{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZPV4AI627DQPOSXLSHU26FYLFS","short_pith_number":"pith:ZPV4AI62","canonical_record":{"source":{"id":"1209.3917","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-18T12:02:02Z","cross_cats_sorted":[],"title_canon_sha256":"d0ff170e5db989c32d7092d9da318d3c106dde54844bc282d52f32399accf453","abstract_canon_sha256":"347c4b93e66aeaaf03fa4bc1483a4d3f880d4daa2c8a67158880acab2b2a852e"},"schema_version":"1.0"},"canonical_sha256":"cbebc023daf8e0f74aeb91e9af170b2c8e79a4f0ad02be56dc1da3b7384a7ea6","source":{"kind":"arxiv","id":"1209.3917","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3917","created_at":"2026-05-18T03:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3917v3","created_at":"2026-05-18T03:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3917","created_at":"2026-05-18T03:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZPV4AI627DQP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZPV4AI627DQPOSXL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZPV4AI62","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZPV4AI627DQPOSXLSHU26FYLFS","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3917","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-18T12:02:02Z","cross_cats_sorted":[],"title_canon_sha256":"d0ff170e5db989c32d7092d9da318d3c106dde54844bc282d52f32399accf453","abstract_canon_sha256":"347c4b93e66aeaaf03fa4bc1483a4d3f880d4daa2c8a67158880acab2b2a852e"},"schema_version":"1.0"},"canonical_sha256":"cbebc023daf8e0f74aeb91e9af170b2c8e79a4f0ad02be56dc1da3b7384a7ea6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:48.057387Z","signature_b64":"o2oIXGMiQOcntfHLC3pxiliBL2MkfE3A6zXcKWxsaGL3C1DL9ad07372Nw/SKTKVfZ2wjcX2xk421GbwK6m+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbebc023daf8e0f74aeb91e9af170b2c8e79a4f0ad02be56dc1da3b7384a7ea6","last_reissued_at":"2026-05-18T03:10:48.056647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:48.056647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3917","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":"2026-05-18T03:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fg3R/zeMA9eowF0Iq10YBFeBLmKJc7oXz+OAp0ONgc5OfgHqlhufc1vQ9M6x6VjksfdL/DD087IRRKRrCAsRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:33:48.244617Z"},"content_sha256":"5750b95502d58c318257025900366af70b6dc9c221963c90ab5d79f773d26819","schema_version":"1.0","event_id":"sha256:5750b95502d58c318257025900366af70b6dc9c221963c90ab5d79f773d26819"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZPV4AI627DQPOSXLSHU26FYLFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Topology of Quantum Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jamie Vicary","submitted_at":"2012-09-18T12:02:02Z","abstract_excerpt":"We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of correctness via local topological operations, giving for the first time a satisfying high-level explanation for why these procedures work. We also investigate generalizations of these algorithms, providing improved analyses of those already in the literature, and a new generalization of the single-shot Grover algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3917","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":"2026-05-18T03:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btlgTijjL4zq7ZllubhukY/AqZ3OH45PniiUeyFnRqnyNNOG2eDe5XUZnFOQRX5jPmj71r0/fG9c0t+rVroYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:33:48.245204Z"},"content_sha256":"3e5ecaba35d55085fca53eb5fe28c61c60e1ff8ae987fba6c0a59ece39dd8032","schema_version":"1.0","event_id":"sha256:3e5ecaba35d55085fca53eb5fe28c61c60e1ff8ae987fba6c0a59ece39dd8032"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPV4AI627DQPOSXLSHU26FYLFS/bundle.json","state_url":"https://pith.science/pith/ZPV4AI627DQPOSXLSHU26FYLFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPV4AI627DQPOSXLSHU26FYLFS/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":"2026-05-30T12:33:48Z","links":{"resolver":"https://pith.science/pith/ZPV4AI627DQPOSXLSHU26FYLFS","bundle":"https://pith.science/pith/ZPV4AI627DQPOSXLSHU26FYLFS/bundle.json","state":"https://pith.science/pith/ZPV4AI627DQPOSXLSHU26FYLFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPV4AI627DQPOSXLSHU26FYLFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZPV4AI627DQPOSXLSHU26FYLFS","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":"347c4b93e66aeaaf03fa4bc1483a4d3f880d4daa2c8a67158880acab2b2a852e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-18T12:02:02Z","title_canon_sha256":"d0ff170e5db989c32d7092d9da318d3c106dde54844bc282d52f32399accf453"},"schema_version":"1.0","source":{"id":"1209.3917","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3917","created_at":"2026-05-18T03:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3917v3","created_at":"2026-05-18T03:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3917","created_at":"2026-05-18T03:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZPV4AI627DQP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZPV4AI627DQPOSXL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZPV4AI62","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:3e5ecaba35d55085fca53eb5fe28c61c60e1ff8ae987fba6c0a59ece39dd8032","target":"graph","created_at":"2026-05-18T03:10:48Z","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 use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of correctness via local topological operations, giving for the first time a satisfying high-level explanation for why these procedures work. We also investigate generalizations of these algorithms, providing improved analyses of those already in the literature, and a new generalization of the single-shot Grover algorithm.","authors_text":"Jamie Vicary","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-18T12:02:02Z","title":"The Topology of Quantum Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3917","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":"sha256:5750b95502d58c318257025900366af70b6dc9c221963c90ab5d79f773d26819","target":"record","created_at":"2026-05-18T03:10:48Z","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":"347c4b93e66aeaaf03fa4bc1483a4d3f880d4daa2c8a67158880acab2b2a852e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-09-18T12:02:02Z","title_canon_sha256":"d0ff170e5db989c32d7092d9da318d3c106dde54844bc282d52f32399accf453"},"schema_version":"1.0","source":{"id":"1209.3917","kind":"arxiv","version":3}},"canonical_sha256":"cbebc023daf8e0f74aeb91e9af170b2c8e79a4f0ad02be56dc1da3b7384a7ea6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbebc023daf8e0f74aeb91e9af170b2c8e79a4f0ad02be56dc1da3b7384a7ea6","first_computed_at":"2026-05-18T03:10:48.056647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:48.056647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2oIXGMiQOcntfHLC3pxiliBL2MkfE3A6zXcKWxsaGL3C1DL9ad07372Nw/SKTKVfZ2wjcX2xk421GbwK6m+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:48.057387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3917","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5750b95502d58c318257025900366af70b6dc9c221963c90ab5d79f773d26819","sha256:3e5ecaba35d55085fca53eb5fe28c61c60e1ff8ae987fba6c0a59ece39dd8032"],"state_sha256":"5f481a43a3a7b5e2be1f453c0c0c6641b29c3a20becff615fd8e90d8a930c42e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bd8/Ipd9O+arNjTGxKi8IShgqCiVK3GAIqE0B+j74h7s//ocD4WNKNif/YPoq+OKvxdPvz4LJPPnwUsBgeKDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:33:48.247816Z","bundle_sha256":"878c6d3b9ef09e58bb021e6261e27992d5a40cbf0a016bddb6b22792759d6fd1"}}