{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:IMGDTYFPYOK2QTX4TID3LBUCFC","short_pith_number":"pith:IMGDTYFP","canonical_record":{"source":{"id":"2401.02119","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-01-04T07:58:47Z","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"title_canon_sha256":"449c1696885e2ebada23b55e5f89c7c1787a31fbeb16555dbe2271963c8bc835","abstract_canon_sha256":"d100434a1dbdd6be618b42342afc91fbddb72bd64702438cd77f48a41c5e4cec"},"schema_version":"1.0"},"canonical_sha256":"430c39e0afc395a84efc9a07b5868228848a6833d4cea0f9cd1358b4c8cd017b","source":{"kind":"arxiv","id":"2401.02119","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.02119","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"2401.02119v2","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.02119","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"IMGDTYFPYOK2","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"pith_short_16","alias_value":"IMGDTYFPYOK2QTX4","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"pith_short_8","alias_value":"IMGDTYFP","created_at":"2026-07-05T07:33:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:IMGDTYFPYOK2QTX4TID3LBUCFC","target":"record","payload":{"canonical_record":{"source":{"id":"2401.02119","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-01-04T07:58:47Z","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"title_canon_sha256":"449c1696885e2ebada23b55e5f89c7c1787a31fbeb16555dbe2271963c8bc835","abstract_canon_sha256":"d100434a1dbdd6be618b42342afc91fbddb72bd64702438cd77f48a41c5e4cec"},"schema_version":"1.0"},"canonical_sha256":"430c39e0afc395a84efc9a07b5868228848a6833d4cea0f9cd1358b4c8cd017b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:33:25.277182Z","signature_b64":"WFDeLPczKxtBD1bsDuXu0Yo/pqyy9hteEWWhenUMpFVx0lLHaOG81kqQIarRDqhDpCGXmiQKChnSI5FvtgRMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"430c39e0afc395a84efc9a07b5868228848a6833d4cea0f9cd1358b4c8cd017b","last_reissued_at":"2026-07-05T07:33:25.276648Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:33:25.276648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.02119","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":"2026-07-05T07:33:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wOZXuKK8Lbm19eqOqTdLm+U5ysuaweSdj52fT95ZUqqpQg71YdFFaJXkIkZGLzZO1Fm4sd5stsj8IRioAOvpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:01:28.224658Z"},"content_sha256":"8137aed0dbed21329620a1d7dcb194f7f51d8ee8ccc783e99c6f5f2d561e17a0","schema_version":"1.0","event_id":"sha256:8137aed0dbed21329620a1d7dcb194f7f51d8ee8ccc783e99c6f5f2d561e17a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:IMGDTYFPYOK2QTX4TID3LBUCFC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Spectral Form Factor in Random Matrix Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.quant-gas","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Chengming Tan, Ren Zhang, Zhiyang Wei","submitted_at":"2024-01-04T07:58:47Z","abstract_excerpt":"The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The definition of SFF in most literature only encapsulates the two-level correlation. In this manuscript, we extend the definition of SSF to include the high-order correlation. Specifically, we introduce the standard deviation of energy levels to define correlation functions, from which the generalized spectral form factor (GSFF) can be obtained by Fourier transf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.02119","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.02119/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":"2026-07-05T07:33:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdRvoPpUtxdYAUkaahBsUrAM5sCnGvuyaZWCsR8SOvZBvJhtK/M42IG05L7ZX71YGzc5fWSa4WkTuCft9ewdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T07:01:28.225203Z"},"content_sha256":"83dd737b142462cedbc72c1b69500a9c4ac5e34e921b1ed8e7350f11fe14589a","schema_version":"1.0","event_id":"sha256:83dd737b142462cedbc72c1b69500a9c4ac5e34e921b1ed8e7350f11fe14589a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IMGDTYFPYOK2QTX4TID3LBUCFC/bundle.json","state_url":"https://pith.science/pith/IMGDTYFPYOK2QTX4TID3LBUCFC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IMGDTYFPYOK2QTX4TID3LBUCFC/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":"2026-08-05T07:01:28Z","links":{"resolver":"https://pith.science/pith/IMGDTYFPYOK2QTX4TID3LBUCFC","bundle":"https://pith.science/pith/IMGDTYFPYOK2QTX4TID3LBUCFC/bundle.json","state":"https://pith.science/pith/IMGDTYFPYOK2QTX4TID3LBUCFC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IMGDTYFPYOK2QTX4TID3LBUCFC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:IMGDTYFPYOK2QTX4TID3LBUCFC","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":"d100434a1dbdd6be618b42342afc91fbddb72bd64702438cd77f48a41c5e4cec","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-01-04T07:58:47Z","title_canon_sha256":"449c1696885e2ebada23b55e5f89c7c1787a31fbeb16555dbe2271963c8bc835"},"schema_version":"1.0","source":{"id":"2401.02119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.02119","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"2401.02119v2","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.02119","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"IMGDTYFPYOK2","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"pith_short_16","alias_value":"IMGDTYFPYOK2QTX4","created_at":"2026-07-05T07:33:25Z"},{"alias_kind":"pith_short_8","alias_value":"IMGDTYFP","created_at":"2026-07-05T07:33:25Z"}],"graph_snapshots":[{"event_id":"sha256:83dd737b142462cedbc72c1b69500a9c4ac5e34e921b1ed8e7350f11fe14589a","target":"graph","created_at":"2026-07-05T07:33:25Z","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/2401.02119/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The definition of SFF in most literature only encapsulates the two-level correlation. In this manuscript, we extend the definition of SSF to include the high-order correlation. Specifically, we introduce the standard deviation of energy levels to define correlation functions, from which the generalized spectral form factor (GSFF) can be obtained by Fourier transf","authors_text":"Chengming Tan, Ren Zhang, Zhiyang Wei","cross_cats":["cond-mat.quant-gas","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-01-04T07:58:47Z","title":"Generalized Spectral Form Factor in Random Matrix Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.02119","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":"sha256:8137aed0dbed21329620a1d7dcb194f7f51d8ee8ccc783e99c6f5f2d561e17a0","target":"record","created_at":"2026-07-05T07:33:25Z","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":"d100434a1dbdd6be618b42342afc91fbddb72bd64702438cd77f48a41c5e4cec","cross_cats_sorted":["cond-mat.quant-gas","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2024-01-04T07:58:47Z","title_canon_sha256":"449c1696885e2ebada23b55e5f89c7c1787a31fbeb16555dbe2271963c8bc835"},"schema_version":"1.0","source":{"id":"2401.02119","kind":"arxiv","version":2}},"canonical_sha256":"430c39e0afc395a84efc9a07b5868228848a6833d4cea0f9cd1358b4c8cd017b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"430c39e0afc395a84efc9a07b5868228848a6833d4cea0f9cd1358b4c8cd017b","first_computed_at":"2026-07-05T07:33:25.276648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:33:25.276648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFDeLPczKxtBD1bsDuXu0Yo/pqyy9hteEWWhenUMpFVx0lLHaOG81kqQIarRDqhDpCGXmiQKChnSI5FvtgRMCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:33:25.277182Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.02119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8137aed0dbed21329620a1d7dcb194f7f51d8ee8ccc783e99c6f5f2d561e17a0","sha256:83dd737b142462cedbc72c1b69500a9c4ac5e34e921b1ed8e7350f11fe14589a"],"state_sha256":"2af5c79d363ebe5712d1cf70f237ec4924006ce41e546023f25502a0194447fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+CWIUZ2LuavIb8bhYN21ctV6DeVrgeY8DnhfA/W0pOEf5+Y+Hr6WAK2If5ReAzKg+9xADlg8+Wjmva8dzOLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T07:01:28.230529Z","bundle_sha256":"d7a9930b0c114484ca91727ed7e3f97f7534ad381aa444de3e6cd1b2cea587ed"}}