{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6Y5UNTH5YQV3GAAXT4UT52OVM6","short_pith_number":"pith:6Y5UNTH5","canonical_record":{"source":{"id":"1603.08948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-29T20:29:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d9d3882c11b7f1ebdcfe97faa92602e62724c17007f1bb3dad162486e9279104","abstract_canon_sha256":"9974432ff1153e64c14be26e2286076d0be86cd976379b33f631ad0bca9c1232"},"schema_version":"1.0"},"canonical_sha256":"f63b46ccfdc42bb300179f293ee9d567a8343445f8a4db05fc9be487bd4cd333","source":{"kind":"arxiv","id":"1603.08948","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08948","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08948v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08948","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"6Y5UNTH5YQV3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6Y5UNTH5YQV3GAAX","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6Y5UNTH5","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6Y5UNTH5YQV3GAAXT4UT52OVM6","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-29T20:29:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d9d3882c11b7f1ebdcfe97faa92602e62724c17007f1bb3dad162486e9279104","abstract_canon_sha256":"9974432ff1153e64c14be26e2286076d0be86cd976379b33f631ad0bca9c1232"},"schema_version":"1.0"},"canonical_sha256":"f63b46ccfdc42bb300179f293ee9d567a8343445f8a4db05fc9be487bd4cd333","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:20.198133Z","signature_b64":"fZX27Ulrv559qkVxzmRi9nfIhpooW0S5C8TzDemh5eC0ae3ckeY842FA9Ed2JbxkV5pq8JUdiRxcYogjK61iDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f63b46ccfdc42bb300179f293ee9d567a8343445f8a4db05fc9be487bd4cd333","last_reissued_at":"2026-05-18T00:45:20.197396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:20.197396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08948","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":"2026-05-18T00:45:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GcRMB3iWrRGkHkyUaexvPoVxMq52+BX95wrxCT58zauC/ANmB4a1OnyYcN3BC9oInI15T6lWfkmNkrv/Zl/+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:15:22.201267Z"},"content_sha256":"6bdeef936eab5c884fc302dc658ad5b659699c788b28803126d9065f3133355d","schema_version":"1.0","event_id":"sha256:6bdeef936eab5c884fc302dc658ad5b659699c788b28803126d9065f3133355d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6Y5UNTH5YQV3GAAXT4UT52OVM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The stationary measure for diagonal quantum walk with one defect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hikari Kawai, Norio Konno, Takako Endo","submitted_at":"2016-03-29T20:29:33Z","abstract_excerpt":"This study is motivated by the previous work [14]. We treat 3 types of the one-dimensional quantum walks (QWs), whose time evolutions are described by diagonal unitary matrix, and diagonal unitary matrices with one defect. In this paper, we call the QW defined by diagonal unitary matrices, \"the diagonal QW\", and we consider the stationary distributions of generally 2-state diagonal QW with one defect, 3-state space-homogeneous diagonal QW, and 3-state diagonal QW with one defect. One of the purposes of our study is to characterize the QWs by the stationary measure, which may lead to answer the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08948","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":"2026-05-18T00:45:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RPsJW+ISHxz7qdfXJAcvX4IzQUZT4sGmN1ieqGnQX5loljfQRUoluZkLwaa6vuF4JJiiT0XJqC3vaJqPsnrJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:15:22.201869Z"},"content_sha256":"c1627393629e5fdfcd49b038270ab1b205fbf2552d78d17e89b9f267406cf7a9","schema_version":"1.0","event_id":"sha256:c1627393629e5fdfcd49b038270ab1b205fbf2552d78d17e89b9f267406cf7a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6/bundle.json","state_url":"https://pith.science/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6/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":"2026-06-01T12:15:22Z","links":{"resolver":"https://pith.science/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6","bundle":"https://pith.science/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6/bundle.json","state":"https://pith.science/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Y5UNTH5YQV3GAAXT4UT52OVM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6Y5UNTH5YQV3GAAXT4UT52OVM6","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":"9974432ff1153e64c14be26e2286076d0be86cd976379b33f631ad0bca9c1232","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-29T20:29:33Z","title_canon_sha256":"d9d3882c11b7f1ebdcfe97faa92602e62724c17007f1bb3dad162486e9279104"},"schema_version":"1.0","source":{"id":"1603.08948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08948","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08948v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08948","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"6Y5UNTH5YQV3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6Y5UNTH5YQV3GAAX","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6Y5UNTH5","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:c1627393629e5fdfcd49b038270ab1b205fbf2552d78d17e89b9f267406cf7a9","target":"graph","created_at":"2026-05-18T00:45:20Z","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":"This study is motivated by the previous work [14]. We treat 3 types of the one-dimensional quantum walks (QWs), whose time evolutions are described by diagonal unitary matrix, and diagonal unitary matrices with one defect. In this paper, we call the QW defined by diagonal unitary matrices, \"the diagonal QW\", and we consider the stationary distributions of generally 2-state diagonal QW with one defect, 3-state space-homogeneous diagonal QW, and 3-state diagonal QW with one defect. One of the purposes of our study is to characterize the QWs by the stationary measure, which may lead to answer the","authors_text":"Hikari Kawai, Norio Konno, Takako Endo","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-29T20:29:33Z","title":"The stationary measure for diagonal quantum walk with one defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08948","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":"sha256:6bdeef936eab5c884fc302dc658ad5b659699c788b28803126d9065f3133355d","target":"record","created_at":"2026-05-18T00:45:20Z","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":"9974432ff1153e64c14be26e2286076d0be86cd976379b33f631ad0bca9c1232","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-29T20:29:33Z","title_canon_sha256":"d9d3882c11b7f1ebdcfe97faa92602e62724c17007f1bb3dad162486e9279104"},"schema_version":"1.0","source":{"id":"1603.08948","kind":"arxiv","version":1}},"canonical_sha256":"f63b46ccfdc42bb300179f293ee9d567a8343445f8a4db05fc9be487bd4cd333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f63b46ccfdc42bb300179f293ee9d567a8343445f8a4db05fc9be487bd4cd333","first_computed_at":"2026-05-18T00:45:20.197396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:20.197396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fZX27Ulrv559qkVxzmRi9nfIhpooW0S5C8TzDemh5eC0ae3ckeY842FA9Ed2JbxkV5pq8JUdiRxcYogjK61iDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:20.198133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bdeef936eab5c884fc302dc658ad5b659699c788b28803126d9065f3133355d","sha256:c1627393629e5fdfcd49b038270ab1b205fbf2552d78d17e89b9f267406cf7a9"],"state_sha256":"a5da345db4d6fc023dff0b5480d6c51875c74c087c7d7be697ab44051f681d01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2SG6tnsuJSoCnhhPzf3bKpCxJtKQSWMcN5Ii1FUdLX18oxbt68Dn77ht8fmak6LAXD2HJwp9k+M+quKEEC7CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:15:22.204135Z","bundle_sha256":"8ac8fe0356b751b1cd80ba61c03909d550e1bfbfecbb63f346464c6e8652a274"}}