{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SJVNFRSYJIDRP6SMGIKZBMHTFY","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":"4b88ae9f46848f8409f443986360748389ce61097e65596092579b386637ac38","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-13T23:25:34Z","title_canon_sha256":"4c830141b00e31a9e020190e6aece95cf4e0e601353546f171b3c8368d1e901e"},"schema_version":"1.0","source":{"id":"1703.04558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04558","created_at":"2026-05-18T00:48:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04558v1","created_at":"2026-05-18T00:48:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04558","created_at":"2026-05-18T00:48:39Z"},{"alias_kind":"pith_short_12","alias_value":"SJVNFRSYJIDR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SJVNFRSYJIDRP6SM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SJVNFRSY","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:a364f92d2248c35ab3e6f3681c16eaf1589dc45d2941054049b944fb3accb8fb","target":"graph","created_at":"2026-05-18T00:48:39Z","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":"In this paper, we introduce a multidimensional generalization of Kitagawa's split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schr\\\"{o}dinger operator with variable coefficients, which is analyzed using the Feshbach map.","authors_text":"Akito Suzuki, Daiju Funakawa, Toru Fuda","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-13T23:25:34Z","title":"Localization of a multi-dimensional quantum walk with one defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04558","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:d3a13ae10477fc5763f23caa783d4d104791da723b31c67de70210767c28bb89","target":"record","created_at":"2026-05-18T00:48:39Z","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":"4b88ae9f46848f8409f443986360748389ce61097e65596092579b386637ac38","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-03-13T23:25:34Z","title_canon_sha256":"4c830141b00e31a9e020190e6aece95cf4e0e601353546f171b3c8368d1e901e"},"schema_version":"1.0","source":{"id":"1703.04558","kind":"arxiv","version":1}},"canonical_sha256":"926ad2c6584a0717fa4c321590b0f32e1476b03f41216317b1ae882ecd842d4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"926ad2c6584a0717fa4c321590b0f32e1476b03f41216317b1ae882ecd842d4d","first_computed_at":"2026-05-18T00:48:39.685535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:39.685535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E2jYjxOPU8KTciAUjmYShkfuKuKmgOi5ivlpqt+/Le23KGfIcrNMxSgrKW1m+vWoKuIlp67Zib4WVm8TKp7FAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:39.686028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3a13ae10477fc5763f23caa783d4d104791da723b31c67de70210767c28bb89","sha256:a364f92d2248c35ab3e6f3681c16eaf1589dc45d2941054049b944fb3accb8fb"],"state_sha256":"0ed1d369da23fd83bb32f4a3e0810b24b941fd74b987c2db14b658314c2639ef"}