{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6S2HON2X4BVHAXG5SRIMLJ2UCN","short_pith_number":"pith:6S2HON2X","canonical_record":{"source":{"id":"1804.05127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-13T21:34:56Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"a8d5433a0fe090325d4582585dcf4591138319b43e26db3e7e04d10913e2da53","abstract_canon_sha256":"3f470693edd1f841af4558e38a155a84bbbf2124520dc230a0d8d4a9f63d0608"},"schema_version":"1.0"},"canonical_sha256":"f4b4773757e06a705cdd9450c5a7541373aade1a50774cd8fc848ffad68ae6f9","source":{"kind":"arxiv","id":"1804.05127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05127","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05127v1","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05127","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"6S2HON2X4BVH","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6S2HON2X4BVHAXG5","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6S2HON2X","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6S2HON2X4BVHAXG5SRIMLJ2UCN","target":"record","payload":{"canonical_record":{"source":{"id":"1804.05127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-13T21:34:56Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"a8d5433a0fe090325d4582585dcf4591138319b43e26db3e7e04d10913e2da53","abstract_canon_sha256":"3f470693edd1f841af4558e38a155a84bbbf2124520dc230a0d8d4a9f63d0608"},"schema_version":"1.0"},"canonical_sha256":"f4b4773757e06a705cdd9450c5a7541373aade1a50774cd8fc848ffad68ae6f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:07.793891Z","signature_b64":"RM0RBcRGTjrzCbQL1IoK2VLHs34cTMWg0nU2EBgQpP5WppV5PxNFPRfmv3XvtkplvZCW5gc6tHGLhL3RKNh8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4b4773757e06a705cdd9450c5a7541373aade1a50774cd8fc848ffad68ae6f9","last_reissued_at":"2026-05-18T00:07:07.793190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:07.793190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.05127","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SpFXu47Nfl0WaYbrXToSRiE2ZhZmHHGnMS1jMUlTBJU5h0bMbssInf3kdv+rbq8UTDI53L/VtVhq7b4F+M0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:05:11.377259Z"},"content_sha256":"9d22de4177c1add430d3f81f695361bb5c1559a8b59f4e1ac32c1dd9257aaa07","schema_version":"1.0","event_id":"sha256:9d22de4177c1add430d3f81f695361bb5c1559a8b59f4e1ac32c1dd9257aaa07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6S2HON2X4BVHAXG5SRIMLJ2UCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Akito Suzuki, Daiju Funakawa, Toru Fuda","submitted_at":"2018-04-13T21:34:56Z","abstract_excerpt":"For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in \\cite{HiSeSu}. In this paper, as an application of the spectral mapping theorem, we investigate the spectrum of a one-dimensional split-step quantum walk. We give a criterion for when there is no eigenvalues around $\\pm 1$ in terms of a discriminant operator. We also provide a criterion for when eigenvalues $\\pm 1$ exist in terms of birth eigenspaces. Moreover, we prove that eigenvectors from the birth eigenspaces decay exponentially at spatial infinity and that the birth eigenspaces a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05127","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+0MiD/+veKze/M9gfXBDnFznKniBpMmUi/bYhrP8MvQEm3v/I0uwKVq0aFul/VD8asvFPPibTYRBT40fAmsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:05:11.378214Z"},"content_sha256":"5ced0c9659d145cff01f8391a0aef738f690e80cbd8192e1cd2bcc916c99e187","schema_version":"1.0","event_id":"sha256:5ced0c9659d145cff01f8391a0aef738f690e80cbd8192e1cd2bcc916c99e187"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN/bundle.json","state_url":"https://pith.science/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T03:05:11Z","links":{"resolver":"https://pith.science/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN","bundle":"https://pith.science/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN/bundle.json","state":"https://pith.science/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6S2HON2X4BVHAXG5SRIMLJ2UCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6S2HON2X4BVHAXG5SRIMLJ2UCN","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":"3f470693edd1f841af4558e38a155a84bbbf2124520dc230a0d8d4a9f63d0608","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-13T21:34:56Z","title_canon_sha256":"a8d5433a0fe090325d4582585dcf4591138319b43e26db3e7e04d10913e2da53"},"schema_version":"1.0","source":{"id":"1804.05127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05127","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05127v1","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05127","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"6S2HON2X4BVH","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6S2HON2X4BVHAXG5","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6S2HON2X","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:5ced0c9659d145cff01f8391a0aef738f690e80cbd8192e1cd2bcc916c99e187","target":"graph","created_at":"2026-05-18T00:07:07Z","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":"For given two unitary and self-adjoint operators on a Hilbert space, a spectral mapping theorem was proved in \\cite{HiSeSu}. In this paper, as an application of the spectral mapping theorem, we investigate the spectrum of a one-dimensional split-step quantum walk. We give a criterion for when there is no eigenvalues around $\\pm 1$ in terms of a discriminant operator. We also provide a criterion for when eigenvalues $\\pm 1$ exist in terms of birth eigenspaces. Moreover, we prove that eigenvectors from the birth eigenspaces decay exponentially at spatial infinity and that the birth eigenspaces a","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":"2018-04-13T21:34:56Z","title":"Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05127","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":"sha256:9d22de4177c1add430d3f81f695361bb5c1559a8b59f4e1ac32c1dd9257aaa07","target":"record","created_at":"2026-05-18T00:07:07Z","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":"3f470693edd1f841af4558e38a155a84bbbf2124520dc230a0d8d4a9f63d0608","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-13T21:34:56Z","title_canon_sha256":"a8d5433a0fe090325d4582585dcf4591138319b43e26db3e7e04d10913e2da53"},"schema_version":"1.0","source":{"id":"1804.05127","kind":"arxiv","version":1}},"canonical_sha256":"f4b4773757e06a705cdd9450c5a7541373aade1a50774cd8fc848ffad68ae6f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4b4773757e06a705cdd9450c5a7541373aade1a50774cd8fc848ffad68ae6f9","first_computed_at":"2026-05-18T00:07:07.793190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:07.793190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RM0RBcRGTjrzCbQL1IoK2VLHs34cTMWg0nU2EBgQpP5WppV5PxNFPRfmv3XvtkplvZCW5gc6tHGLhL3RKNh8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:07.793891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d22de4177c1add430d3f81f695361bb5c1559a8b59f4e1ac32c1dd9257aaa07","sha256:5ced0c9659d145cff01f8391a0aef738f690e80cbd8192e1cd2bcc916c99e187"],"state_sha256":"d6a2317b378ac6e176cc507a24b90af5b10c73c908d71c0e353fc94e39f533c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HttEgzIGpmivoqKJzZqqRKNI9KgJYHmr2KhkF3N6omzyXQuIXJ8N64TSd311H2t+0E+P+2w7DtTTK82ewoG/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T03:05:11.382279Z","bundle_sha256":"5ceeb4ee5e369d2c90b4f1f43410815c30d40291fd4912ab5bedfd489b257eb9"}}