{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z2N2O5PBN6WTYSDLBGWKM5L4LA","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":"c4faa04e8cd38873e38e681055466c45af9d843990f7c7e35c4df102ed0ae6f7","cross_cats_sorted":["cs.CC","cs.DM","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-18T22:28:20Z","title_canon_sha256":"b44d31498eb2cc2d69de4bba61f36bbf9d41bc0bb9b4b96d40a19452979c9148"},"schema_version":"1.0","source":{"id":"1706.05738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05738","created_at":"2026-05-18T00:38:25Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05738v2","created_at":"2026-05-18T00:38:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05738","created_at":"2026-05-18T00:38:25Z"},{"alias_kind":"pith_short_12","alias_value":"Z2N2O5PBN6WT","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2N2O5PBN6WTYSDL","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2N2O5PB","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:4e5fcdc11a4eaa60b366342519e4deb3138e5b53299f2689719b6ffac3d2b9a3","target":"graph","created_at":"2026-05-18T00:38:25Z","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 study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\\mathcal{P}$ and sample access to an unknown discrete distribution $\\mathbf{P}$, we want to distinguish (with high probability) between the case that $\\mathbf{P} \\in \\mathcal{P}$ and the case that $\\mathbf{P}$ is $\\epsilon$-far, in total variation distance, from every distribution in $\\mathcal{P}$. This is the prototypical hypothesis testing problem that has received significant attention in statistics and, more recently, in the","authors_text":"Alistair Stewart, Cl\\'ement L. Canonne, Ilias Diakonikolas","cross_cats":["cs.CC","cs.DM","math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-18T22:28:20Z","title":"Fourier-Based Testing for Families of Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05738","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":"sha256:235ad9ac94b4430bab841e15e32ee8f52ee6669e7a69dbc51b0de72cd9a394d3","target":"record","created_at":"2026-05-18T00:38:25Z","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":"c4faa04e8cd38873e38e681055466c45af9d843990f7c7e35c4df102ed0ae6f7","cross_cats_sorted":["cs.CC","cs.DM","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-18T22:28:20Z","title_canon_sha256":"b44d31498eb2cc2d69de4bba61f36bbf9d41bc0bb9b4b96d40a19452979c9148"},"schema_version":"1.0","source":{"id":"1706.05738","kind":"arxiv","version":2}},"canonical_sha256":"ce9ba775e16fad3c486b09aca6757c581deb4b40c77bfec3774c52308f66ff3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce9ba775e16fad3c486b09aca6757c581deb4b40c77bfec3774c52308f66ff3a","first_computed_at":"2026-05-18T00:38:25.877413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:25.877413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jer69o8fVqNQ0yZfD3Ld9AaUHQFL+kxF/wx6qCh4wL2ebM8edwuZcaAQEf60gcRveIFUSIaA7/fzYH1RlfsuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:25.878245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:235ad9ac94b4430bab841e15e32ee8f52ee6669e7a69dbc51b0de72cd9a394d3","sha256:4e5fcdc11a4eaa60b366342519e4deb3138e5b53299f2689719b6ffac3d2b9a3"],"state_sha256":"05360e6d02a80c7e46257dfcc271a992d1f2cee6bb9c85d9a0ad276cb52584c4"}