{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SRM5DRH4DLJWULKBWB4ZHOW2OW","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":"17140ada9da0d3212671e847c4d4bbb500fab5a72cd030f1701890231efbac05","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-31T15:01:56Z","title_canon_sha256":"6cff8af77d68515bf9231597cf6c1e3af134cefa8cd1bc40f2f2392b4e82c260"},"schema_version":"1.0","source":{"id":"1401.0154","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0154","created_at":"2026-05-18T02:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0154v2","created_at":"2026-05-18T02:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0154","created_at":"2026-05-18T02:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"SRM5DRH4DLJW","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SRM5DRH4DLJWULKB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SRM5DRH4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:5fc74476369a7d8ce561d8d658eadfdf8a812654ad32baa1fa30562867902eac","target":"graph","created_at":"2026-05-18T02:39:38Z","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":"We propose a twisted Szegedy walk for estimating the limit behavior of a discrete-time quantum walk on a crystal lattice, an infinite abelian covering graph, whose notion was introduced by [14]. First, we show that the spectrum of the twisted Szegedy walk on the quotient graph can be expressed by mapping the spectrum of a twisted random walk onto the unit circle. Secondly, we show that the spatial Fourier transform of the twisted Szegedy walk on a finite graph with appropriate parameters becomes the Grover walk on its infinite abelian covering graph. Finally, as an application, we show that if","authors_text":"Etsuo Segawa, Iwao Sato, Norio Konno, Yusuke Higuchi","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-31T15:01:56Z","title":"Spectral and asymptotic properties of Grover walks on crystal lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0154","kind":"arxiv","version":2},"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":"sha256:6f061978bec31345ea344103d6b304827af3fa2bc52543df316dae20ec241568","target":"record","created_at":"2026-05-18T02:39:38Z","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":"17140ada9da0d3212671e847c4d4bbb500fab5a72cd030f1701890231efbac05","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-31T15:01:56Z","title_canon_sha256":"6cff8af77d68515bf9231597cf6c1e3af134cefa8cd1bc40f2f2392b4e82c260"},"schema_version":"1.0","source":{"id":"1401.0154","kind":"arxiv","version":2}},"canonical_sha256":"9459d1c4fc1ad36a2d41b07993bada75b186d1b7ebf91d5706566bf9a35bdb01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9459d1c4fc1ad36a2d41b07993bada75b186d1b7ebf91d5706566bf9a35bdb01","first_computed_at":"2026-05-18T02:39:38.239451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:38.239451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YEdI1O/lWao40HfrSP713p1S+N+Z+WJgxBG9eL7E/MOdA/bdmQh0bMgtbcxGFzzwyOxx04UM7JPSxBlJ8Q9UDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:38.239871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0154","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f061978bec31345ea344103d6b304827af3fa2bc52543df316dae20ec241568","sha256:5fc74476369a7d8ce561d8d658eadfdf8a812654ad32baa1fa30562867902eac"],"state_sha256":"663264c1f120799762f517b6906d594ba41d626ab9660e1cec1886a0fc58cddf"}