{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AHQWYKAVFKH73KMLI7NREDI72I","short_pith_number":"pith:AHQWYKAV","canonical_record":{"source":{"id":"1207.3614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-16T09:56:31Z","cross_cats_sorted":[],"title_canon_sha256":"6b185cdcc8d5a39054d016d0b504174b887a57b3117075a58dfcbc834f945cd1","abstract_canon_sha256":"31dab6e2f388869a9d0b0377fe57b56049f618396892cd00c03364fd554c53c9"},"schema_version":"1.0"},"canonical_sha256":"01e16c28152a8ffda98b47db120d1fd22ab9eae6e9a3c596b088ffdff4742bbb","source":{"kind":"arxiv","id":"1207.3614","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3614","created_at":"2026-05-18T01:56:18Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3614v3","created_at":"2026-05-18T01:56:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3614","created_at":"2026-05-18T01:56:18Z"},{"alias_kind":"pith_short_12","alias_value":"AHQWYKAVFKH7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHQWYKAVFKH73KML","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHQWYKAV","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AHQWYKAVFKH73KMLI7NREDI72I","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-16T09:56:31Z","cross_cats_sorted":[],"title_canon_sha256":"6b185cdcc8d5a39054d016d0b504174b887a57b3117075a58dfcbc834f945cd1","abstract_canon_sha256":"31dab6e2f388869a9d0b0377fe57b56049f618396892cd00c03364fd554c53c9"},"schema_version":"1.0"},"canonical_sha256":"01e16c28152a8ffda98b47db120d1fd22ab9eae6e9a3c596b088ffdff4742bbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:18.189385Z","signature_b64":"+75DqeL4kYAv8qAqt6F27SKTrHH6qHfiaCGjOSG9HquJsrQcNbsF6ZApKtQLwMJsZLTb+zFdgA7KYDT3EKDhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01e16c28152a8ffda98b47db120d1fd22ab9eae6e9a3c596b088ffdff4742bbb","last_reissued_at":"2026-05-18T01:56:18.188846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:18.188846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3614","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:56:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmiIMuxj9UFgklOMsGFVgBs8sA1fhvgVf+P92+ESChrYtmWsWlV930Hd1tH8cDLpCW44wqxpCTImcjbtWIDcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:20:07.437348Z"},"content_sha256":"65b89bcafc5d04ba4ac42cc28bfd7afd2337f09ed77db060e65b430fe4d6483b","schema_version":"1.0","event_id":"sha256:65b89bcafc5d04ba4ac42cc28bfd7afd2337f09ed77db060e65b430fe4d6483b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AHQWYKAVFKH73KMLI7NREDI72I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"N-dimensional alternate coined quantum walks from a dispersion relation perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Carlo Di Franco, Eugenio Rold\\'an, Fernando Silva, Germ\\'an J. de Valc\\'arcel","submitted_at":"2012-07-16T09:56:31Z","abstract_excerpt":"We propose an alternative definition of an N-dimensional coined quantum walk by generalizing a recent proposal [Di Franco et al., Phys. Rev. Lett. 106, 080502 (2011)]. This N-dimensional alternate quantum walk, AQW_N, in contrast with the standard definition of the N-dimensional quantum walk, QW_N, requires only a coin-qubit. We discuss the quantum diffusion properties of AQW_2 and AQW_3 by analyzing their dispersion relations that reveal, in particular, the existence of diabolical points. This allows us to highlight interesting similarities with other well known physical phenomena. We also de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3614","kind":"arxiv","version":3},"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":"2026-05-18T01:56:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2fYjDhhfRmfFZv3a2PGhTvUJqRu84gJ8Y6YcNCj5IP4+V3Tf/4xODzlE4I4EdAfjPjldMty0Ro9cPatOHdbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:20:07.438037Z"},"content_sha256":"9bfef88e61af267d548a22c32b6ff1876887da343b9f6b89c3185f91a8c1ec80","schema_version":"1.0","event_id":"sha256:9bfef88e61af267d548a22c32b6ff1876887da343b9f6b89c3185f91a8c1ec80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHQWYKAVFKH73KMLI7NREDI72I/bundle.json","state_url":"https://pith.science/pith/AHQWYKAVFKH73KMLI7NREDI72I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHQWYKAVFKH73KMLI7NREDI72I/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":"2026-05-31T04:20:07Z","links":{"resolver":"https://pith.science/pith/AHQWYKAVFKH73KMLI7NREDI72I","bundle":"https://pith.science/pith/AHQWYKAVFKH73KMLI7NREDI72I/bundle.json","state":"https://pith.science/pith/AHQWYKAVFKH73KMLI7NREDI72I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHQWYKAVFKH73KMLI7NREDI72I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AHQWYKAVFKH73KMLI7NREDI72I","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":"31dab6e2f388869a9d0b0377fe57b56049f618396892cd00c03364fd554c53c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-16T09:56:31Z","title_canon_sha256":"6b185cdcc8d5a39054d016d0b504174b887a57b3117075a58dfcbc834f945cd1"},"schema_version":"1.0","source":{"id":"1207.3614","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3614","created_at":"2026-05-18T01:56:18Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3614v3","created_at":"2026-05-18T01:56:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3614","created_at":"2026-05-18T01:56:18Z"},{"alias_kind":"pith_short_12","alias_value":"AHQWYKAVFKH7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHQWYKAVFKH73KML","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHQWYKAV","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:9bfef88e61af267d548a22c32b6ff1876887da343b9f6b89c3185f91a8c1ec80","target":"graph","created_at":"2026-05-18T01:56:18Z","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 an alternative definition of an N-dimensional coined quantum walk by generalizing a recent proposal [Di Franco et al., Phys. Rev. Lett. 106, 080502 (2011)]. This N-dimensional alternate quantum walk, AQW_N, in contrast with the standard definition of the N-dimensional quantum walk, QW_N, requires only a coin-qubit. We discuss the quantum diffusion properties of AQW_2 and AQW_3 by analyzing their dispersion relations that reveal, in particular, the existence of diabolical points. This allows us to highlight interesting similarities with other well known physical phenomena. We also de","authors_text":"Carlo Di Franco, Eugenio Rold\\'an, Fernando Silva, Germ\\'an J. de Valc\\'arcel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-16T09:56:31Z","title":"N-dimensional alternate coined quantum walks from a dispersion relation perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3614","kind":"arxiv","version":3},"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":"sha256:65b89bcafc5d04ba4ac42cc28bfd7afd2337f09ed77db060e65b430fe4d6483b","target":"record","created_at":"2026-05-18T01:56:18Z","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":"31dab6e2f388869a9d0b0377fe57b56049f618396892cd00c03364fd554c53c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-16T09:56:31Z","title_canon_sha256":"6b185cdcc8d5a39054d016d0b504174b887a57b3117075a58dfcbc834f945cd1"},"schema_version":"1.0","source":{"id":"1207.3614","kind":"arxiv","version":3}},"canonical_sha256":"01e16c28152a8ffda98b47db120d1fd22ab9eae6e9a3c596b088ffdff4742bbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01e16c28152a8ffda98b47db120d1fd22ab9eae6e9a3c596b088ffdff4742bbb","first_computed_at":"2026-05-18T01:56:18.188846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:18.188846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+75DqeL4kYAv8qAqt6F27SKTrHH6qHfiaCGjOSG9HquJsrQcNbsF6ZApKtQLwMJsZLTb+zFdgA7KYDT3EKDhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:18.189385Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3614","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65b89bcafc5d04ba4ac42cc28bfd7afd2337f09ed77db060e65b430fe4d6483b","sha256:9bfef88e61af267d548a22c32b6ff1876887da343b9f6b89c3185f91a8c1ec80"],"state_sha256":"edcfdfa6c9cad6805bad1e9a837f50aac7e18ae04824adb4b739ac5c03607465"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZipAci8J5F+guRR6atD2rq6ffex3KUueK8Ymw2sXhzpmUXfD6HDb6vbRSKt2SFgabPBDodjUXYkM2dZVpWEhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:20:07.441635Z","bundle_sha256":"2dc566e9cabdcdcb087532cbd2346c6f7fd0380266e4f73d5e260b61084982df"}}