{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QGJTUUZB5XCOYPS23462HMD3NT","short_pith_number":"pith:QGJTUUZB","schema_version":"1.0","canonical_sha256":"81933a5321edc4ec3e5adf3da3b07b6cff7ad1828d718f9954560a53207f163e","source":{"kind":"arxiv","id":"1111.6630","version":1},"attestation_state":"computed","paper":{"title":"The Quantum Walk of F. Riesz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"F. A. Grunbaum, L. Velazquez","submitted_at":"2011-11-28T21:57:58Z","abstract_excerpt":"We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that are not traditionally allowed. We illustrate this in the case of a very interesting measure, originally proposed by F. Riesz for a different purpose."},"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":"1111.6630","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T21:57:58Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"e45f27efd0e1d943cc384cca9c4937ffe617d5f69785ea043fc34d0a8c98dde2","abstract_canon_sha256":"862c89fa608199dd8b48b333109687f1fa3cada623339a19fa020bdf56e6a061"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:28.861380Z","signature_b64":"Pye7sIerFIa3/+eN81REC++An6zpUvq+VbrZy6N/AClFd+BAi+bYnnxXD1IG00J9sIlTulej/NJDjjykhEoUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81933a5321edc4ec3e5adf3da3b07b6cff7ad1828d718f9954560a53207f163e","last_reissued_at":"2026-05-18T04:07:28.860847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:28.860847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Quantum Walk of F. Riesz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"F. A. Grunbaum, L. Velazquez","submitted_at":"2011-11-28T21:57:58Z","abstract_excerpt":"We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that are not traditionally allowed. We illustrate this in the case of a very interesting measure, originally proposed by F. Riesz for a different purpose."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6630","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.6630","created_at":"2026-05-18T04:07:28.860905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6630v1","created_at":"2026-05-18T04:07:28.860905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6630","created_at":"2026-05-18T04:07:28.860905+00:00"},{"alias_kind":"pith_short_12","alias_value":"QGJTUUZB5XCO","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QGJTUUZB5XCOYPS2","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QGJTUUZB","created_at":"2026-05-18T12:26:39.201973+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/QGJTUUZB5XCOYPS23462HMD3NT","json":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT.json","graph_json":"https://pith.science/api/pith-number/QGJTUUZB5XCOYPS23462HMD3NT/graph.json","events_json":"https://pith.science/api/pith-number/QGJTUUZB5XCOYPS23462HMD3NT/events.json","paper":"https://pith.science/paper/QGJTUUZB"},"agent_actions":{"view_html":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT","download_json":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT.json","view_paper":"https://pith.science/paper/QGJTUUZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6630&json=true","fetch_graph":"https://pith.science/api/pith-number/QGJTUUZB5XCOYPS23462HMD3NT/graph.json","fetch_events":"https://pith.science/api/pith-number/QGJTUUZB5XCOYPS23462HMD3NT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT/action/storage_attestation","attest_author":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT/action/author_attestation","sign_citation":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT/action/citation_signature","submit_replication":"https://pith.science/pith/QGJTUUZB5XCOYPS23462HMD3NT/action/replication_record"}},"created_at":"2026-05-18T04:07:28.860905+00:00","updated_at":"2026-05-18T04:07:28.860905+00:00"}