{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LW2NWNGD4V4RGBCMRIIYM6LUCH","short_pith_number":"pith:LW2NWNGD","schema_version":"1.0","canonical_sha256":"5db4db34c3e57913044c8a1186797411fadc60f82f0adb6d6f2e01c6ac3112e8","source":{"kind":"arxiv","id":"1109.1866","version":2},"attestation_state":"computed","paper":{"title":"Quantum Walks on the Line with Phase Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Marcos Villagra, Masaki Nakanishi, Shigeru Yamashita, Yasuhiko Nakashima","submitted_at":"2011-09-09T00:35:26Z","abstract_excerpt":"In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being addressed: {\\it Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps?} This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin op"},"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":"1109.1866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-09-09T00:35:26Z","cross_cats_sorted":[],"title_canon_sha256":"f1091cb2a6a6803742d690376dd483f0286319be737331ba5d2784d849d6bde4","abstract_canon_sha256":"e456a7a4d98ddb1ef41cde0dbac843dd8897630ba9174d0ff0d89b5a8b3fd8eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.703367Z","signature_b64":"9NRYRsoBO7BE7z7tYcB5/96G51n8KmSJPK2IuOFo5UTzeGjepMCB9yfWT7NLXJH53nLdfCcwOyPvYtW9ltMoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5db4db34c3e57913044c8a1186797411fadc60f82f0adb6d6f2e01c6ac3112e8","last_reissued_at":"2026-05-18T03:37:41.702762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.702762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Walks on the Line with Phase Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Marcos Villagra, Masaki Nakanishi, Shigeru Yamashita, Yasuhiko Nakashima","submitted_at":"2011-09-09T00:35:26Z","abstract_excerpt":"In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being addressed: {\\it Given a graph, what is the probability that a quantum walk arrives at a given vertex after some number of steps?} This is a very natural question, and for random walks it can be answered by several different combinatorial arguments. For quantum walks this is a highly non-trivial task. Furthermore, this was only achieved before for one specific coin op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1866","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":""},"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":"1109.1866","created_at":"2026-05-18T03:37:41.702839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.1866v2","created_at":"2026-05-18T03:37:41.702839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1866","created_at":"2026-05-18T03:37:41.702839+00:00"},{"alias_kind":"pith_short_12","alias_value":"LW2NWNGD4V4R","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LW2NWNGD4V4RGBCM","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LW2NWNGD","created_at":"2026-05-18T12:26:34.985390+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/LW2NWNGD4V4RGBCMRIIYM6LUCH","json":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH.json","graph_json":"https://pith.science/api/pith-number/LW2NWNGD4V4RGBCMRIIYM6LUCH/graph.json","events_json":"https://pith.science/api/pith-number/LW2NWNGD4V4RGBCMRIIYM6LUCH/events.json","paper":"https://pith.science/paper/LW2NWNGD"},"agent_actions":{"view_html":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH","download_json":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH.json","view_paper":"https://pith.science/paper/LW2NWNGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.1866&json=true","fetch_graph":"https://pith.science/api/pith-number/LW2NWNGD4V4RGBCMRIIYM6LUCH/graph.json","fetch_events":"https://pith.science/api/pith-number/LW2NWNGD4V4RGBCMRIIYM6LUCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH/action/storage_attestation","attest_author":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH/action/author_attestation","sign_citation":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH/action/citation_signature","submit_replication":"https://pith.science/pith/LW2NWNGD4V4RGBCMRIIYM6LUCH/action/replication_record"}},"created_at":"2026-05-18T03:37:41.702839+00:00","updated_at":"2026-05-18T03:37:41.702839+00:00"}