{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:S2RDGBXP7A2NCTLGXP57KGMGKW","short_pith_number":"pith:S2RDGBXP","schema_version":"1.0","canonical_sha256":"96a23306eff834d14d66bbfbf51986558a148ed77c53349ab18d4b295f67ab7d","source":{"kind":"arxiv","id":"2410.18915","version":4},"attestation_state":"computed","paper":{"title":"Testing Support Size More Efficiently Than Learning Histograms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Nathaniel Harms, Renato Ferreira Pinto Jr.","submitted_at":"2024-10-24T17:05:34Z","abstract_excerpt":"Consider two problems about an unknown probability distribution $p$:\n  1. How many samples from $p$ are required to test if $p$ is supported on $n$ elements or not? Specifically, given samples from $p$, determine whether it is supported on at most $n$ elements, or it is \"$\\epsilon$-far\" (in total variation distance) from being supported on $n$ elements.\n  2. Given $m$ samples from $p$, what is the largest lower bound on its support size that we can produce?\n  The best known upper bound for problem (1) uses a general algorithm for learning the histogram of the distribution $p$, which requires $"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.18915","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2024-10-24T17:05:34Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b2b88dca19008bfcf54628df2115189839acf3e637c5ca6980d41220d93fbdcb","abstract_canon_sha256":"4dc3a6b1f33b20cd3d88eeb7d788e0ee30747c2d76d1834448472b781162ee5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:03.556159Z","signature_b64":"UFdga5gLVZG0ttXrtEW14XmRVDZyG32SHBSff/t80+JiLu873m1GzN29oWTSezMisBBWg2+ejfXFnAIKCiXZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96a23306eff834d14d66bbfbf51986558a148ed77c53349ab18d4b295f67ab7d","last_reissued_at":"2026-05-21T01:05:03.555232Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:03.555232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing Support Size More Efficiently Than Learning Histograms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Nathaniel Harms, Renato Ferreira Pinto Jr.","submitted_at":"2024-10-24T17:05:34Z","abstract_excerpt":"Consider two problems about an unknown probability distribution $p$:\n  1. How many samples from $p$ are required to test if $p$ is supported on $n$ elements or not? Specifically, given samples from $p$, determine whether it is supported on at most $n$ elements, or it is \"$\\epsilon$-far\" (in total variation distance) from being supported on $n$ elements.\n  2. Given $m$ samples from $p$, what is the largest lower bound on its support size that we can produce?\n  The best known upper bound for problem (1) uses a general algorithm for learning the histogram of the distribution $p$, which requires $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18915","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.18915/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2410.18915","created_at":"2026-05-21T01:05:03.555356+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.18915v4","created_at":"2026-05-21T01:05:03.555356+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.18915","created_at":"2026-05-21T01:05:03.555356+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2RDGBXP7A2N","created_at":"2026-05-21T01:05:03.555356+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2RDGBXP7A2NCTLG","created_at":"2026-05-21T01:05:03.555356+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2RDGBXP","created_at":"2026-05-21T01:05:03.555356+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW","json":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW.json","graph_json":"https://pith.science/api/pith-number/S2RDGBXP7A2NCTLGXP57KGMGKW/graph.json","events_json":"https://pith.science/api/pith-number/S2RDGBXP7A2NCTLGXP57KGMGKW/events.json","paper":"https://pith.science/paper/S2RDGBXP"},"agent_actions":{"view_html":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW","download_json":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW.json","view_paper":"https://pith.science/paper/S2RDGBXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.18915&json=true","fetch_graph":"https://pith.science/api/pith-number/S2RDGBXP7A2NCTLGXP57KGMGKW/graph.json","fetch_events":"https://pith.science/api/pith-number/S2RDGBXP7A2NCTLGXP57KGMGKW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW/action/storage_attestation","attest_author":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW/action/author_attestation","sign_citation":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW/action/citation_signature","submit_replication":"https://pith.science/pith/S2RDGBXP7A2NCTLGXP57KGMGKW/action/replication_record"}},"created_at":"2026-05-21T01:05:03.555356+00:00","updated_at":"2026-05-21T01:05:03.555356+00:00"}