{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6Z4A4PEXRDPN3TRL6PUVXDOWF5","short_pith_number":"pith:6Z4A4PEX","canonical_record":{"source":{"id":"1205.1625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-08T08:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"c6bb03cbfe96fa97bce93702b9182bd8013f639012e39de93f0d62ecb52d78d9","abstract_canon_sha256":"13614ae3fe72f91b2b2841286620196d64ed2ea3a11227d415d3a4d0ee9bebd8"},"schema_version":"1.0"},"canonical_sha256":"f6780e3c9788deddce2bf3e95b8dd62f525f5b213611a0fd8ec726a03fe284c7","source":{"kind":"arxiv","id":"1205.1625","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1625","created_at":"2026-05-18T03:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1625v2","created_at":"2026-05-18T03:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1625","created_at":"2026-05-18T03:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"6Z4A4PEXRDPN","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6Z4A4PEXRDPN3TRL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6Z4A4PEX","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6Z4A4PEXRDPN3TRL6PUVXDOWF5","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-08T08:14:17Z","cross_cats_sorted":[],"title_canon_sha256":"c6bb03cbfe96fa97bce93702b9182bd8013f639012e39de93f0d62ecb52d78d9","abstract_canon_sha256":"13614ae3fe72f91b2b2841286620196d64ed2ea3a11227d415d3a4d0ee9bebd8"},"schema_version":"1.0"},"canonical_sha256":"f6780e3c9788deddce2bf3e95b8dd62f525f5b213611a0fd8ec726a03fe284c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:41.455404Z","signature_b64":"0vZW5gjiCHw0HTTniV+nX+ecMji7CgFo53TCQ3MDlalo9Rf8n+dVrbF6J6vll8a/ZQbQjGeq+YxWwuXvgGkxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6780e3c9788deddce2bf3e95b8dd62f525f5b213611a0fd8ec726a03fe284c7","last_reissued_at":"2026-05-18T03:22:41.454666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:41.454666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1625","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":"2026-05-18T03:22:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2TLPWEJ6vKKwibeZdgI2No5gX7WYbZoYb7VPgBTlUT5qTpXFhb+OcaxAkqN104+Zg2Pr/T0hsg6/5c4NKR1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T16:54:49.035739Z"},"content_sha256":"0ffcbf4a9507fbca53b05c4ae5544c1110410f3e28b922bbd005104678cde67f","schema_version":"1.0","event_id":"sha256:0ffcbf4a9507fbca53b05c4ae5544c1110410f3e28b922bbd005104678cde67f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6Z4A4PEXRDPN3TRL6PUVXDOWF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New spectral relations between products and powers of isotropic random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Swiech, M.A. Nowak, Z. Burda","submitted_at":"2012-05-08T08:14:17Z","abstract_excerpt":"We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble (IUE) is equal to the eigenvalue density of n-th power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation one can derive the limiting density of the product of n independent identically distributed non-hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices. We also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1625","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":"2026-05-18T03:22:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/ooufzmbLCQf83gLyHdYsGJ2JOiO/yeKS3pt33nNxq2NLEDoOjKwwibhLJ80zHrq8mle3XAxguyuyQoIbU5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T16:54:49.036079Z"},"content_sha256":"937ecfe879b863c5fcc434f123bc3593b553e3e955fa811954a470ddc2bc7471","schema_version":"1.0","event_id":"sha256:937ecfe879b863c5fcc434f123bc3593b553e3e955fa811954a470ddc2bc7471"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5/bundle.json","state_url":"https://pith.science/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5/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":"2026-06-04T16:54:49Z","links":{"resolver":"https://pith.science/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5","bundle":"https://pith.science/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5/bundle.json","state":"https://pith.science/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Z4A4PEXRDPN3TRL6PUVXDOWF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6Z4A4PEXRDPN3TRL6PUVXDOWF5","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":"13614ae3fe72f91b2b2841286620196d64ed2ea3a11227d415d3a4d0ee9bebd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-08T08:14:17Z","title_canon_sha256":"c6bb03cbfe96fa97bce93702b9182bd8013f639012e39de93f0d62ecb52d78d9"},"schema_version":"1.0","source":{"id":"1205.1625","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1625","created_at":"2026-05-18T03:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1625v2","created_at":"2026-05-18T03:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1625","created_at":"2026-05-18T03:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"6Z4A4PEXRDPN","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6Z4A4PEXRDPN3TRL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6Z4A4PEX","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:937ecfe879b863c5fcc434f123bc3593b553e3e955fa811954a470ddc2bc7471","target":"graph","created_at":"2026-05-18T03:22:41Z","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"},"paper":{"abstract_excerpt":"We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble (IUE) is equal to the eigenvalue density of n-th power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation one can derive the limiting density of the product of n independent identically distributed non-hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices. We also","authors_text":"A. Swiech, M.A. Nowak, Z. Burda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-08T08:14:17Z","title":"New spectral relations between products and powers of isotropic random matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1625","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":"sha256:0ffcbf4a9507fbca53b05c4ae5544c1110410f3e28b922bbd005104678cde67f","target":"record","created_at":"2026-05-18T03:22:41Z","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":"13614ae3fe72f91b2b2841286620196d64ed2ea3a11227d415d3a4d0ee9bebd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-05-08T08:14:17Z","title_canon_sha256":"c6bb03cbfe96fa97bce93702b9182bd8013f639012e39de93f0d62ecb52d78d9"},"schema_version":"1.0","source":{"id":"1205.1625","kind":"arxiv","version":2}},"canonical_sha256":"f6780e3c9788deddce2bf3e95b8dd62f525f5b213611a0fd8ec726a03fe284c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6780e3c9788deddce2bf3e95b8dd62f525f5b213611a0fd8ec726a03fe284c7","first_computed_at":"2026-05-18T03:22:41.454666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:41.454666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0vZW5gjiCHw0HTTniV+nX+ecMji7CgFo53TCQ3MDlalo9Rf8n+dVrbF6J6vll8a/ZQbQjGeq+YxWwuXvgGkxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:41.455404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1625","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ffcbf4a9507fbca53b05c4ae5544c1110410f3e28b922bbd005104678cde67f","sha256:937ecfe879b863c5fcc434f123bc3593b553e3e955fa811954a470ddc2bc7471"],"state_sha256":"63e964d83f07333de193560ea8a8e303d562e669b84883084c99b3bbf591c48d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSQHVFFKLwSHWibMWV/Iv896VfY6FWUYpg2pW9Y1zSqfYLHheIw4CMDhJ78lPipBAlm/CuAlK4zBUhSV+4eKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T16:54:49.038021Z","bundle_sha256":"e0b1571745c18cf82383dff522f124b5fccc698625e8af264622b6f54b1df08f"}}