{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BDSTKOSD2L5UIBPVOAGGSQQR6F","short_pith_number":"pith:BDSTKOSD","canonical_record":{"source":{"id":"1210.3279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-11T15:54:33Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"4fdc952b66762a5f80860498962aa93daa1b850c92906ffd9179b20981e734c9","abstract_canon_sha256":"bf50de76512efe7c99e8cb5c78b383011065d6236c7cb017dff4eeb8f4d74ef8"},"schema_version":"1.0"},"canonical_sha256":"08e5353a43d2fb4405f5700c694211f1635342ef9cce584f5ca86651afbf9a56","source":{"kind":"arxiv","id":"1210.3279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3279","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3279v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3279","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"BDSTKOSD2L5U","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BDSTKOSD2L5UIBPV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BDSTKOSD","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BDSTKOSD2L5UIBPVOAGGSQQR6F","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-11T15:54:33Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"4fdc952b66762a5f80860498962aa93daa1b850c92906ffd9179b20981e734c9","abstract_canon_sha256":"bf50de76512efe7c99e8cb5c78b383011065d6236c7cb017dff4eeb8f4d74ef8"},"schema_version":"1.0"},"canonical_sha256":"08e5353a43d2fb4405f5700c694211f1635342ef9cce584f5ca86651afbf9a56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:23.042535Z","signature_b64":"9ljih/QbYIYdpJz+86Rx4pY2U/dGK1KaziQsP/vi+fGVPZum/+hJ9z6xQHHfNQ6SZNzfBzrwYLvcuR76LNnXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08e5353a43d2fb4405f5700c694211f1635342ef9cce584f5ca86651afbf9a56","last_reissued_at":"2026-05-18T03:38:23.041840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:23.041840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3279","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wBrwxvo/FUHWjB0zxgj6teCIMWdqk7pUT4ckU3a4XrgLm4aoW2t1FiAnOcLWMf+y64B1fvBHKUYFLZk7F5ChDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:02:04.221041Z"},"content_sha256":"f179c58f0157beda77cbf45769864b9433c240a3c68925374cada053cbeb17db","schema_version":"1.0","event_id":"sha256:f179c58f0157beda77cbf45769864b9433c240a3c68925374cada053cbeb17db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BDSTKOSD2L5UIBPVOAGGSQQR6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Power of Non-Adaptive Learning Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Aleksandrs Belovs, Ansis Rosmanis","submitted_at":"2012-10-11T15:54:33Z","abstract_excerpt":"We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates in the input string, not the precise values therein.\n  Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for all certificate structures. By this, we mean that there exists a function possessing the certificate structure and such that a learning graph gives an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3279","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":"2026-05-18T03:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVz2+kIfsOfp225nJHbQ9G3rUeuZaDhgbnZF1oU7uWTgTunnH1HhNP+2ywcGlvjeTmzH6Z6BOuOfV5UGWo5/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:02:04.221789Z"},"content_sha256":"248f29b8423b8685c5d48b73c0f19752b1da0b13ae513dd3d21791a52843b654","schema_version":"1.0","event_id":"sha256:248f29b8423b8685c5d48b73c0f19752b1da0b13ae513dd3d21791a52843b654"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F/bundle.json","state_url":"https://pith.science/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F/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":"2026-06-09T06:02:04Z","links":{"resolver":"https://pith.science/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F","bundle":"https://pith.science/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F/bundle.json","state":"https://pith.science/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDSTKOSD2L5UIBPVOAGGSQQR6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BDSTKOSD2L5UIBPVOAGGSQQR6F","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":"bf50de76512efe7c99e8cb5c78b383011065d6236c7cb017dff4eeb8f4d74ef8","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-11T15:54:33Z","title_canon_sha256":"4fdc952b66762a5f80860498962aa93daa1b850c92906ffd9179b20981e734c9"},"schema_version":"1.0","source":{"id":"1210.3279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3279","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3279v2","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3279","created_at":"2026-05-18T03:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"BDSTKOSD2L5U","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"BDSTKOSD2L5UIBPV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"BDSTKOSD","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:248f29b8423b8685c5d48b73c0f19752b1da0b13ae513dd3d21791a52843b654","target":"graph","created_at":"2026-05-18T03:38:23Z","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 notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates in the input string, not the precise values therein.\n  Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for all certificate structures. By this, we mean that there exists a function possessing the certificate structure and such that a learning graph gives an ","authors_text":"Aleksandrs Belovs, Ansis Rosmanis","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-11T15:54:33Z","title":"On the Power of Non-Adaptive Learning Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3279","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:f179c58f0157beda77cbf45769864b9433c240a3c68925374cada053cbeb17db","target":"record","created_at":"2026-05-18T03:38:23Z","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":"bf50de76512efe7c99e8cb5c78b383011065d6236c7cb017dff4eeb8f4d74ef8","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-11T15:54:33Z","title_canon_sha256":"4fdc952b66762a5f80860498962aa93daa1b850c92906ffd9179b20981e734c9"},"schema_version":"1.0","source":{"id":"1210.3279","kind":"arxiv","version":2}},"canonical_sha256":"08e5353a43d2fb4405f5700c694211f1635342ef9cce584f5ca86651afbf9a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08e5353a43d2fb4405f5700c694211f1635342ef9cce584f5ca86651afbf9a56","first_computed_at":"2026-05-18T03:38:23.041840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:23.041840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ljih/QbYIYdpJz+86Rx4pY2U/dGK1KaziQsP/vi+fGVPZum/+hJ9z6xQHHfNQ6SZNzfBzrwYLvcuR76LNnXAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:23.042535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f179c58f0157beda77cbf45769864b9433c240a3c68925374cada053cbeb17db","sha256:248f29b8423b8685c5d48b73c0f19752b1da0b13ae513dd3d21791a52843b654"],"state_sha256":"724c176f018ea10cd6e417cf3fb51dc9227422d3a61a6562d5d1ccb2c8a6861a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWLOMOasKSJaIzO418HdTIl8ZYPF8VJXvMYePJjXY3KrdQCoPLYNG/Knl0rUwv+YWBJQLIpbojewoe+OgpVGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:02:04.226257Z","bundle_sha256":"2ebf23dceef41995b9d9c9f0f1cff6282f4ddc67c7894e77a3bdc4cf964f203d"}}