{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BFQMLEQGPQXLWSSLSIGUHKJVBO","short_pith_number":"pith:BFQMLEQG","canonical_record":{"source":{"id":"1311.3585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T17:23:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"02d0008286311698e4baa5f7a518dbf165bb7c698735b815cc62dbf6d8b29f3f","abstract_canon_sha256":"0e13498d81ea7abeeef442eb6796246be30efe927bea6a974e059f3434a354e5"},"schema_version":"1.0"},"canonical_sha256":"0960c592067c2ebb4a4b920d43a9350baa4cfca9c488c6ed65f8b3ba74ef2aaa","source":{"kind":"arxiv","id":"1311.3585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3585","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3585v1","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3585","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"BFQMLEQGPQXL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BFQMLEQGPQXLWSSL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BFQMLEQG","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BFQMLEQGPQXLWSSLSIGUHKJVBO","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T17:23:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"02d0008286311698e4baa5f7a518dbf165bb7c698735b815cc62dbf6d8b29f3f","abstract_canon_sha256":"0e13498d81ea7abeeef442eb6796246be30efe927bea6a974e059f3434a354e5"},"schema_version":"1.0"},"canonical_sha256":"0960c592067c2ebb4a4b920d43a9350baa4cfca9c488c6ed65f8b3ba74ef2aaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:31.628825Z","signature_b64":"YXC1tWOXHssq+kW/c3PihzI9Gn15XavqP/nTgPbA+up2TWAlQbYXFFE/CftDMfvZvaJ+SOHRpGGQKJo/hDENBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0960c592067c2ebb4a4b920d43a9350baa4cfca9c488c6ed65f8b3ba74ef2aaa","last_reissued_at":"2026-05-18T03:03:31.628256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:31.628256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3585","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":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jXFR38AnooyxScQRyfJulvuMaTBmy6Q5ZN+8l4K+TsUUIKpbUCz8qvqL1kXCrZ1fmC4M4318K7B6NH12RHPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:13:59.599954Z"},"content_sha256":"ca164ab1298ea0b674df307bb9841dc577b5d9e7011f237b6b1f4711a96a9cb3","schema_version":"1.0","event_id":"sha256:ca164ab1298ea0b674df307bb9841dc577b5d9e7011f237b6b1f4711a96a9cb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BFQMLEQGPQXLWSSLSIGUHKJVBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random unitary matrices associated to a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Karol \\.Zyczkowski, Pawe{\\l} Kondratiuk","submitted_at":"2013-11-14T17:23:30Z","abstract_excerpt":"We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order $n^2$. The global evolution operator is represented by a unitary matrix of size $N=n^k$. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to Haar random unitary matrices provided the corresponding graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3585","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":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/kFV9cd3Zk+1BIYpnQzCniBT3gLy+QR+4v1ksSzhp/qx68nQIA82rwS7Zj6r478ZG6zaBWcGSmBuJzpz9tm9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:13:59.600628Z"},"content_sha256":"a7d7d5043e0ad300b32d1da28cc327d73f840b587cd9ac136ed3ac31e14ec4aa","schema_version":"1.0","event_id":"sha256:a7d7d5043e0ad300b32d1da28cc327d73f840b587cd9ac136ed3ac31e14ec4aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO/bundle.json","state_url":"https://pith.science/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO/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":"2026-05-30T06:13:59Z","links":{"resolver":"https://pith.science/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO","bundle":"https://pith.science/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO/bundle.json","state":"https://pith.science/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFQMLEQGPQXLWSSLSIGUHKJVBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BFQMLEQGPQXLWSSLSIGUHKJVBO","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":"0e13498d81ea7abeeef442eb6796246be30efe927bea6a974e059f3434a354e5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T17:23:30Z","title_canon_sha256":"02d0008286311698e4baa5f7a518dbf165bb7c698735b815cc62dbf6d8b29f3f"},"schema_version":"1.0","source":{"id":"1311.3585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3585","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3585v1","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3585","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"BFQMLEQGPQXL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BFQMLEQGPQXLWSSL","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BFQMLEQG","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:a7d7d5043e0ad300b32d1da28cc327d73f840b587cd9ac136ed3ac31e14ec4aa","target":"graph","created_at":"2026-05-18T03:03:31Z","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 analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order $n^2$. The global evolution operator is represented by a unitary matrix of size $N=n^k$. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to Haar random unitary matrices provided the corresponding graph","authors_text":"Karol \\.Zyczkowski, Pawe{\\l} Kondratiuk","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T17:23:30Z","title":"Random unitary matrices associated to a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3585","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:ca164ab1298ea0b674df307bb9841dc577b5d9e7011f237b6b1f4711a96a9cb3","target":"record","created_at":"2026-05-18T03:03:31Z","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":"0e13498d81ea7abeeef442eb6796246be30efe927bea6a974e059f3434a354e5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-11-14T17:23:30Z","title_canon_sha256":"02d0008286311698e4baa5f7a518dbf165bb7c698735b815cc62dbf6d8b29f3f"},"schema_version":"1.0","source":{"id":"1311.3585","kind":"arxiv","version":1}},"canonical_sha256":"0960c592067c2ebb4a4b920d43a9350baa4cfca9c488c6ed65f8b3ba74ef2aaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0960c592067c2ebb4a4b920d43a9350baa4cfca9c488c6ed65f8b3ba74ef2aaa","first_computed_at":"2026-05-18T03:03:31.628256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:31.628256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXC1tWOXHssq+kW/c3PihzI9Gn15XavqP/nTgPbA+up2TWAlQbYXFFE/CftDMfvZvaJ+SOHRpGGQKJo/hDENBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:31.628825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca164ab1298ea0b674df307bb9841dc577b5d9e7011f237b6b1f4711a96a9cb3","sha256:a7d7d5043e0ad300b32d1da28cc327d73f840b587cd9ac136ed3ac31e14ec4aa"],"state_sha256":"1a0a6f29e4211afe483ca2da397969d10580d05f68ab6b62b5c6c2950d054897"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIJA4EhT3t1UBS1N6KJiVnWPI3MnPu+oB7Y0SjbWx916z/DbffKtLF7Dd4AG9IPP21GLKoi9HlLrl6WLtprWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:13:59.603678Z","bundle_sha256":"42a931e2ca29d05f1000620e91b9c217f2224acadd43510b800f3665e317eb0f"}}