{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:56V55DSVZSKBD6O7YX5MIRL42X","short_pith_number":"pith:56V55DSV","canonical_record":{"source":{"id":"1504.06396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-24T05:09:21Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"b1a86c09666ba424c31f6165192ef1cd8ac627ed0f91ac4a17878ff08ce75e77","abstract_canon_sha256":"d6fa2145f7c4326e421acd08cc6fd03a70d90c636ef3e42d319e3356e5149599"},"schema_version":"1.0"},"canonical_sha256":"efabde8e55cc9411f9dfc5fac4457cd5c1937dbedadb0955974efbcb4e96e04d","source":{"kind":"arxiv","id":"1504.06396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06396","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06396v1","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06396","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"56V55DSVZSKB","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"56V55DSVZSKBD6O7","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"56V55DSV","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:56V55DSVZSKBD6O7YX5MIRL42X","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-24T05:09:21Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"b1a86c09666ba424c31f6165192ef1cd8ac627ed0f91ac4a17878ff08ce75e77","abstract_canon_sha256":"d6fa2145f7c4326e421acd08cc6fd03a70d90c636ef3e42d319e3356e5149599"},"schema_version":"1.0"},"canonical_sha256":"efabde8e55cc9411f9dfc5fac4457cd5c1937dbedadb0955974efbcb4e96e04d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:53.779645Z","signature_b64":"IjipTVvo8Q0VWS3F7L8JJPpNGfUUFEO31CxA4K+C0TLZQUCALjvpCOfsUd6YupBfHLHQrAxmnQy5iDofS/EABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efabde8e55cc9411f9dfc5fac4457cd5c1937dbedadb0955974efbcb4e96e04d","last_reissued_at":"2026-05-18T02:17:53.778906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:53.778906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06396","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":"2026-05-18T02:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"067IE7ItGJmQkRmBKh5comjQBJZPptMQ60r9oKFPmeS52hrnkye2UZCXReW+Qh1u0RoamcBSSedBA8FJnO0NDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:25:47.545261Z"},"content_sha256":"f29698db2670a5961fb5283b2b0addba1e2ad3d649db9f601005135cc6eaca85","schema_version":"1.0","event_id":"sha256:f29698db2670a5961fb5283b2b0addba1e2ad3d649db9f601005135cc6eaca85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:56V55DSVZSKBD6O7YX5MIRL42X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodicity for the Hadamard walk on cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Masato Takei, Norio Konno, Yuki Shimizu","submitted_at":"2015-04-24T05:09:21Z","abstract_excerpt":"The present paper treats the period T_N of the Hadamard walk on a cycle C_N with N vertices. Dukes (2014) considered the periodicity of more general quantum walks on C_N and showed T_2 =2, T_4=8, T_8=24 for the Hadamard walk case. We prove that the Hadamard walk does not have any period except for his case, i.e., N=2, 4, 8. Our method is based on a path counting and cyclotomic polynomials which is different from his approach based on the property of eigenvalues for unitary matrix that determines the evolution of the walk."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06396","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":"2026-05-18T02:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5soAGUJQJgD9qCuNgvvoDm1W76lUHCD/yexAbb63zsheQWtebh+JxNxiIzMR/JNcrd5tbLADp04BZoC8t2KHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:25:47.545633Z"},"content_sha256":"41bb0d0f35ad36b4536d27c6d36c929553d2034e18dfe38481afebaa6dfea6f0","schema_version":"1.0","event_id":"sha256:41bb0d0f35ad36b4536d27c6d36c929553d2034e18dfe38481afebaa6dfea6f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56V55DSVZSKBD6O7YX5MIRL42X/bundle.json","state_url":"https://pith.science/pith/56V55DSVZSKBD6O7YX5MIRL42X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56V55DSVZSKBD6O7YX5MIRL42X/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":"2026-06-03T18:25:47Z","links":{"resolver":"https://pith.science/pith/56V55DSVZSKBD6O7YX5MIRL42X","bundle":"https://pith.science/pith/56V55DSVZSKBD6O7YX5MIRL42X/bundle.json","state":"https://pith.science/pith/56V55DSVZSKBD6O7YX5MIRL42X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56V55DSVZSKBD6O7YX5MIRL42X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:56V55DSVZSKBD6O7YX5MIRL42X","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":"d6fa2145f7c4326e421acd08cc6fd03a70d90c636ef3e42d319e3356e5149599","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-24T05:09:21Z","title_canon_sha256":"b1a86c09666ba424c31f6165192ef1cd8ac627ed0f91ac4a17878ff08ce75e77"},"schema_version":"1.0","source":{"id":"1504.06396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06396","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06396v1","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06396","created_at":"2026-05-18T02:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"56V55DSVZSKB","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"56V55DSVZSKBD6O7","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"56V55DSV","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:41bb0d0f35ad36b4536d27c6d36c929553d2034e18dfe38481afebaa6dfea6f0","target":"graph","created_at":"2026-05-18T02:17:53Z","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":"The present paper treats the period T_N of the Hadamard walk on a cycle C_N with N vertices. Dukes (2014) considered the periodicity of more general quantum walks on C_N and showed T_2 =2, T_4=8, T_8=24 for the Hadamard walk case. We prove that the Hadamard walk does not have any period except for his case, i.e., N=2, 4, 8. Our method is based on a path counting and cyclotomic polynomials which is different from his approach based on the property of eigenvalues for unitary matrix that determines the evolution of the walk.","authors_text":"Masato Takei, Norio Konno, Yuki Shimizu","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-24T05:09:21Z","title":"Periodicity for the Hadamard walk on cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06396","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:f29698db2670a5961fb5283b2b0addba1e2ad3d649db9f601005135cc6eaca85","target":"record","created_at":"2026-05-18T02:17:53Z","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":"d6fa2145f7c4326e421acd08cc6fd03a70d90c636ef3e42d319e3356e5149599","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-04-24T05:09:21Z","title_canon_sha256":"b1a86c09666ba424c31f6165192ef1cd8ac627ed0f91ac4a17878ff08ce75e77"},"schema_version":"1.0","source":{"id":"1504.06396","kind":"arxiv","version":1}},"canonical_sha256":"efabde8e55cc9411f9dfc5fac4457cd5c1937dbedadb0955974efbcb4e96e04d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efabde8e55cc9411f9dfc5fac4457cd5c1937dbedadb0955974efbcb4e96e04d","first_computed_at":"2026-05-18T02:17:53.778906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:53.778906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IjipTVvo8Q0VWS3F7L8JJPpNGfUUFEO31CxA4K+C0TLZQUCALjvpCOfsUd6YupBfHLHQrAxmnQy5iDofS/EABg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:53.779645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29698db2670a5961fb5283b2b0addba1e2ad3d649db9f601005135cc6eaca85","sha256:41bb0d0f35ad36b4536d27c6d36c929553d2034e18dfe38481afebaa6dfea6f0"],"state_sha256":"71a7a3860aa792c288137909d703de24143b72799791732aa1f3972b4bb57c3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xZ+OHYzqLLfVTFbNI0i3fYA2B9v+sVUub8jLfTF7samqXCSLItPijVMpZquMVHeuuKLOqJwe9B2MS99X/U/IDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:25:47.547575Z","bundle_sha256":"d949af055d341af2874b4f1787e09de41d8a33b0cdf2754aaa841e3d191ee028"}}