{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NRJKX5RWT73U2LRINR6YBF6ZY3","short_pith_number":"pith:NRJKX5RW","canonical_record":{"source":{"id":"1210.1014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T07:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"10554febfe97f7100c446d9e8ea43d6057b5d282b4089af136eb33b2eea7ee3c","abstract_canon_sha256":"2ed25dc045f3356e8c55324e7b48dbd7544f55c524122153901e66086bc5a16c"},"schema_version":"1.0"},"canonical_sha256":"6c52abf6369ff74d2e286c7d8097d9c6f4e24eb6f6ea3c949fa1b3d1ea92892f","source":{"kind":"arxiv","id":"1210.1014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1014","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1014v1","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1014","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"NRJKX5RWT73U","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NRJKX5RWT73U2LRI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NRJKX5RW","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NRJKX5RWT73U2LRINR6YBF6ZY3","target":"record","payload":{"canonical_record":{"source":{"id":"1210.1014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T07:57:01Z","cross_cats_sorted":[],"title_canon_sha256":"10554febfe97f7100c446d9e8ea43d6057b5d282b4089af136eb33b2eea7ee3c","abstract_canon_sha256":"2ed25dc045f3356e8c55324e7b48dbd7544f55c524122153901e66086bc5a16c"},"schema_version":"1.0"},"canonical_sha256":"6c52abf6369ff74d2e286c7d8097d9c6f4e24eb6f6ea3c949fa1b3d1ea92892f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:13.070037Z","signature_b64":"+acGi2wtzQKKsQVr73Xn3qdy5tNOdqPziFftErtv8/jT6ZGp7mySr4ne0KV7/U985hJuRzVp7N9ll9gR/NGxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c52abf6369ff74d2e286c7d8097d9c6f4e24eb6f6ea3c949fa1b3d1ea92892f","last_reissued_at":"2026-05-18T03:44:13.069562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:13.069562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.1014","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":"2026-05-18T03:44:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xV7dzvlriJ0fAMgqRMFQRfUc+93B48peeRXXBbqWPzwrDjT/hSRkwFoxK7fKVwYaWDeCle0TawZWSq4lZZHeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:01:39.060345Z"},"content_sha256":"955a4452b3f9299fc4b0798201028294d8ca0047c6ce0087c5e19925d156a559","schema_version":"1.0","event_id":"sha256:955a4452b3f9299fc4b0798201028294d8ca0047c6ce0087c5e19925d156a559"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NRJKX5RWT73U2LRINR6YBF6ZY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Quantum Query Algorithms for Triangle Finding and Associativity Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Frederic Magniez, Miklos Santha, Troy Lee","submitted_at":"2012-10-03T07:57:01Z","abstract_excerpt":"We show that the quantum query complexity of detecting if an $n$-vertex graph contains a triangle is $O(n^{9/7})$. This improves the previous best algorithm of Belovs making $O(n^{35/27})$ queries. For the problem of determining if an operation $\\circ : S \\times S \\rightarrow S$ is associative, we give an algorithm making $O(|S|^{10/7})$ queries, the first improvement to the trivial $O(|S|^{3/2})$ application of Grover search.\n  Our algorithms are designed using the learning graph framework of Belovs. We give a family of algorithms for detecting constant-sized subgraphs, which can possibly be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1014","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":"2026-05-18T03:44:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DbImwwh4yCwPs56ISMfBClydQE0F4AJ4FSb5PGvPyimtW8rUVNmnbEK/jB2PDANqr4+Kzv2ibFHetB8ccFwSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:01:39.060929Z"},"content_sha256":"27d333effe0971633b925a72186fc6717f97fa6e4085ee02d7cb70dee8af2d6e","schema_version":"1.0","event_id":"sha256:27d333effe0971633b925a72186fc6717f97fa6e4085ee02d7cb70dee8af2d6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRJKX5RWT73U2LRINR6YBF6ZY3/bundle.json","state_url":"https://pith.science/pith/NRJKX5RWT73U2LRINR6YBF6ZY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRJKX5RWT73U2LRINR6YBF6ZY3/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":"2026-06-07T05:01:39Z","links":{"resolver":"https://pith.science/pith/NRJKX5RWT73U2LRINR6YBF6ZY3","bundle":"https://pith.science/pith/NRJKX5RWT73U2LRINR6YBF6ZY3/bundle.json","state":"https://pith.science/pith/NRJKX5RWT73U2LRINR6YBF6ZY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRJKX5RWT73U2LRINR6YBF6ZY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NRJKX5RWT73U2LRINR6YBF6ZY3","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":"2ed25dc045f3356e8c55324e7b48dbd7544f55c524122153901e66086bc5a16c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T07:57:01Z","title_canon_sha256":"10554febfe97f7100c446d9e8ea43d6057b5d282b4089af136eb33b2eea7ee3c"},"schema_version":"1.0","source":{"id":"1210.1014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.1014","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.1014v1","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1014","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"NRJKX5RWT73U","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NRJKX5RWT73U2LRI","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NRJKX5RW","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:27d333effe0971633b925a72186fc6717f97fa6e4085ee02d7cb70dee8af2d6e","target":"graph","created_at":"2026-05-18T03:44:13Z","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 show that the quantum query complexity of detecting if an $n$-vertex graph contains a triangle is $O(n^{9/7})$. This improves the previous best algorithm of Belovs making $O(n^{35/27})$ queries. For the problem of determining if an operation $\\circ : S \\times S \\rightarrow S$ is associative, we give an algorithm making $O(|S|^{10/7})$ queries, the first improvement to the trivial $O(|S|^{3/2})$ application of Grover search.\n  Our algorithms are designed using the learning graph framework of Belovs. We give a family of algorithms for detecting constant-sized subgraphs, which can possibly be ","authors_text":"Frederic Magniez, Miklos Santha, Troy Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T07:57:01Z","title":"Improved Quantum Query Algorithms for Triangle Finding and Associativity Testing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1014","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":"sha256:955a4452b3f9299fc4b0798201028294d8ca0047c6ce0087c5e19925d156a559","target":"record","created_at":"2026-05-18T03:44:13Z","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":"2ed25dc045f3356e8c55324e7b48dbd7544f55c524122153901e66086bc5a16c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-03T07:57:01Z","title_canon_sha256":"10554febfe97f7100c446d9e8ea43d6057b5d282b4089af136eb33b2eea7ee3c"},"schema_version":"1.0","source":{"id":"1210.1014","kind":"arxiv","version":1}},"canonical_sha256":"6c52abf6369ff74d2e286c7d8097d9c6f4e24eb6f6ea3c949fa1b3d1ea92892f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c52abf6369ff74d2e286c7d8097d9c6f4e24eb6f6ea3c949fa1b3d1ea92892f","first_computed_at":"2026-05-18T03:44:13.069562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:13.069562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+acGi2wtzQKKsQVr73Xn3qdy5tNOdqPziFftErtv8/jT6ZGp7mySr4ne0KV7/U985hJuRzVp7N9ll9gR/NGxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:13.070037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.1014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:955a4452b3f9299fc4b0798201028294d8ca0047c6ce0087c5e19925d156a559","sha256:27d333effe0971633b925a72186fc6717f97fa6e4085ee02d7cb70dee8af2d6e"],"state_sha256":"936ff8ef4bbf69ac1c6636444170576c7264c0a9b6952ab6e50c136013a76647"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCzgGhxFEcBd5yK3Fzi3aYqW4Oxx2Erlry+YHeT0jILxB7p87bUCf5q6DeN2FyISQ1nP+QV9XQflOpzRo8yzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:01:39.064080Z","bundle_sha256":"77149383e7ed0e9a4e060f898e631d5ebca1475795e2f8865e9c6aac09571bac"}}