{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7XRGAJQZWS6ZKQENGNTST4DBQM","short_pith_number":"pith:7XRGAJQZ","canonical_record":{"source":{"id":"2504.14362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-19T17:38:11Z","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"title_canon_sha256":"3f9805ea907b5936c2d688012ebf51fb05b794e0c117b1295dcf5248274d11df","abstract_canon_sha256":"82a28ba9d889f6f721498d94802198ce8b5ea653ba378f45d3ae4df12d283f74"},"schema_version":"1.0"},"canonical_sha256":"fde2602619b4bd95408d336729f0618337b7d98cc4db419cba118dd7f78d0c5a","source":{"kind":"arxiv","id":"2504.14362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14362","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14362v2","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14362","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"7XRGAJQZWS6Z","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"pith_short_16","alias_value":"7XRGAJQZWS6ZKQEN","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"pith_short_8","alias_value":"7XRGAJQZ","created_at":"2026-07-05T10:53:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7XRGAJQZWS6ZKQENGNTST4DBQM","target":"record","payload":{"canonical_record":{"source":{"id":"2504.14362","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-19T17:38:11Z","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"title_canon_sha256":"3f9805ea907b5936c2d688012ebf51fb05b794e0c117b1295dcf5248274d11df","abstract_canon_sha256":"82a28ba9d889f6f721498d94802198ce8b5ea653ba378f45d3ae4df12d283f74"},"schema_version":"1.0"},"canonical_sha256":"fde2602619b4bd95408d336729f0618337b7d98cc4db419cba118dd7f78d0c5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:53:54.332063Z","signature_b64":"oQFVUIezoy7xg+nIPOHI44pVqjtd1lXVPhgW2+7s3payt3ow7NaVaAT8OSd9bTt1aTkbqNjponbyJE8EZeTPBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fde2602619b4bd95408d336729f0618337b7d98cc4db419cba118dd7f78d0c5a","last_reissued_at":"2026-07-05T10:53:54.331520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:53:54.331520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.14362","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":"2026-07-05T10:53:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gs2IGitL7C6IHokzlZro+8LB8Y1DdRAAfcHKNIhnTcj9oO3eXjBYZ2aINfbbfkP48XqKO5x/GYOiRmtTbtwsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:14:27.185648Z"},"content_sha256":"820c23141f768fbb6e91ec2f18693ed909cfc5d655d76ff229c255837bff1350","schema_version":"1.0","event_id":"sha256:820c23141f768fbb6e91ec2f18693ed909cfc5d655d76ff229c255837bff1350"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7XRGAJQZWS6ZKQENGNTST4DBQM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Average Spread Complexity and the Higher-Order Level Spacing","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"hep-th","authors_text":"Amin Faraji Astaneh, Niloofar Vardian","submitted_at":"2025-04-19T17:38:11Z","abstract_excerpt":"We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level spacing, we observe the characteristic slope-dip-ramp-plateau structure. Further investigation reveals that certain matrix models exhibit additional iterative peaks, motivating us to generalize the known spacing distributions to higher-order level spacings. While this structure persists in chaotic systems, we find that integrable systems can also display similar fe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14362","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/2504.14362/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":"2026-07-05T10:53:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFSr6ke9AqOYg2qiFsJWKguvGxopKBQxpFXXxftCT8yfK7kx+TLBpOsA/06yy8VSYA+FwG/r6D0yaydLe/lrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:14:27.186641Z"},"content_sha256":"1455587ad43223291a3b52bf168823378092f4b6629a5b80f9ffb415f3b7d474","schema_version":"1.0","event_id":"sha256:1455587ad43223291a3b52bf168823378092f4b6629a5b80f9ffb415f3b7d474"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XRGAJQZWS6ZKQENGNTST4DBQM/bundle.json","state_url":"https://pith.science/pith/7XRGAJQZWS6ZKQENGNTST4DBQM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XRGAJQZWS6ZKQENGNTST4DBQM/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":"2026-08-03T23:14:27Z","links":{"resolver":"https://pith.science/pith/7XRGAJQZWS6ZKQENGNTST4DBQM","bundle":"https://pith.science/pith/7XRGAJQZWS6ZKQENGNTST4DBQM/bundle.json","state":"https://pith.science/pith/7XRGAJQZWS6ZKQENGNTST4DBQM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XRGAJQZWS6ZKQENGNTST4DBQM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7XRGAJQZWS6ZKQENGNTST4DBQM","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":"82a28ba9d889f6f721498d94802198ce8b5ea653ba378f45d3ae4df12d283f74","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-19T17:38:11Z","title_canon_sha256":"3f9805ea907b5936c2d688012ebf51fb05b794e0c117b1295dcf5248274d11df"},"schema_version":"1.0","source":{"id":"2504.14362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.14362","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"2504.14362v2","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.14362","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"7XRGAJQZWS6Z","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"pith_short_16","alias_value":"7XRGAJQZWS6ZKQEN","created_at":"2026-07-05T10:53:54Z"},{"alias_kind":"pith_short_8","alias_value":"7XRGAJQZ","created_at":"2026-07-05T10:53:54Z"}],"graph_snapshots":[{"event_id":"sha256:1455587ad43223291a3b52bf168823378092f4b6629a5b80f9ffb415f3b7d474","target":"graph","created_at":"2026-07-05T10:53:54Z","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/2504.14362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level spacing, we observe the characteristic slope-dip-ramp-plateau structure. Further investigation reveals that certain matrix models exhibit additional iterative peaks, motivating us to generalize the known spacing distributions to higher-order level spacings. While this structure persists in chaotic systems, we find that integrable systems can also display similar fe","authors_text":"Amin Faraji Astaneh, Niloofar Vardian","cross_cats":["cond-mat.stat-mech","quant-ph"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-19T17:38:11Z","title":"Average Spread Complexity and the Higher-Order Level Spacing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14362","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":"sha256:820c23141f768fbb6e91ec2f18693ed909cfc5d655d76ff229c255837bff1350","target":"record","created_at":"2026-07-05T10:53:54Z","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":"82a28ba9d889f6f721498d94802198ce8b5ea653ba378f45d3ae4df12d283f74","cross_cats_sorted":["cond-mat.stat-mech","quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"hep-th","submitted_at":"2025-04-19T17:38:11Z","title_canon_sha256":"3f9805ea907b5936c2d688012ebf51fb05b794e0c117b1295dcf5248274d11df"},"schema_version":"1.0","source":{"id":"2504.14362","kind":"arxiv","version":2}},"canonical_sha256":"fde2602619b4bd95408d336729f0618337b7d98cc4db419cba118dd7f78d0c5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fde2602619b4bd95408d336729f0618337b7d98cc4db419cba118dd7f78d0c5a","first_computed_at":"2026-07-05T10:53:54.331520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:53:54.331520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oQFVUIezoy7xg+nIPOHI44pVqjtd1lXVPhgW2+7s3payt3ow7NaVaAT8OSd9bTt1aTkbqNjponbyJE8EZeTPBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:53:54.332063Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.14362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:820c23141f768fbb6e91ec2f18693ed909cfc5d655d76ff229c255837bff1350","sha256:1455587ad43223291a3b52bf168823378092f4b6629a5b80f9ffb415f3b7d474"],"state_sha256":"745ac252bfe18f7d6638ed1ebc3b548f2bf10298a0a2a7ef90689332f1fec292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvMICErrw9HfRFT9stgB5cDgVDIzrhO6J/zWiROAhdIPGIBkUhNc/BmYUcpLa/dpqXVXY2nkQdFAAzJaAnnMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T23:14:27.192771Z","bundle_sha256":"8b4cfb10a71bff03d489ec6cc65bc0e6f3f994a45901da1cf7051f9fbb32a701"}}