{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:OWNWRMK75TKB3VHUZY4MPUYF7C","short_pith_number":"pith:OWNWRMK7","canonical_record":{"source":{"id":"2208.05107","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-10T02:01:44Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"a1cdd95ea8c4143e3c4c354409627b078f822edfe3b165e74a3604f369eb95db","abstract_canon_sha256":"1020297b4296a3d64b3be7bf33caa1bacc6c12b7168a73caf8b8201e97e64379"},"schema_version":"1.0"},"canonical_sha256":"759b68b15fecd41dd4f4ce38c7d305f89dc3992e12cba16cd0c098babe93f84b","source":{"kind":"arxiv","id":"2208.05107","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05107","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05107v1","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05107","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"OWNWRMK75TKB","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"pith_short_16","alias_value":"OWNWRMK75TKB3VHU","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"pith_short_8","alias_value":"OWNWRMK7","created_at":"2026-07-05T04:47:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:OWNWRMK75TKB3VHUZY4MPUYF7C","target":"record","payload":{"canonical_record":{"source":{"id":"2208.05107","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-10T02:01:44Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"a1cdd95ea8c4143e3c4c354409627b078f822edfe3b165e74a3604f369eb95db","abstract_canon_sha256":"1020297b4296a3d64b3be7bf33caa1bacc6c12b7168a73caf8b8201e97e64379"},"schema_version":"1.0"},"canonical_sha256":"759b68b15fecd41dd4f4ce38c7d305f89dc3992e12cba16cd0c098babe93f84b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:47:32.354006Z","signature_b64":"WezUawWNiMuXEgRj3gmFcuylSqj+gppNrqKVbhaZIQZ7HoF0xNEXt13wRRWK+Cip1lPHdN8dQ03h8z3PEcUrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"759b68b15fecd41dd4f4ce38c7d305f89dc3992e12cba16cd0c098babe93f84b","last_reissued_at":"2026-07-05T04:47:32.353611Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:47:32.353611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.05107","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":"2026-07-05T04:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dx7GwNEfj07wRb4Ju5D300zRAycjIb30+mYJvVP1mzUBm2cV9LwJVnEqDFQfRKwm9QnukpLIZQmQzv9TXTQRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T00:19:29.091939Z"},"content_sha256":"15baec2d8d1699f3027e68de720ca3ed83710837fbda115a9cacecb2062c3740","schema_version":"1.0","event_id":"sha256:15baec2d8d1699f3027e68de720ca3ed83710837fbda115a9cacecb2062c3740"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:OWNWRMK75TKB3VHUZY4MPUYF7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional revival on abelian Cayley graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"Gaojun Luo, Xiwang Cao","submitted_at":"2022-08-10T02:01:44Z","abstract_excerpt":"Fractional revival, known as a quantum transport phenomenon, is essential for entanglement generation in quantum spin networks. The concept of fractional revival is a generalization of perfect state transfer and periodicity on graphs. In this paper, we propose a sufficient and necessary condition for abelian Cayley graphs having fractional revival between any two distinct vertices. With this characterization, two general constructions of abelian Cayley graphs having fractional revival is presented. Meanwhile, we establish several new families of abelian Cayley graphs admitting fractional reviv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05107","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.05107/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":"2026-07-05T04:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDk/w24NjzYBGFQM6lDQnZF0pMMjLX4j5DZq6vPXFu1C/7nZG6sYtSHv1rhU+IIsybqQCP1r9EgxHp5dzM8eAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T00:19:29.092427Z"},"content_sha256":"6d5d3384d1cf3687f65b4e978f1914a875fe7ae955526f0aff1d1fa0216a29b4","schema_version":"1.0","event_id":"sha256:6d5d3384d1cf3687f65b4e978f1914a875fe7ae955526f0aff1d1fa0216a29b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWNWRMK75TKB3VHUZY4MPUYF7C/bundle.json","state_url":"https://pith.science/pith/OWNWRMK75TKB3VHUZY4MPUYF7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWNWRMK75TKB3VHUZY4MPUYF7C/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":"2026-08-24T00:19:29Z","links":{"resolver":"https://pith.science/pith/OWNWRMK75TKB3VHUZY4MPUYF7C","bundle":"https://pith.science/pith/OWNWRMK75TKB3VHUZY4MPUYF7C/bundle.json","state":"https://pith.science/pith/OWNWRMK75TKB3VHUZY4MPUYF7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWNWRMK75TKB3VHUZY4MPUYF7C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OWNWRMK75TKB3VHUZY4MPUYF7C","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":"1020297b4296a3d64b3be7bf33caa1bacc6c12b7168a73caf8b8201e97e64379","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-10T02:01:44Z","title_canon_sha256":"a1cdd95ea8c4143e3c4c354409627b078f822edfe3b165e74a3604f369eb95db"},"schema_version":"1.0","source":{"id":"2208.05107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05107","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05107v1","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05107","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"OWNWRMK75TKB","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"pith_short_16","alias_value":"OWNWRMK75TKB3VHU","created_at":"2026-07-05T04:47:32Z"},{"alias_kind":"pith_short_8","alias_value":"OWNWRMK7","created_at":"2026-07-05T04:47:32Z"}],"graph_snapshots":[{"event_id":"sha256:6d5d3384d1cf3687f65b4e978f1914a875fe7ae955526f0aff1d1fa0216a29b4","target":"graph","created_at":"2026-07-05T04:47:32Z","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/2208.05107/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fractional revival, known as a quantum transport phenomenon, is essential for entanglement generation in quantum spin networks. The concept of fractional revival is a generalization of perfect state transfer and periodicity on graphs. In this paper, we propose a sufficient and necessary condition for abelian Cayley graphs having fractional revival between any two distinct vertices. With this characterization, two general constructions of abelian Cayley graphs having fractional revival is presented. Meanwhile, we establish several new families of abelian Cayley graphs admitting fractional reviv","authors_text":"Gaojun Luo, Xiwang Cao","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-10T02:01:44Z","title":"Fractional revival on abelian Cayley graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05107","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":"sha256:15baec2d8d1699f3027e68de720ca3ed83710837fbda115a9cacecb2062c3740","target":"record","created_at":"2026-07-05T04:47:32Z","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":"1020297b4296a3d64b3be7bf33caa1bacc6c12b7168a73caf8b8201e97e64379","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-10T02:01:44Z","title_canon_sha256":"a1cdd95ea8c4143e3c4c354409627b078f822edfe3b165e74a3604f369eb95db"},"schema_version":"1.0","source":{"id":"2208.05107","kind":"arxiv","version":1}},"canonical_sha256":"759b68b15fecd41dd4f4ce38c7d305f89dc3992e12cba16cd0c098babe93f84b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"759b68b15fecd41dd4f4ce38c7d305f89dc3992e12cba16cd0c098babe93f84b","first_computed_at":"2026-07-05T04:47:32.353611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:32.353611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WezUawWNiMuXEgRj3gmFcuylSqj+gppNrqKVbhaZIQZ7HoF0xNEXt13wRRWK+Cip1lPHdN8dQ03h8z3PEcUrAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:32.354006Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.05107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15baec2d8d1699f3027e68de720ca3ed83710837fbda115a9cacecb2062c3740","sha256:6d5d3384d1cf3687f65b4e978f1914a875fe7ae955526f0aff1d1fa0216a29b4"],"state_sha256":"d3523675d2eda59dc0eb5eef267dc99751033f241f47af9bdd95c64399be2292"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dWnmlMonpzv1d3P6PfnZYyb3g4Ei64pDKqFnr/667vTchJl18vOZmApa08ZClJmPmQzcRZoC0laiEhrtrn+HDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T00:19:29.097230Z","bundle_sha256":"d7d440182a4fd80a95d12cb7e2fb1e2ef4a0a2905780b3eb5b346919505cb4a9"}}