{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:IIHJUSPALG5565QERBKPDXBHGY","short_pith_number":"pith:IIHJUSPA","schema_version":"1.0","canonical_sha256":"420e9a49e059bbdf76048854f1dc27363edabbe264b0e1f08ce3ecb3bb9142d3","source":{"kind":"arxiv","id":"2206.07209","version":2},"attestation_state":"computed","paper":{"title":"On Approximating Total Variation Distance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"cs.DS","authors_text":"A. Pavan, Arnab Bhattacharyya, Dimitrios Myrisiotis, Kuldeep S. Meel, N. V. Vinodchandran, Sutanu Gayen","submitted_at":"2022-06-14T23:33:30Z","abstract_excerpt":"Total variation distance (TV distance) is a fundamental notion of distance between probability distributions. In this work, we introduce and study the problem of computing the TV distance of two product distributions over the domain $\\{0,1\\}^n$. In particular, we establish the following results.\n  1. The problem of exactly computing the TV distance of two product distributions is $\\#\\mathsf{P}$-complete. This is in stark contrast with other distance measures such as KL, Chi-square, and Hellinger which tensorize over the marginals leading to efficient algorithms.\n  2. There is a fully polynomia"},"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":"2206.07209","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-06-14T23:33:30Z","cross_cats_sorted":["cs.CC","cs.DM"],"title_canon_sha256":"35f0cd40d01faa3c78d8a4237e2f6531ecdc6d267d79d7ae67f150ebff0160ec","abstract_canon_sha256":"c3185d323a463a4879d562f25060dec0fbd9f7a1314348f5bf92786ab4a2d010"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:42:02.106765Z","signature_b64":"0HBklGnyhQD9pW1BU9CIhIf+jXR382fG8d1TvEYJNCFRXDlr/XW0uQb/weHcasdq+idYLhfp4nU7Pu7P8a3QAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"420e9a49e059bbdf76048854f1dc27363edabbe264b0e1f08ce3ecb3bb9142d3","last_reissued_at":"2026-07-05T06:42:02.106340Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:42:02.106340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Approximating Total Variation Distance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"cs.DS","authors_text":"A. Pavan, Arnab Bhattacharyya, Dimitrios Myrisiotis, Kuldeep S. Meel, N. V. Vinodchandran, Sutanu Gayen","submitted_at":"2022-06-14T23:33:30Z","abstract_excerpt":"Total variation distance (TV distance) is a fundamental notion of distance between probability distributions. In this work, we introduce and study the problem of computing the TV distance of two product distributions over the domain $\\{0,1\\}^n$. In particular, we establish the following results.\n  1. The problem of exactly computing the TV distance of two product distributions is $\\#\\mathsf{P}$-complete. This is in stark contrast with other distance measures such as KL, Chi-square, and Hellinger which tensorize over the marginals leading to efficient algorithms.\n  2. There is a fully polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.07209","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.07209/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":"2206.07209","created_at":"2026-07-05T06:42:02.106391+00:00"},{"alias_kind":"arxiv_version","alias_value":"2206.07209v2","created_at":"2026-07-05T06:42:02.106391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.07209","created_at":"2026-07-05T06:42:02.106391+00:00"},{"alias_kind":"pith_short_12","alias_value":"IIHJUSPALG55","created_at":"2026-07-05T06:42:02.106391+00:00"},{"alias_kind":"pith_short_16","alias_value":"IIHJUSPALG5565QE","created_at":"2026-07-05T06:42:02.106391+00:00"},{"alias_kind":"pith_short_8","alias_value":"IIHJUSPA","created_at":"2026-07-05T06:42:02.106391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.19662","citing_title":"When Tabular Foundation Models Meet Strategic Tabular Data: A Prior Alignment Approach","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY","json":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY.json","graph_json":"https://pith.science/api/pith-number/IIHJUSPALG5565QERBKPDXBHGY/graph.json","events_json":"https://pith.science/api/pith-number/IIHJUSPALG5565QERBKPDXBHGY/events.json","paper":"https://pith.science/paper/IIHJUSPA"},"agent_actions":{"view_html":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY","download_json":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY.json","view_paper":"https://pith.science/paper/IIHJUSPA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2206.07209&json=true","fetch_graph":"https://pith.science/api/pith-number/IIHJUSPALG5565QERBKPDXBHGY/graph.json","fetch_events":"https://pith.science/api/pith-number/IIHJUSPALG5565QERBKPDXBHGY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY/action/storage_attestation","attest_author":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY/action/author_attestation","sign_citation":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY/action/citation_signature","submit_replication":"https://pith.science/pith/IIHJUSPALG5565QERBKPDXBHGY/action/replication_record"}},"created_at":"2026-07-05T06:42:02.106391+00:00","updated_at":"2026-07-05T06:42:02.106391+00:00"}