{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XJVEKLMVYMGDO4YXHNFRXMSGTZ","short_pith_number":"pith:XJVEKLMV","canonical_record":{"source":{"id":"1412.3003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-09T15:56:17Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"95dd21198d272ea75c7c8a27329905c3b572d913a8bf7bc959f47e5abba0d4c0","abstract_canon_sha256":"4fcc3614cbf2f88d787aa7aeea814088f72dce528e24ddbb58a2e938ee698447"},"schema_version":"1.0"},"canonical_sha256":"ba6a452d95c30c3773173b4b1bb2469e512573be7e1418518be0aa4f506a6f3a","source":{"kind":"arxiv","id":"1412.3003","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3003","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3003v2","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3003","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"XJVEKLMVYMGD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XJVEKLMVYMGDO4YX","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XJVEKLMV","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XJVEKLMVYMGDO4YXHNFRXMSGTZ","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3003","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-09T15:56:17Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"95dd21198d272ea75c7c8a27329905c3b572d913a8bf7bc959f47e5abba0d4c0","abstract_canon_sha256":"4fcc3614cbf2f88d787aa7aeea814088f72dce528e24ddbb58a2e938ee698447"},"schema_version":"1.0"},"canonical_sha256":"ba6a452d95c30c3773173b4b1bb2469e512573be7e1418518be0aa4f506a6f3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:20.404736Z","signature_b64":"gSLo5Y7VDa8ypW1yOvYbumA7c2l0jnURk7PYYeCPmluOUwSv1jdqmEDPKCvNGcM7HmWKKg7iEKHIfPR6WfB9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba6a452d95c30c3773173b4b1bb2469e512573be7e1418518be0aa4f506a6f3a","last_reissued_at":"2026-05-18T01:41:20.404184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:20.404184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3003","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":"2026-05-18T01:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2l9vqUuuXZp9Nh9hHvrZsqE8iBZxtnhNWHXvgOytxbthQ/qXlnXxnjkU1SZ+5RG8mbVkftcPZOdADZ47BxpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:40:08.696680Z"},"content_sha256":"7a99ce3ff87bc97fcb45daf23ac607fc87e8516ee1609d5210e043091d6eb137","schema_version":"1.0","event_id":"sha256:7a99ce3ff87bc97fcb45daf23ac607fc87e8516ee1609d5210e043091d6eb137"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XJVEKLMVYMGDO4YXHNFRXMSGTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J. R. Ipsen","submitted_at":"2014-12-09T15:56:17Z","abstract_excerpt":"We study the joint density of eigenvalues for products of independent rectangular real, complex and quaternionic Ginibre matrices. In the limit where the number of matrices tends to infinity, it is shown that the joint probability density function for the eigenvalues forms a permanental point process for all three classes. The moduli of the eigenvalues become uncorrelated and log-normal distributed, while the distribution for the phases of the eigenvalues depends on whether real, complex or quaternionic Ginibre matrices are considered. In the derivation for a product of real matrices, we expli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3003","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":""},"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":"2026-05-18T01:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Aee2a/1OwDwZ5mywXrSQWKPejUGso5L2o3QrfWY0f27ndObekfkCeTO8EH5MLipFAhZfrLLkglISncSZbGjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:40:08.697494Z"},"content_sha256":"b7cac3845b1c1f1e288e14a76e1870c2969907f629eb93b11a3ea170c6a4c7cc","schema_version":"1.0","event_id":"sha256:b7cac3845b1c1f1e288e14a76e1870c2969907f629eb93b11a3ea170c6a4c7cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ/bundle.json","state_url":"https://pith.science/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ/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":"2026-06-10T05:40:08Z","links":{"resolver":"https://pith.science/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ","bundle":"https://pith.science/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ/bundle.json","state":"https://pith.science/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJVEKLMVYMGDO4YXHNFRXMSGTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XJVEKLMVYMGDO4YXHNFRXMSGTZ","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":"4fcc3614cbf2f88d787aa7aeea814088f72dce528e24ddbb58a2e938ee698447","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-09T15:56:17Z","title_canon_sha256":"95dd21198d272ea75c7c8a27329905c3b572d913a8bf7bc959f47e5abba0d4c0"},"schema_version":"1.0","source":{"id":"1412.3003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3003","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3003v2","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3003","created_at":"2026-05-18T01:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"XJVEKLMVYMGD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XJVEKLMVYMGDO4YX","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XJVEKLMV","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:b7cac3845b1c1f1e288e14a76e1870c2969907f629eb93b11a3ea170c6a4c7cc","target":"graph","created_at":"2026-05-18T01:41:20Z","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 study the joint density of eigenvalues for products of independent rectangular real, complex and quaternionic Ginibre matrices. In the limit where the number of matrices tends to infinity, it is shown that the joint probability density function for the eigenvalues forms a permanental point process for all three classes. The moduli of the eigenvalues become uncorrelated and log-normal distributed, while the distribution for the phases of the eigenvalues depends on whether real, complex or quaternionic Ginibre matrices are considered. In the derivation for a product of real matrices, we expli","authors_text":"J. R. Ipsen","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-09T15:56:17Z","title":"Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3003","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":"sha256:7a99ce3ff87bc97fcb45daf23ac607fc87e8516ee1609d5210e043091d6eb137","target":"record","created_at":"2026-05-18T01:41:20Z","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":"4fcc3614cbf2f88d787aa7aeea814088f72dce528e24ddbb58a2e938ee698447","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-09T15:56:17Z","title_canon_sha256":"95dd21198d272ea75c7c8a27329905c3b572d913a8bf7bc959f47e5abba0d4c0"},"schema_version":"1.0","source":{"id":"1412.3003","kind":"arxiv","version":2}},"canonical_sha256":"ba6a452d95c30c3773173b4b1bb2469e512573be7e1418518be0aa4f506a6f3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba6a452d95c30c3773173b4b1bb2469e512573be7e1418518be0aa4f506a6f3a","first_computed_at":"2026-05-18T01:41:20.404184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:20.404184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSLo5Y7VDa8ypW1yOvYbumA7c2l0jnURk7PYYeCPmluOUwSv1jdqmEDPKCvNGcM7HmWKKg7iEKHIfPR6WfB9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:20.404736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a99ce3ff87bc97fcb45daf23ac607fc87e8516ee1609d5210e043091d6eb137","sha256:b7cac3845b1c1f1e288e14a76e1870c2969907f629eb93b11a3ea170c6a4c7cc"],"state_sha256":"d09ba9ded6500f98e8213b301c172e6699596f6c2f375455b31a8d616bf4d2fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YrykkkvERYDfEI+vg4AkaxsWjQMIR7R+lg7I9bBPgRIRAkT5uiHZBL3uvBhz37d/NFJZ01woT5ZHJ5x1apaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:40:08.701543Z","bundle_sha256":"5d9319fd4f3cc337f3a3533a41b30f576959a6f6a414cb080b7e18afbbeafe36"}}