{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QBYVVESRDU4ITMTUEUBQZKR5Z6","short_pith_number":"pith:QBYVVESR","canonical_record":{"source":{"id":"1302.2081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-08T16:41:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"670efca0f488d861e0f98742127d5bd5efb43c20c76f242a15445193de125114","abstract_canon_sha256":"5c97e539e6fd9b98bb9aa6edfae5d0e0e74012c91dae2c11037b3332fba798e7"},"schema_version":"1.0"},"canonical_sha256":"80715a92511d3889b27425030caa3dcfa88245f083faf87e34e7028f0b30c5b0","source":{"kind":"arxiv","id":"1302.2081","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2081","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2081v1","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2081","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"pith_short_12","alias_value":"QBYVVESRDU4I","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QBYVVESRDU4ITMTU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QBYVVESR","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QBYVVESRDU4ITMTUEUBQZKR5Z6","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-08T16:41:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"670efca0f488d861e0f98742127d5bd5efb43c20c76f242a15445193de125114","abstract_canon_sha256":"5c97e539e6fd9b98bb9aa6edfae5d0e0e74012c91dae2c11037b3332fba798e7"},"schema_version":"1.0"},"canonical_sha256":"80715a92511d3889b27425030caa3dcfa88245f083faf87e34e7028f0b30c5b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:33.834468Z","signature_b64":"5IRTrVMUxDry0Rp0LTVOc3H1axMl6ozIkK9oCRjIm1FGEGXpIyhdJ2wTC4dWjMQpmkG19TkbhrSdfPd99ouFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80715a92511d3889b27425030caa3dcfa88245f083faf87e34e7028f0b30c5b0","last_reissued_at":"2026-05-18T03:09:33.833749Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:33.833749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2081","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":"2026-05-18T03:09:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"du59X6lUSJysOWQeFeDyFN2eJ4ewT6JlK1vgVUeZP+ruphOZui4g21uWy5irJc/Y1NGLJ2KUfXbZpQ/s1yFPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:04:59.250557Z"},"content_sha256":"07d4a7443791041f4214981025dde96724bd77de1ec55221f93ce234a17e7e8f","schema_version":"1.0","event_id":"sha256:07d4a7443791041f4214981025dde96724bd77de1ec55221f93ce234a17e7e8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QBYVVESRDU4ITMTUEUBQZKR5Z6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation and spectral properties of quantum walks in electric fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A. Alberti, A. H. Werner, C. Cedzich, M. Genske, R. F. Werner, T. Ryb\\'ar","submitted_at":"2013-02-08T16:41:10Z","abstract_excerpt":"We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\\Phi$, e.g., on whether $\\Phi/(2\\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2081","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":"2026-05-18T03:09:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSG0NJduLBqUuvljEsfTadA9JpICPD71yiAMatH6vufjTwYf6csuryoPg4p8dXLmaFKU5iT9u0Ieq6bGPZDpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:04:59.250915Z"},"content_sha256":"0238d93ac30250f2357dd65889c5e3017f3008b5d28b92099fc91d48a3b77b38","schema_version":"1.0","event_id":"sha256:0238d93ac30250f2357dd65889c5e3017f3008b5d28b92099fc91d48a3b77b38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6/bundle.json","state_url":"https://pith.science/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6/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":"2026-06-03T09:04:59Z","links":{"resolver":"https://pith.science/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6","bundle":"https://pith.science/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6/bundle.json","state":"https://pith.science/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBYVVESRDU4ITMTUEUBQZKR5Z6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QBYVVESRDU4ITMTUEUBQZKR5Z6","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":"5c97e539e6fd9b98bb9aa6edfae5d0e0e74012c91dae2c11037b3332fba798e7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-08T16:41:10Z","title_canon_sha256":"670efca0f488d861e0f98742127d5bd5efb43c20c76f242a15445193de125114"},"schema_version":"1.0","source":{"id":"1302.2081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2081","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2081v1","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2081","created_at":"2026-05-18T03:09:33Z"},{"alias_kind":"pith_short_12","alias_value":"QBYVVESRDU4I","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QBYVVESRDU4ITMTU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QBYVVESR","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:0238d93ac30250f2357dd65889c5e3017f3008b5d28b92099fc91d48a3b77b38","target":"graph","created_at":"2026-05-18T03:09:33Z","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 study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\\Phi$, e.g., on whether $\\Phi/(2\\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions ","authors_text":"A. Alberti, A. H. Werner, C. Cedzich, M. Genske, R. F. Werner, T. Ryb\\'ar","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-08T16:41:10Z","title":"Propagation and spectral properties of quantum walks in electric fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2081","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":"sha256:07d4a7443791041f4214981025dde96724bd77de1ec55221f93ce234a17e7e8f","target":"record","created_at":"2026-05-18T03:09:33Z","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":"5c97e539e6fd9b98bb9aa6edfae5d0e0e74012c91dae2c11037b3332fba798e7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-08T16:41:10Z","title_canon_sha256":"670efca0f488d861e0f98742127d5bd5efb43c20c76f242a15445193de125114"},"schema_version":"1.0","source":{"id":"1302.2081","kind":"arxiv","version":1}},"canonical_sha256":"80715a92511d3889b27425030caa3dcfa88245f083faf87e34e7028f0b30c5b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80715a92511d3889b27425030caa3dcfa88245f083faf87e34e7028f0b30c5b0","first_computed_at":"2026-05-18T03:09:33.833749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:33.833749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5IRTrVMUxDry0Rp0LTVOc3H1axMl6ozIkK9oCRjIm1FGEGXpIyhdJ2wTC4dWjMQpmkG19TkbhrSdfPd99ouFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:33.834468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07d4a7443791041f4214981025dde96724bd77de1ec55221f93ce234a17e7e8f","sha256:0238d93ac30250f2357dd65889c5e3017f3008b5d28b92099fc91d48a3b77b38"],"state_sha256":"5e0190a86fa524d76af322555d48a6f4c023480f760e8561c9c5ede3c521f11f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IQxodRR1cNDMGnLimbGN2YA6sI8MDpk3aQryq9v+Pk1rILJOJyzT7HA/6o+n1lCEP7DsbjnsuFEiVjWIfCrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:04:59.252862Z","bundle_sha256":"c87a9bfbb87dd4a180ab8832af540954c89853c782536fe573f40e8d890eda7a"}}