{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TYS437WFTEWYJ6ABECTPIKAOP2","short_pith_number":"pith:TYS437WF","canonical_record":{"source":{"id":"1606.02139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"d46c00fc82938b7b9f0b70f82f2fd2942194532b21ba1776ee36b13f245bbd6f","abstract_canon_sha256":"2dc182b26cc570ad30bcd2fda657338e5927880e42d43630c5841934fa3d1843"},"schema_version":"1.0"},"canonical_sha256":"9e25cdfec5992d84f80120a6f4280e7e9843eced8577c9218a92e258b9ba5daa","source":{"kind":"arxiv","id":"1606.02139","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02139","created_at":"2026-05-18T00:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02139v2","created_at":"2026-05-18T00:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02139","created_at":"2026-05-18T00:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"TYS437WFTEWY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TYS437WFTEWYJ6AB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TYS437WF","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TYS437WFTEWYJ6ABECTPIKAOP2","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:50:14Z","cross_cats_sorted":[],"title_canon_sha256":"d46c00fc82938b7b9f0b70f82f2fd2942194532b21ba1776ee36b13f245bbd6f","abstract_canon_sha256":"2dc182b26cc570ad30bcd2fda657338e5927880e42d43630c5841934fa3d1843"},"schema_version":"1.0"},"canonical_sha256":"9e25cdfec5992d84f80120a6f4280e7e9843eced8577c9218a92e258b9ba5daa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:00.004859Z","signature_b64":"1AUXvTNFFlkiE5HJyiMK0ugBH8Zh9CDc0EvJfr5nMacz+hHYKHEn3kmPF2Ztz8BkP83elYJXFliUlmu3Uoo7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e25cdfec5992d84f80120a6f4280e7e9843eced8577c9218a92e258b9ba5daa","last_reissued_at":"2026-05-18T00:54:00.004512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:00.004512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02139","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7jrPcOsqOYE0nmq7EIqAnsohFKSgRUCkbaCOoRMO7BcE6hrQlLOe7mZn0oDvIHovxSzRGcbljm7jOR7ZS2e9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:00:17.981993Z"},"content_sha256":"9646b8aa3f4a2474f30c848061d0089ef2600ec25ac51368864e468e690d70e6","schema_version":"1.0","event_id":"sha256:9646b8aa3f4a2474f30c848061d0089ef2600ec25ac51368864e468e690d70e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TYS437WFTEWYJ6ABECTPIKAOP2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full Characterization of Oscillatory Localization of Quantum Walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis, Thomas G. Wong","submitted_at":"2016-06-07T13:50:14Z","abstract_excerpt":"Discrete-time quantum walks are well-known for exhibiting localization, a quantum phenomenon where the walker remains at its initial location with high probability. In companion with a joint Letter, we introduce oscillatory localization, where the walker alternates between two states. The walk is given by the flip-flop shift, which is easily defined on non-lattice graphs, and the Grover coin. Extremely simple examples of the localization exist, such as a walker jumping back and forth between two vertices of the complete graph. We show that only two kinds of states, called flip states and unifo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02139","kind":"arxiv","version":2},"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":"2026-05-18T00:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Y85bnURHIbm9/NwGXmfUDE1OwYJDD41qG6HXdpXqGB/uS0SP9gDJbnKYMspJnmcaBltm8Qsdi3htj9BUPAQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:00:17.982610Z"},"content_sha256":"dab2fadb0a1ba419d2cf506388dd7ab4b2fac875e609a2f85edf292973942cfc","schema_version":"1.0","event_id":"sha256:dab2fadb0a1ba419d2cf506388dd7ab4b2fac875e609a2f85edf292973942cfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYS437WFTEWYJ6ABECTPIKAOP2/bundle.json","state_url":"https://pith.science/pith/TYS437WFTEWYJ6ABECTPIKAOP2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYS437WFTEWYJ6ABECTPIKAOP2/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":"2026-05-25T19:00:17Z","links":{"resolver":"https://pith.science/pith/TYS437WFTEWYJ6ABECTPIKAOP2","bundle":"https://pith.science/pith/TYS437WFTEWYJ6ABECTPIKAOP2/bundle.json","state":"https://pith.science/pith/TYS437WFTEWYJ6ABECTPIKAOP2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYS437WFTEWYJ6ABECTPIKAOP2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TYS437WFTEWYJ6ABECTPIKAOP2","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":"2dc182b26cc570ad30bcd2fda657338e5927880e42d43630c5841934fa3d1843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:50:14Z","title_canon_sha256":"d46c00fc82938b7b9f0b70f82f2fd2942194532b21ba1776ee36b13f245bbd6f"},"schema_version":"1.0","source":{"id":"1606.02139","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02139","created_at":"2026-05-18T00:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02139v2","created_at":"2026-05-18T00:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02139","created_at":"2026-05-18T00:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"TYS437WFTEWY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TYS437WFTEWYJ6AB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TYS437WF","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:dab2fadb0a1ba419d2cf506388dd7ab4b2fac875e609a2f85edf292973942cfc","target":"graph","created_at":"2026-05-18T00:54:00Z","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":"Discrete-time quantum walks are well-known for exhibiting localization, a quantum phenomenon where the walker remains at its initial location with high probability. In companion with a joint Letter, we introduce oscillatory localization, where the walker alternates between two states. The walk is given by the flip-flop shift, which is easily defined on non-lattice graphs, and the Grover coin. Extremely simple examples of the localization exist, such as a walker jumping back and forth between two vertices of the complete graph. We show that only two kinds of states, called flip states and unifo","authors_text":"Andris Ambainis, Jevg\\=enijs Vihrovs, Kri\\v{s}j\\=anis Pr\\=usis, Thomas G. Wong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:50:14Z","title":"Full Characterization of Oscillatory Localization of Quantum Walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02139","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":"sha256:9646b8aa3f4a2474f30c848061d0089ef2600ec25ac51368864e468e690d70e6","target":"record","created_at":"2026-05-18T00:54:00Z","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":"2dc182b26cc570ad30bcd2fda657338e5927880e42d43630c5841934fa3d1843","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-06-07T13:50:14Z","title_canon_sha256":"d46c00fc82938b7b9f0b70f82f2fd2942194532b21ba1776ee36b13f245bbd6f"},"schema_version":"1.0","source":{"id":"1606.02139","kind":"arxiv","version":2}},"canonical_sha256":"9e25cdfec5992d84f80120a6f4280e7e9843eced8577c9218a92e258b9ba5daa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e25cdfec5992d84f80120a6f4280e7e9843eced8577c9218a92e258b9ba5daa","first_computed_at":"2026-05-18T00:54:00.004512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:00.004512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1AUXvTNFFlkiE5HJyiMK0ugBH8Zh9CDc0EvJfr5nMacz+hHYKHEn3kmPF2Ztz8BkP83elYJXFliUlmu3Uoo7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:00.004859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02139","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9646b8aa3f4a2474f30c848061d0089ef2600ec25ac51368864e468e690d70e6","sha256:dab2fadb0a1ba419d2cf506388dd7ab4b2fac875e609a2f85edf292973942cfc"],"state_sha256":"22c27e96344360dcf1a9e1dabefa1773149af8512f66a8cd25e76e406bbfb4fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3MQyzlZM2hqUJyXBoUdAwamXWUOOlyust4X31IqszrCHqO1/4Wp/XMrQnqP8iiHTf4UvjyeF6Y9QQv3z2g7fCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:00:17.985594Z","bundle_sha256":"df4dc950d30596434f9f2db64447ac9c47caf9902bcacb2198b8cd6aaab7c98b"}}