{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5TZ273PXXWUMPFLLV2DQPIF63R","short_pith_number":"pith:5TZ273PX","canonical_record":{"source":{"id":"1112.0173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-01T13:26:51Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"ce9cbdee5f6f30b263927a351aea320ee87ab6732e30164bae2b524dcbc5e8e6","abstract_canon_sha256":"fc77b70520c59b0d7c7e88aa1600519eb002b5d937e4f8c75f8baee82fbe89d4"},"schema_version":"1.0"},"canonical_sha256":"ecf3afedf7bda8c7956bae8707a0bedc6119ef2ddf24635dff0123dadda7adb6","source":{"kind":"arxiv","id":"1112.0173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0173","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0173v1","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0173","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"5TZ273PXXWUM","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5TZ273PXXWUMPFLL","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5TZ273PX","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5TZ273PXXWUMPFLLV2DQPIF63R","target":"record","payload":{"canonical_record":{"source":{"id":"1112.0173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-01T13:26:51Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"ce9cbdee5f6f30b263927a351aea320ee87ab6732e30164bae2b524dcbc5e8e6","abstract_canon_sha256":"fc77b70520c59b0d7c7e88aa1600519eb002b5d937e4f8c75f8baee82fbe89d4"},"schema_version":"1.0"},"canonical_sha256":"ecf3afedf7bda8c7956bae8707a0bedc6119ef2ddf24635dff0123dadda7adb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:06.312260Z","signature_b64":"P17wQD1KIEV6U35KpD8dIP1psAeEc7keKwNuYRRd5zMrqB8g7Ny+dI/38wSIuIqJTT9UPSXQu2EsNuRJVDLACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecf3afedf7bda8c7956bae8707a0bedc6119ef2ddf24635dff0123dadda7adb6","last_reissued_at":"2026-05-18T04:07:06.311816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:06.311816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.0173","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INRzSTKangpi8AYGvw7fDAJ7c+4sFvFns8OO1I2IzcYFvGpVjcm0sE5qcDqKY64kZpDgflPdhccrqePY0qNtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:09:34.181549Z"},"content_sha256":"79459b2a5e82768e97f30549e3ecda68814f0fe07fe6d5811efc135b7e67c7a4","schema_version":"1.0","event_id":"sha256:79459b2a5e82768e97f30549e3ecda68814f0fe07fe6d5811efc135b7e67c7a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5TZ273PXXWUMPFLLV2DQPIF63R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random matrix theory for mixed regular-chaotic dynamics in the super-extensive regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"A. Abd El-Hady, A. Y. Abul-Magd","submitted_at":"2011-12-01T13:26:51Z","abstract_excerpt":"We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical expressions for the level-spacing distributions, which are strictly valid for 2 \\times 2 random-matrix ensembles, as usually done in the standard RMT. We compare the results with spacing distributions, numerically calculated for random matrix ensembles describing a harmonic oscillator perturbed by Gaussian orthogonal and unitary ensembles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0173","kind":"arxiv","version":1},"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":"2026-05-18T04:07:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4stPlqGrDtZyGwAOlzD+nj9PmdDkrZha5kIIM1SQPZDA6izOD14vwzRJzyJHBf8iu8lvw8NZEmaCgSS0nAJcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:09:34.182202Z"},"content_sha256":"984b6f9a250defa376f1d14cab474972c818894e4f039fddfb6443e8195b89a3","schema_version":"1.0","event_id":"sha256:984b6f9a250defa376f1d14cab474972c818894e4f039fddfb6443e8195b89a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TZ273PXXWUMPFLLV2DQPIF63R/bundle.json","state_url":"https://pith.science/pith/5TZ273PXXWUMPFLLV2DQPIF63R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TZ273PXXWUMPFLLV2DQPIF63R/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":"2026-06-12T00:09:34Z","links":{"resolver":"https://pith.science/pith/5TZ273PXXWUMPFLLV2DQPIF63R","bundle":"https://pith.science/pith/5TZ273PXXWUMPFLLV2DQPIF63R/bundle.json","state":"https://pith.science/pith/5TZ273PXXWUMPFLLV2DQPIF63R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TZ273PXXWUMPFLLV2DQPIF63R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5TZ273PXXWUMPFLLV2DQPIF63R","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":"fc77b70520c59b0d7c7e88aa1600519eb002b5d937e4f8c75f8baee82fbe89d4","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-01T13:26:51Z","title_canon_sha256":"ce9cbdee5f6f30b263927a351aea320ee87ab6732e30164bae2b524dcbc5e8e6"},"schema_version":"1.0","source":{"id":"1112.0173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0173","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0173v1","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0173","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"5TZ273PXXWUM","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5TZ273PXXWUMPFLL","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5TZ273PX","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:984b6f9a250defa376f1d14cab474972c818894e4f039fddfb6443e8195b89a3","target":"graph","created_at":"2026-05-18T04:07:06Z","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 apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical expressions for the level-spacing distributions, which are strictly valid for 2 \\times 2 random-matrix ensembles, as usually done in the standard RMT. We compare the results with spacing distributions, numerically calculated for random matrix ensembles describing a harmonic oscillator perturbed by Gaussian orthogonal and unitary ensembles.","authors_text":"A. Abd El-Hady, A. Y. Abul-Magd","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-01T13:26:51Z","title":"Random matrix theory for mixed regular-chaotic dynamics in the super-extensive regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0173","kind":"arxiv","version":1},"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":"sha256:79459b2a5e82768e97f30549e3ecda68814f0fe07fe6d5811efc135b7e67c7a4","target":"record","created_at":"2026-05-18T04:07:06Z","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":"fc77b70520c59b0d7c7e88aa1600519eb002b5d937e4f8c75f8baee82fbe89d4","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-01T13:26:51Z","title_canon_sha256":"ce9cbdee5f6f30b263927a351aea320ee87ab6732e30164bae2b524dcbc5e8e6"},"schema_version":"1.0","source":{"id":"1112.0173","kind":"arxiv","version":1}},"canonical_sha256":"ecf3afedf7bda8c7956bae8707a0bedc6119ef2ddf24635dff0123dadda7adb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecf3afedf7bda8c7956bae8707a0bedc6119ef2ddf24635dff0123dadda7adb6","first_computed_at":"2026-05-18T04:07:06.311816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:06.311816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P17wQD1KIEV6U35KpD8dIP1psAeEc7keKwNuYRRd5zMrqB8g7Ny+dI/38wSIuIqJTT9UPSXQu2EsNuRJVDLACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:06.312260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79459b2a5e82768e97f30549e3ecda68814f0fe07fe6d5811efc135b7e67c7a4","sha256:984b6f9a250defa376f1d14cab474972c818894e4f039fddfb6443e8195b89a3"],"state_sha256":"a47c6774d1f90567b4139dfa58e99d33a949875d79d1961a4170d77838f5d42f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zA8Ux1o0ZYwWq34vXehQrbTw0Ci5c2iEucS+VKVnYP9nS/SYR8yfLANzEEUS7AUMviScgJWtTT1P3m5ZY91TBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:09:34.185698Z","bundle_sha256":"00c7b325d1fb1446d385390202e0f3e2cdc29a38c9910a78aca80489313fc892"}}