15:20:24Z","abstract_excerpt":"We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average correlation matrix $\\langle x_{i} x_{j}\\rangle$ of Lanczos coefficients and the resulting distribution of the variance of Lanczos coefficients. Their resulting statistics are the Wishart distribution and the (rescaled) chi-square distribution respectively, which are independent of the distributions of initial operators and become the normal distribution in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18436","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.18436/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:34:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cozKxuQ5AA4QspTo2o+x8uIQK9ySbMUB5KJh0AH78OmgxS7vvsQ7YG+raUHWEq6XQeeewKLWSoFC9MeXF64rDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:16:34.488499Z"},"content_sha256":"9fd41f127c1b25769a50be973bb8b83551e04b28ff4d0ec57a57ae2260b2cf69","schema_version":"1.0","event_id":"sha256:9fd41f127c1b25769a50be973bb8b83551e04b28ff4d0ec57a57ae2260b2cf69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA/bundle.json","state_url":"https://pith.science/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA/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":"2026-08-12T20:16:34Z","links":{"resolver":"https://pith.science/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA","bundle":"https://pith.science/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA/bundle.json","state":"https://pith.science/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7OG7ZQ45M5GDIYCIUS2PHQRKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:J7OG7ZQ45M5GDIYCIUS2PHQRKA","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":"8ef4e6fb6c012dfba7d3c83f2ab650a179653bd03b1c706f3f3e491ffd66cce1","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-11-27T15:20:24Z","title_canon_sha256":"008db328f24477d293133ac6be981875b19e4c5fbd303e430900f724bd1b6136"},"schema_version":"1.0","source":{"id":"2411.18436","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18436","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18436v3","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18436","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"pith_short_12","alias_value":"J7OG7ZQ45M5G","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"pith_short_16","alias_value":"J7OG7ZQ45M5GDIYC","created_at":"2026-07-05T10:34:41Z"},{"alias_kind":"pith_short_8","alias_value":"J7OG7ZQ4","created_at":"2026-07-05T10:34:41Z"}],"graph_snapshots":[{"event_id":"sha256:9fd41f127c1b25769a50be973bb8b83551e04b28ff4d0ec57a57ae2260b2cf69","target":"graph","created_at":"2026-07-05T10:34:41Z","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/2411.18436/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average correlation matrix $\\langle x_{i} x_{j}\\rangle$ of Lanczos coefficients and the resulting distribution of the variance of Lanczos coefficients. Their resulting statistics are the Wishart distribution and the (rescaled) chi-square distribution respectively, which are independent of the distributions of initial operators and become the normal distribution in the ","authors_text":"Wei Fan, Zhuoran Li","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-11-27T15:20:24Z","title":"Statistical features of quantum chaos using the Krylov operator complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18436","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":"sha256:04003c841e6c8aa9808308cc8d0f79702a59e8f7d4187bf779007be64b085858","target":"record","created_at":"2026-07-05T10:34:41Z","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":"8ef4e6fb6c012dfba7d3c83f2ab650a179653bd03b1c706f3f3e491ffd66cce1","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-11-27T15:20:24Z","title_canon_sha256":"008db328f24477d293133ac6be981875b19e4c5fbd303e430900f724bd1b6136"},"schema_version":"1.0","source":{"id":"2411.18436","kind":"arxiv","version":3}},"canonical_sha256":"4fdc6fe61ceb3a61a3024525a79e11502415712e465b44743b3d62c273395488","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fdc6fe61ceb3a61a3024525a79e11502415712e465b44743b3d62c273395488","first_computed_at":"2026-07-05T10:34:41.428931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:34:41.428931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+lt3pgkYf2UGcJcIEybh4Hhs+PVC92uaxIfcsNLJn1wY+IHBtYWAdOH1VctV2nIya+34P7lcymxIGYXrPTrSCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:34:41.429503Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18436","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04003c841e6c8aa9808308cc8d0f79702a59e8f7d4187bf779007be64b085858","sha256:9fd41f127c1b25769a50be973bb8b83551e04b28ff4d0ec57a57ae2260b2cf69"],"state_sha256":"b88621bfc741bfafeffb5765344989a524fd6991572014442d364199306328f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uRzEM7TEonWg3Ffq4MGeWG3xfN4TnFmk0xQBlQ/A4MN3Q3tokHHacG60UqdlBByjh3sFk/fZSex+gpM9lhrRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T20:16:34.501334Z","bundle_sha256":"5c0d64e6d8298a8886a3a592f99e7c73dc8d7e21ee953f0b8b0dcf59042e407c"}}