{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:PD37L7YIZDVRJ3TSFTI2V6WN3R","short_pith_number":"pith:PD37L7YI","canonical_record":{"source":{"id":"2008.01224","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-03T22:15:01Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"478b35eabf9830e12702bfcfc2254963cb33d9783a85c7848776f690776e3333","abstract_canon_sha256":"d5dc63b7f7911efb8c20be17c4e6ad47681b962b36007d576cf50a58b8be18d7"},"schema_version":"1.0"},"canonical_sha256":"78f7f5ff08c8eb14ee722cd1aafacddc65e14bf288f6cd914f626de9b7fe3b1a","source":{"kind":"arxiv","id":"2008.01224","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01224","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01224v2","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01224","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"PD37L7YIZDVR","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"pith_short_16","alias_value":"PD37L7YIZDVRJ3TS","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"pith_short_8","alias_value":"PD37L7YI","created_at":"2026-07-05T05:06:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:PD37L7YIZDVRJ3TSFTI2V6WN3R","target":"record","payload":{"canonical_record":{"source":{"id":"2008.01224","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-03T22:15:01Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"478b35eabf9830e12702bfcfc2254963cb33d9783a85c7848776f690776e3333","abstract_canon_sha256":"d5dc63b7f7911efb8c20be17c4e6ad47681b962b36007d576cf50a58b8be18d7"},"schema_version":"1.0"},"canonical_sha256":"78f7f5ff08c8eb14ee722cd1aafacddc65e14bf288f6cd914f626de9b7fe3b1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:49.162307Z","signature_b64":"BAXvaIS9DIoRhDJiqg5gM5z8tJWDa4dhAXg3ELPxEm3CyK4ehLETan5oXkhhGz22jhtzWUpeGre6FkNUidowAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f7f5ff08c8eb14ee722cd1aafacddc65e14bf288f6cd914f626de9b7fe3b1a","last_reissued_at":"2026-07-05T05:06:49.161897Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:49.161897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.01224","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":"2026-07-05T05:06:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FSBeHVuPxsiQDm88iuUSPMOnjqmX1A0v1ZYMmSM74WApawM1OzbIyxY474lBj5SfjdQaS//lRlDzX8r+vjcrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T07:41:07.594145Z"},"content_sha256":"b74d3d9b50385ee39ba0e02c2ff42d5f82c30cba0e62964a33f6c6ec6c8ebbf0","schema_version":"1.0","event_id":"sha256:b74d3d9b50385ee39ba0e02c2ff42d5f82c30cba0e62964a33f6c6ec6c8ebbf0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:PD37L7YIZDVRJ3TSFTI2V6WN3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factoring Discrete Quantum Walks on Distance Regular Graphs into Continuous Quantum Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"Hanmeng Zhan","submitted_at":"2020-08-03T22:15:01Z","abstract_excerpt":"We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$ is a product of at most $d$ commuting transition matrices of continuous-time quantum walks, each on some distance digraph of the line digraph of $X$. We also obtain a similar factorization for any graph $X$ in a Bose Mesner algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01224","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.01224/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":"2026-07-05T05:06:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYss3fbvwxbVPZUKOuzZSoc1IktyUQivU4SHmMfH4C5mxvyf1/o9jEhuRWasg4ckKzWNrkxTX1KVSgqB1A92Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T07:41:07.594665Z"},"content_sha256":"793baf6b1c86c2dd6371e08421842148883abc49fa2c1498e840523cf3fa4151","schema_version":"1.0","event_id":"sha256:793baf6b1c86c2dd6371e08421842148883abc49fa2c1498e840523cf3fa4151"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R/bundle.json","state_url":"https://pith.science/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R/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":"2026-08-21T07:41:07Z","links":{"resolver":"https://pith.science/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R","bundle":"https://pith.science/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R/bundle.json","state":"https://pith.science/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PD37L7YIZDVRJ3TSFTI2V6WN3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:PD37L7YIZDVRJ3TSFTI2V6WN3R","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":"d5dc63b7f7911efb8c20be17c4e6ad47681b962b36007d576cf50a58b8be18d7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-03T22:15:01Z","title_canon_sha256":"478b35eabf9830e12702bfcfc2254963cb33d9783a85c7848776f690776e3333"},"schema_version":"1.0","source":{"id":"2008.01224","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.01224","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"2008.01224v2","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.01224","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"PD37L7YIZDVR","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"pith_short_16","alias_value":"PD37L7YIZDVRJ3TS","created_at":"2026-07-05T05:06:49Z"},{"alias_kind":"pith_short_8","alias_value":"PD37L7YI","created_at":"2026-07-05T05:06:49Z"}],"graph_snapshots":[{"event_id":"sha256:793baf6b1c86c2dd6371e08421842148883abc49fa2c1498e840523cf3fa4151","target":"graph","created_at":"2026-07-05T05:06:49Z","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/2008.01224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$ is a product of at most $d$ commuting transition matrices of continuous-time quantum walks, each on some distance digraph of the line digraph of $X$. We also obtain a similar factorization for any graph $X$ in a Bose Mesner algebra.","authors_text":"Hanmeng Zhan","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-03T22:15:01Z","title":"Factoring Discrete Quantum Walks on Distance Regular Graphs into Continuous Quantum Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.01224","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:b74d3d9b50385ee39ba0e02c2ff42d5f82c30cba0e62964a33f6c6ec6c8ebbf0","target":"record","created_at":"2026-07-05T05:06:49Z","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":"d5dc63b7f7911efb8c20be17c4e6ad47681b962b36007d576cf50a58b8be18d7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-03T22:15:01Z","title_canon_sha256":"478b35eabf9830e12702bfcfc2254963cb33d9783a85c7848776f690776e3333"},"schema_version":"1.0","source":{"id":"2008.01224","kind":"arxiv","version":2}},"canonical_sha256":"78f7f5ff08c8eb14ee722cd1aafacddc65e14bf288f6cd914f626de9b7fe3b1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f7f5ff08c8eb14ee722cd1aafacddc65e14bf288f6cd914f626de9b7fe3b1a","first_computed_at":"2026-07-05T05:06:49.161897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:49.161897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BAXvaIS9DIoRhDJiqg5gM5z8tJWDa4dhAXg3ELPxEm3CyK4ehLETan5oXkhhGz22jhtzWUpeGre6FkNUidowAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:49.162307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.01224","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b74d3d9b50385ee39ba0e02c2ff42d5f82c30cba0e62964a33f6c6ec6c8ebbf0","sha256:793baf6b1c86c2dd6371e08421842148883abc49fa2c1498e840523cf3fa4151"],"state_sha256":"2afd1e016a940e94690f85e62370c565c7c83d668015f13b7c177cf917b3e4b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfuXZ/PoH5uPStxHVkjqPMjUQKNJBD1uKwSTYoo3jGBuQC3qs2/g1OmnFEgr7NiI5BU5Se+JzsgKN2lKkPQYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T07:41:07.599586Z","bundle_sha256":"184055aa8b3635aa8f8180c0dea62d32bcafbb47933cda2531b028e9f4db1689"}}