{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VALTQAQBNLAQ62ERIVLGJTXC5T","short_pith_number":"pith:VALTQAQB","schema_version":"1.0","canonical_sha256":"a8173802016ac10f6891455664cee2ecd470403b50e7d2260a18fa1c161987d4","source":{"kind":"arxiv","id":"1404.1509","version":4},"attestation_state":"computed","paper":{"title":"A limit theorem for a 3-period time-dependent quantum walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"quant-ph","authors_text":"F. Alberto Gr\\\"unbaum, Takuya Machida","submitted_at":"2014-04-05T19:33:11Z","abstract_excerpt":"We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator. In this paper we take a 3-periodic time evolution as the rule. For such a quantum walk, we get a limit distribution which expresses the asymptotic behavior of the walker after a long time. The limit distribution is different from that of a time-independent quantum walk or a 2-period time-dependent quantum walk. We give some analytical results and then consider a number of variants of our model and in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1404.1509","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-04-05T19:33:11Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e415726c43a27862c6fd4c8aa7096f1282beb88fd673c08e9307678c5a23c9b2","abstract_canon_sha256":"7cb374730444417f4a7365900efd9411ceca35cc0c2e6d052e455fa94db1c720"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:53.631305Z","signature_b64":"sUeKwv9ZkNNcfsPZeZ/yV03K9/RYlSj7GK9Duxwg3AFHc2SqR7xm3prYTEyz0vKkUN3irORe+9Pi6VXUNEhPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8173802016ac10f6891455664cee2ecd470403b50e7d2260a18fa1c161987d4","last_reissued_at":"2026-05-18T01:59:53.630859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:53.630859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A limit theorem for a 3-period time-dependent quantum walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"quant-ph","authors_text":"F. Alberto Gr\\\"unbaum, Takuya Machida","submitted_at":"2014-04-05T19:33:11Z","abstract_excerpt":"We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator. In this paper we take a 3-periodic time evolution as the rule. For such a quantum walk, we get a limit distribution which expresses the asymptotic behavior of the walker after a long time. The limit distribution is different from that of a time-independent quantum walk or a 2-period time-dependent quantum walk. We give some analytical results and then consider a number of variants of our model and in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1509","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.1509","created_at":"2026-05-18T01:59:53.630926+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1509v4","created_at":"2026-05-18T01:59:53.630926+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1509","created_at":"2026-05-18T01:59:53.630926+00:00"},{"alias_kind":"pith_short_12","alias_value":"VALTQAQBNLAQ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VALTQAQBNLAQ62ER","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VALTQAQB","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T","json":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T.json","graph_json":"https://pith.science/api/pith-number/VALTQAQBNLAQ62ERIVLGJTXC5T/graph.json","events_json":"https://pith.science/api/pith-number/VALTQAQBNLAQ62ERIVLGJTXC5T/events.json","paper":"https://pith.science/paper/VALTQAQB"},"agent_actions":{"view_html":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T","download_json":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T.json","view_paper":"https://pith.science/paper/VALTQAQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1509&json=true","fetch_graph":"https://pith.science/api/pith-number/VALTQAQBNLAQ62ERIVLGJTXC5T/graph.json","fetch_events":"https://pith.science/api/pith-number/VALTQAQBNLAQ62ERIVLGJTXC5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T/action/storage_attestation","attest_author":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T/action/author_attestation","sign_citation":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T/action/citation_signature","submit_replication":"https://pith.science/pith/VALTQAQBNLAQ62ERIVLGJTXC5T/action/replication_record"}},"created_at":"2026-05-18T01:59:53.630926+00:00","updated_at":"2026-05-18T01:59:53.630926+00:00"}