{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2QD75LLYGGT4T4S2YEMSPWZHMD","short_pith_number":"pith:2QD75LLY","canonical_record":{"source":{"id":"1608.02198","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-07T09:35:44Z","cross_cats_sorted":["cs.CC","stat.ML"],"title_canon_sha256":"9a1d2275817a71c494ec6fcf8d6cf319a4333f01f11c5f5ead74b8833d8445b2","abstract_canon_sha256":"ae5d9a063d63b7ec7b1261c99a124df19dcb82fd8bada9793db9c6c22453b310"},"schema_version":"1.0"},"canonical_sha256":"d407fead7831a7c9f25ac11927db2760db081ae21f78c802289b26d212ac7598","source":{"kind":"arxiv","id":"1608.02198","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02198","created_at":"2026-05-18T00:46:20Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02198v3","created_at":"2026-05-18T00:46:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02198","created_at":"2026-05-18T00:46:20Z"},{"alias_kind":"pith_short_12","alias_value":"2QD75LLYGGT4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2QD75LLYGGT4T4S2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2QD75LLY","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2QD75LLYGGT4T4S2YEMSPWZHMD","target":"record","payload":{"canonical_record":{"source":{"id":"1608.02198","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-07T09:35:44Z","cross_cats_sorted":["cs.CC","stat.ML"],"title_canon_sha256":"9a1d2275817a71c494ec6fcf8d6cf319a4333f01f11c5f5ead74b8833d8445b2","abstract_canon_sha256":"ae5d9a063d63b7ec7b1261c99a124df19dcb82fd8bada9793db9c6c22453b310"},"schema_version":"1.0"},"canonical_sha256":"d407fead7831a7c9f25ac11927db2760db081ae21f78c802289b26d212ac7598","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:20.837128Z","signature_b64":"bGF5FIXdoqkM0NvQy32FeZgqAs5fjFTXWoOqEK+IUDcsLk1tW6E9Orko6Ni2RgWqOzN7n7tFrT/gpfmxJeObDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d407fead7831a7c9f25ac11927db2760db081ae21f78c802289b26d212ac7598","last_reissued_at":"2026-05-18T00:46:20.836769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:20.836769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.02198","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":"2026-05-18T00:46:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+BTSyK6wd62Uby5ATizii9eHQuJFoA8JWAFuy0uxZI09jU42Ie40bnJ0ME5HHSXtygJ+XfemgWkt0ebx5IVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:37:03.800994Z"},"content_sha256":"8ab020051abdd7fb82fbe35204d85921f0172d874d7dbd4ca8412f08ade72f0a","schema_version":"1.0","event_id":"sha256:8ab020051abdd7fb82fbe35204d85921f0172d874d7dbd4ca8412f08ade72f0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2QD75LLYGGT4T4S2YEMSPWZHMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A General Characterization of the Statistical Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Vitaly Feldman","submitted_at":"2016-08-07T09:35:44Z","abstract_excerpt":"Statistical query (SQ) algorithms are algorithms that have access to an {\\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\\phi:X \\rightarrow [-1,1]$, the oracle returns an estimate of ${\\bf E}_{ x\\sim D}[\\phi(x)]$ within some tolerance $\\tau_\\phi$ that roughly corresponds to the number of samples.\n  In this work we demonstrate that the complexity of solving general problems over distributions using SQ algorithms can be captured by a relatively simple notion of statistical dimension that we introduce. SQ algorithms capture a broad spectr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02198","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":"2026-05-18T00:46:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyUdwmsW+NVwI1RoZV4DBOafdZy7XqxUkDfxuRcwdBHhoju6eKlX/XauHt71bzbv8EcwbjBToDAcQZDjZIzbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:37:03.801670Z"},"content_sha256":"1561246aadb1abda9d3c8475a5c43b2256a0fd3134275a82b7d29f9a159312dd","schema_version":"1.0","event_id":"sha256:1561246aadb1abda9d3c8475a5c43b2256a0fd3134275a82b7d29f9a159312dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2QD75LLYGGT4T4S2YEMSPWZHMD/bundle.json","state_url":"https://pith.science/pith/2QD75LLYGGT4T4S2YEMSPWZHMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2QD75LLYGGT4T4S2YEMSPWZHMD/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":"2026-05-27T12:37:03Z","links":{"resolver":"https://pith.science/pith/2QD75LLYGGT4T4S2YEMSPWZHMD","bundle":"https://pith.science/pith/2QD75LLYGGT4T4S2YEMSPWZHMD/bundle.json","state":"https://pith.science/pith/2QD75LLYGGT4T4S2YEMSPWZHMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2QD75LLYGGT4T4S2YEMSPWZHMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2QD75LLYGGT4T4S2YEMSPWZHMD","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":"ae5d9a063d63b7ec7b1261c99a124df19dcb82fd8bada9793db9c6c22453b310","cross_cats_sorted":["cs.CC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-07T09:35:44Z","title_canon_sha256":"9a1d2275817a71c494ec6fcf8d6cf319a4333f01f11c5f5ead74b8833d8445b2"},"schema_version":"1.0","source":{"id":"1608.02198","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02198","created_at":"2026-05-18T00:46:20Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02198v3","created_at":"2026-05-18T00:46:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02198","created_at":"2026-05-18T00:46:20Z"},{"alias_kind":"pith_short_12","alias_value":"2QD75LLYGGT4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2QD75LLYGGT4T4S2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2QD75LLY","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:1561246aadb1abda9d3c8475a5c43b2256a0fd3134275a82b7d29f9a159312dd","target":"graph","created_at":"2026-05-18T00:46:20Z","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":"Statistical query (SQ) algorithms are algorithms that have access to an {\\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\\phi:X \\rightarrow [-1,1]$, the oracle returns an estimate of ${\\bf E}_{ x\\sim D}[\\phi(x)]$ within some tolerance $\\tau_\\phi$ that roughly corresponds to the number of samples.\n  In this work we demonstrate that the complexity of solving general problems over distributions using SQ algorithms can be captured by a relatively simple notion of statistical dimension that we introduce. SQ algorithms capture a broad spectr","authors_text":"Vitaly Feldman","cross_cats":["cs.CC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-07T09:35:44Z","title":"A General Characterization of the Statistical Query Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02198","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":"sha256:8ab020051abdd7fb82fbe35204d85921f0172d874d7dbd4ca8412f08ade72f0a","target":"record","created_at":"2026-05-18T00:46:20Z","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":"ae5d9a063d63b7ec7b1261c99a124df19dcb82fd8bada9793db9c6c22453b310","cross_cats_sorted":["cs.CC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-07T09:35:44Z","title_canon_sha256":"9a1d2275817a71c494ec6fcf8d6cf319a4333f01f11c5f5ead74b8833d8445b2"},"schema_version":"1.0","source":{"id":"1608.02198","kind":"arxiv","version":3}},"canonical_sha256":"d407fead7831a7c9f25ac11927db2760db081ae21f78c802289b26d212ac7598","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d407fead7831a7c9f25ac11927db2760db081ae21f78c802289b26d212ac7598","first_computed_at":"2026-05-18T00:46:20.836769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:20.836769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bGF5FIXdoqkM0NvQy32FeZgqAs5fjFTXWoOqEK+IUDcsLk1tW6E9Orko6Ni2RgWqOzN7n7tFrT/gpfmxJeObDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:20.837128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02198","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ab020051abdd7fb82fbe35204d85921f0172d874d7dbd4ca8412f08ade72f0a","sha256:1561246aadb1abda9d3c8475a5c43b2256a0fd3134275a82b7d29f9a159312dd"],"state_sha256":"069c56b1acc708f9ac8659a963f7cb8d36a4a1f1954edcbddb32508503fed929"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"haqzYqi5Fgv9Xk3aHDkcDie5o5cKjBfD6X0FTH7NRS9LOjjxidvPmE9bVD+ziygfgYy6rlSI5pqtQQXEqI3yBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:37:03.805345Z","bundle_sha256":"4544358ced4c8908877c02223f2dcd3c5e2a250298fabcbfe389869f68c845a0"}}