{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YJAMKYGNRYIKOCZX42RR3VD2UW","short_pith_number":"pith:YJAMKYGN","canonical_record":{"source":{"id":"1203.2603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-12T19:59:08Z","cross_cats_sorted":[],"title_canon_sha256":"e0dd6090d98e05208d5274221f267d7a6416b5384f7a217094b0ea92d9094a50","abstract_canon_sha256":"ad12dedbc204f09d6b6d7113a0f990697b7cdfc835af3f722587fc3a64af95ac"},"schema_version":"1.0"},"canonical_sha256":"c240c560cd8e10a70b37e6a31dd47aa5828c2e0a85fc72bd3c11c693d65fac84","source":{"kind":"arxiv","id":"1203.2603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2603","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2603v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2603","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"YJAMKYGNRYIK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YJAMKYGNRYIKOCZX","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YJAMKYGN","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YJAMKYGNRYIKOCZX42RR3VD2UW","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-12T19:59:08Z","cross_cats_sorted":[],"title_canon_sha256":"e0dd6090d98e05208d5274221f267d7a6416b5384f7a217094b0ea92d9094a50","abstract_canon_sha256":"ad12dedbc204f09d6b6d7113a0f990697b7cdfc835af3f722587fc3a64af95ac"},"schema_version":"1.0"},"canonical_sha256":"c240c560cd8e10a70b37e6a31dd47aa5828c2e0a85fc72bd3c11c693d65fac84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.347956Z","signature_b64":"uRkHJmIYthfEclJCdsCHM39t1kUttvHNikf4zmsK3xpaDhPJuBS+9Dc1AZdWvCNO8NzCv2F0yD3tzUFn1z6HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c240c560cd8e10a70b37e6a31dd47aa5828c2e0a85fc72bd3c11c693d65fac84","last_reissued_at":"2026-05-18T03:40:26.347522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.347522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2603","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehsNvkkZVs2l68LUG2WPYElOglSj9LxlzmN/AWgPPwvmp3l3HNZ6sqoawxuHaYRFbscqDDK3Vzc+m9DyM5+hDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:14:34.391482Z"},"content_sha256":"e5880cb1b3996ebc1d75a9ab90b0bd7f29823441fde66a6b367ce74fefd4c98b","schema_version":"1.0","event_id":"sha256:e5880cb1b3996ebc1d75a9ab90b0bd7f29823441fde66a6b367ce74fefd4c98b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YJAMKYGNRYIKOCZX42RR3VD2UW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Span programs and quantum algorithms for st-connectivity and claw detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Aleksandrs Belovs, Ben W. Reichardt","submitted_at":"2012-03-12T19:59:08Z","abstract_excerpt":"We introduce a span program that decides st-connectivity, and generalize the span program to develop quantum algorithms for several graph problems. First, we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries to the n x n adjacency matrix to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected. We also show that if T is a path, a star with two subdivided legs, or a subdivision of a claw, its presence as a subgraph in the input graph G can be detected with O(n) quantum queries to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2603","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":"2026-05-18T03:40:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXTtZ5zyWbkex0Px1fQ0X4/tLVIU27CNURrfcKGcX3asou5j6PGxKt+NivaJr63NMLHKh50ETFVBYR1yL6NYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:14:34.392131Z"},"content_sha256":"0c9478c0475d9bd5ca3ef2760356e2c730390ae2420672dde17ab5f84ecb2b1d","schema_version":"1.0","event_id":"sha256:0c9478c0475d9bd5ca3ef2760356e2c730390ae2420672dde17ab5f84ecb2b1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJAMKYGNRYIKOCZX42RR3VD2UW/bundle.json","state_url":"https://pith.science/pith/YJAMKYGNRYIKOCZX42RR3VD2UW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJAMKYGNRYIKOCZX42RR3VD2UW/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":"2026-06-09T06:14:34Z","links":{"resolver":"https://pith.science/pith/YJAMKYGNRYIKOCZX42RR3VD2UW","bundle":"https://pith.science/pith/YJAMKYGNRYIKOCZX42RR3VD2UW/bundle.json","state":"https://pith.science/pith/YJAMKYGNRYIKOCZX42RR3VD2UW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJAMKYGNRYIKOCZX42RR3VD2UW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YJAMKYGNRYIKOCZX42RR3VD2UW","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":"ad12dedbc204f09d6b6d7113a0f990697b7cdfc835af3f722587fc3a64af95ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-12T19:59:08Z","title_canon_sha256":"e0dd6090d98e05208d5274221f267d7a6416b5384f7a217094b0ea92d9094a50"},"schema_version":"1.0","source":{"id":"1203.2603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2603","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2603v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2603","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"YJAMKYGNRYIK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YJAMKYGNRYIKOCZX","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YJAMKYGN","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:0c9478c0475d9bd5ca3ef2760356e2c730390ae2420672dde17ab5f84ecb2b1d","target":"graph","created_at":"2026-05-18T03:40:26Z","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 introduce a span program that decides st-connectivity, and generalize the span program to develop quantum algorithms for several graph problems. First, we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries to the n x n adjacency matrix to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected. We also show that if T is a path, a star with two subdivided legs, or a subdivision of a claw, its presence as a subgraph in the input graph G can be detected with O(n) quantum queries to t","authors_text":"Aleksandrs Belovs, Ben W. Reichardt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-12T19:59:08Z","title":"Span programs and quantum algorithms for st-connectivity and claw detection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2603","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:e5880cb1b3996ebc1d75a9ab90b0bd7f29823441fde66a6b367ce74fefd4c98b","target":"record","created_at":"2026-05-18T03:40:26Z","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":"ad12dedbc204f09d6b6d7113a0f990697b7cdfc835af3f722587fc3a64af95ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-03-12T19:59:08Z","title_canon_sha256":"e0dd6090d98e05208d5274221f267d7a6416b5384f7a217094b0ea92d9094a50"},"schema_version":"1.0","source":{"id":"1203.2603","kind":"arxiv","version":1}},"canonical_sha256":"c240c560cd8e10a70b37e6a31dd47aa5828c2e0a85fc72bd3c11c693d65fac84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c240c560cd8e10a70b37e6a31dd47aa5828c2e0a85fc72bd3c11c693d65fac84","first_computed_at":"2026-05-18T03:40:26.347522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.347522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uRkHJmIYthfEclJCdsCHM39t1kUttvHNikf4zmsK3xpaDhPJuBS+9Dc1AZdWvCNO8NzCv2F0yD3tzUFn1z6HDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.347956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5880cb1b3996ebc1d75a9ab90b0bd7f29823441fde66a6b367ce74fefd4c98b","sha256:0c9478c0475d9bd5ca3ef2760356e2c730390ae2420672dde17ab5f84ecb2b1d"],"state_sha256":"2d6bf72d680bcde3ae7d6e5e9b9cf7650db93c7135c7ad91f0f9e256331eb919"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fYEaYFNhLUW6PR29pm1vCS1E7Gei+cV37S2t8SJF+JHeLb/XL3EuRVploVY6V9cBQ7S0enUe7LFUgP33kX0CDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:14:34.395747Z","bundle_sha256":"9188edb67dbea2f58faa0e25ba202f08b1f9e6be08223f38ee18776a0728ec3f"}}