{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AGQSJFCPQE5PFG3ZJ2ENBCPMFS","short_pith_number":"pith:AGQSJFCP","canonical_record":{"source":{"id":"1009.2019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-09-10T14:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"87350f6c18213aa8743a8e52d83117db4b74081dba971c89bcdf747bc656decf","abstract_canon_sha256":"c87619d464e56192e8bf4aaeef5cbcff932c317a091165cfbbff2f70c29c5a92"},"schema_version":"1.0"},"canonical_sha256":"01a124944f813af29b794e88d089ec2c8d95afaf5ed497dae2b955e835c5f381","source":{"kind":"arxiv","id":"1009.2019","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2019","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2019v2","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2019","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"AGQSJFCPQE5P","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AGQSJFCPQE5PFG3Z","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AGQSJFCP","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AGQSJFCPQE5PFG3ZJ2ENBCPMFS","target":"record","payload":{"canonical_record":{"source":{"id":"1009.2019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-09-10T14:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"87350f6c18213aa8743a8e52d83117db4b74081dba971c89bcdf747bc656decf","abstract_canon_sha256":"c87619d464e56192e8bf4aaeef5cbcff932c317a091165cfbbff2f70c29c5a92"},"schema_version":"1.0"},"canonical_sha256":"01a124944f813af29b794e88d089ec2c8d95afaf5ed497dae2b955e835c5f381","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:47.975748Z","signature_b64":"NbvTFIdQmlsnAEFhnluSAyX79+DyknqP2wPtV2UEou7M6sSbfoJlC/YMBJKO4Q5wEWHuYWPc4Rl783tsWHdQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01a124944f813af29b794e88d089ec2c8d95afaf5ed497dae2b955e835c5f381","last_reissued_at":"2026-05-18T04:23:47.975038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:47.975038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.2019","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":"2026-05-18T04:23:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnmPZEBwGl7aQUFoW67KNgj7sAdzIq+tLkt2oGi+L33Q1DEwzsYETxatJV2eTE++zYfnKp1xYvX/EaAU4WlyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:20:25.792581Z"},"content_sha256":"1d9c16a6099bcb76db5f79835d545979c7608e7cb45c71d95763a22132849692","schema_version":"1.0","event_id":"sha256:1d9c16a6099bcb76db5f79835d545979c7608e7cb45c71d95763a22132849692"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AGQSJFCPQE5PFG3ZJ2ENBCPMFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic evolution of quantum walks with random coin","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Albert H. Werner, Andre Ahlbrecht, Holger Vogts, Reinhard F. Werner","submitted_at":"2010-09-10T14:19:21Z","abstract_excerpt":"We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any unitary operator, which commutes with translations, and couples only sites at a finite distance from each other. For example, a single step of the walk could be composed of any finite succession of different shift and coin operations in the usual sense, with any lattice dimension and coin dimension. We find ballistic scaling, and establish a direct method for com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2019","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":"2026-05-18T04:23:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z42qJwU1YAKW/Wioe66Nut4huQCx2lUleC/3Qme7jCenUgksghr0NoMHoDZzZj59oBFDWbcIN1rwF4RJe6zvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:20:25.793157Z"},"content_sha256":"e92a22c4d61107c1cb3f210f0e9eb67d96fee3655a3231d2e8e6910d8179580c","schema_version":"1.0","event_id":"sha256:e92a22c4d61107c1cb3f210f0e9eb67d96fee3655a3231d2e8e6910d8179580c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS/bundle.json","state_url":"https://pith.science/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS/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":"2026-05-26T02:20:25Z","links":{"resolver":"https://pith.science/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS","bundle":"https://pith.science/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS/bundle.json","state":"https://pith.science/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGQSJFCPQE5PFG3ZJ2ENBCPMFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AGQSJFCPQE5PFG3ZJ2ENBCPMFS","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":"c87619d464e56192e8bf4aaeef5cbcff932c317a091165cfbbff2f70c29c5a92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-09-10T14:19:21Z","title_canon_sha256":"87350f6c18213aa8743a8e52d83117db4b74081dba971c89bcdf747bc656decf"},"schema_version":"1.0","source":{"id":"1009.2019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2019","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2019v2","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2019","created_at":"2026-05-18T04:23:47Z"},{"alias_kind":"pith_short_12","alias_value":"AGQSJFCPQE5P","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AGQSJFCPQE5PFG3Z","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AGQSJFCP","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e92a22c4d61107c1cb3f210f0e9eb67d96fee3655a3231d2e8e6910d8179580c","target":"graph","created_at":"2026-05-18T04:23:47Z","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 the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any unitary operator, which commutes with translations, and couples only sites at a finite distance from each other. For example, a single step of the walk could be composed of any finite succession of different shift and coin operations in the usual sense, with any lattice dimension and coin dimension. We find ballistic scaling, and establish a direct method for com","authors_text":"Albert H. Werner, Andre Ahlbrecht, Holger Vogts, Reinhard F. Werner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-09-10T14:19:21Z","title":"Asymptotic evolution of quantum walks with random coin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2019","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":"sha256:1d9c16a6099bcb76db5f79835d545979c7608e7cb45c71d95763a22132849692","target":"record","created_at":"2026-05-18T04:23:47Z","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":"c87619d464e56192e8bf4aaeef5cbcff932c317a091165cfbbff2f70c29c5a92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-09-10T14:19:21Z","title_canon_sha256":"87350f6c18213aa8743a8e52d83117db4b74081dba971c89bcdf747bc656decf"},"schema_version":"1.0","source":{"id":"1009.2019","kind":"arxiv","version":2}},"canonical_sha256":"01a124944f813af29b794e88d089ec2c8d95afaf5ed497dae2b955e835c5f381","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01a124944f813af29b794e88d089ec2c8d95afaf5ed497dae2b955e835c5f381","first_computed_at":"2026-05-18T04:23:47.975038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:47.975038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbvTFIdQmlsnAEFhnluSAyX79+DyknqP2wPtV2UEou7M6sSbfoJlC/YMBJKO4Q5wEWHuYWPc4Rl783tsWHdQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:47.975748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d9c16a6099bcb76db5f79835d545979c7608e7cb45c71d95763a22132849692","sha256:e92a22c4d61107c1cb3f210f0e9eb67d96fee3655a3231d2e8e6910d8179580c"],"state_sha256":"1055911ab17669e6cc67bea8696d322b91d06d69d98d1ddf9cc5d2d6a68e3f4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zy/ilkrabeMFQKY4+v7ER5qpSk+AS53jzq3Agflu1wJO9zEwArMul4Ci47PTWw/G2qf5s9/G16gh5RY9BLMSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:20:25.796033Z","bundle_sha256":"f3dbb2db230a0c60d10d0084be6015bb8f45dd007c224003472057c236243358"}}