{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:U5PG7M7XZWT53VKTR7CU3VIAX3","short_pith_number":"pith:U5PG7M7X","canonical_record":{"source":{"id":"2309.14696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-09-26T06:17:53Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6250bc13be0e83b254707c009c8232695d1994731edca992539f23e0d7761357","abstract_canon_sha256":"fcf73ade92c4d43b73270c140844859d9749aede3b158e7160b3ac3b2ead56bb"},"schema_version":"1.0"},"canonical_sha256":"a75e6fb3f7cda7ddd5538fc54dd500beeabe9b8faae9f335ec6d9f85aea13e64","source":{"kind":"arxiv","id":"2309.14696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.14696","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"2309.14696v1","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.14696","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"U5PG7M7XZWT5","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"pith_short_16","alias_value":"U5PG7M7XZWT53VKT","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"pith_short_8","alias_value":"U5PG7M7X","created_at":"2026-07-05T06:54:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:U5PG7M7XZWT53VKTR7CU3VIAX3","target":"record","payload":{"canonical_record":{"source":{"id":"2309.14696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-09-26T06:17:53Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"6250bc13be0e83b254707c009c8232695d1994731edca992539f23e0d7761357","abstract_canon_sha256":"fcf73ade92c4d43b73270c140844859d9749aede3b158e7160b3ac3b2ead56bb"},"schema_version":"1.0"},"canonical_sha256":"a75e6fb3f7cda7ddd5538fc54dd500beeabe9b8faae9f335ec6d9f85aea13e64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:28.725447Z","signature_b64":"I+5cSs4rwnvphzlli4+EMpjlylFL32JPg4iv6iTEe4jrx0ZfS0ijX9rhugwn8vwmWPrpQ3h3+NZoFPRubrw6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a75e6fb3f7cda7ddd5538fc54dd500beeabe9b8faae9f335ec6d9f85aea13e64","last_reissued_at":"2026-07-05T06:54:28.725035Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:28.725035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.14696","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+3ySvAHWvFTYam38M3zzK9wv9IN7WioCAc4zPVDm2w5ZkV/RJrXH4ZdeAjCJ72anfaGyA0mpl69HmX71anaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:13:21.381844Z"},"content_sha256":"18b892d1a57c99595982cd40e503ea1abc24ca78f206c3f84b9b6f1ed158ec74","schema_version":"1.0","event_id":"sha256:18b892d1a57c99595982cd40e503ea1abc24ca78f206c3f84b9b6f1ed158ec74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:U5PG7M7XZWT53VKTR7CU3VIAX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Deterministically Approximating Total Variation Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Liqiang Liu, Tianren Liu, Weiming Feng","submitted_at":"2023-09-26T06:17:53Z","abstract_excerpt":"Total variation distance (TV distance) is an important measure for the difference between two distributions. Recently, there has been progress in approximating the TV distance between product distributions: a deterministic algorithm for a restricted class of product distributions (Bhattacharyya, Gayen, Meel, Myrisiotis, Pavan and Vinodchandran 2023) and a randomized algorithm for general product distributions (Feng, Guo, Jerrum and Wang 2023). We give a deterministic fully polynomial-time approximation algorithm (FPTAS) for the TV distance between product distributions. Given two product distr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14696","kind":"arxiv","version":1},"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/2309.14696/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:54:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6TSqTC2hF+bbByOOobW6qr7UPiHDhHc6kgyv2cpl9QWqlE21srT0XWHjDjY0Jmcgjl+LBEISnu0dWszeOp+ACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T04:13:21.382627Z"},"content_sha256":"96938dcfb4912bef01d028500c94b1ccf41740a375c19b698ded5b10ccf930ed","schema_version":"1.0","event_id":"sha256:96938dcfb4912bef01d028500c94b1ccf41740a375c19b698ded5b10ccf930ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U5PG7M7XZWT53VKTR7CU3VIAX3/bundle.json","state_url":"https://pith.science/pith/U5PG7M7XZWT53VKTR7CU3VIAX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U5PG7M7XZWT53VKTR7CU3VIAX3/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":"2026-08-10T04:13:21Z","links":{"resolver":"https://pith.science/pith/U5PG7M7XZWT53VKTR7CU3VIAX3","bundle":"https://pith.science/pith/U5PG7M7XZWT53VKTR7CU3VIAX3/bundle.json","state":"https://pith.science/pith/U5PG7M7XZWT53VKTR7CU3VIAX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U5PG7M7XZWT53VKTR7CU3VIAX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:U5PG7M7XZWT53VKTR7CU3VIAX3","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":"fcf73ade92c4d43b73270c140844859d9749aede3b158e7160b3ac3b2ead56bb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-09-26T06:17:53Z","title_canon_sha256":"6250bc13be0e83b254707c009c8232695d1994731edca992539f23e0d7761357"},"schema_version":"1.0","source":{"id":"2309.14696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.14696","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"arxiv_version","alias_value":"2309.14696v1","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.14696","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"pith_short_12","alias_value":"U5PG7M7XZWT5","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"pith_short_16","alias_value":"U5PG7M7XZWT53VKT","created_at":"2026-07-05T06:54:28Z"},{"alias_kind":"pith_short_8","alias_value":"U5PG7M7X","created_at":"2026-07-05T06:54:28Z"}],"graph_snapshots":[{"event_id":"sha256:96938dcfb4912bef01d028500c94b1ccf41740a375c19b698ded5b10ccf930ed","target":"graph","created_at":"2026-07-05T06:54:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.14696/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Total variation distance (TV distance) is an important measure for the difference between two distributions. Recently, there has been progress in approximating the TV distance between product distributions: a deterministic algorithm for a restricted class of product distributions (Bhattacharyya, Gayen, Meel, Myrisiotis, Pavan and Vinodchandran 2023) and a randomized algorithm for general product distributions (Feng, Guo, Jerrum and Wang 2023). We give a deterministic fully polynomial-time approximation algorithm (FPTAS) for the TV distance between product distributions. Given two product distr","authors_text":"Liqiang Liu, Tianren Liu, Weiming Feng","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-09-26T06:17:53Z","title":"On Deterministically Approximating Total Variation Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14696","kind":"arxiv","version":1},"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":"sha256:18b892d1a57c99595982cd40e503ea1abc24ca78f206c3f84b9b6f1ed158ec74","target":"record","created_at":"2026-07-05T06:54:28Z","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":"fcf73ade92c4d43b73270c140844859d9749aede3b158e7160b3ac3b2ead56bb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2023-09-26T06:17:53Z","title_canon_sha256":"6250bc13be0e83b254707c009c8232695d1994731edca992539f23e0d7761357"},"schema_version":"1.0","source":{"id":"2309.14696","kind":"arxiv","version":1}},"canonical_sha256":"a75e6fb3f7cda7ddd5538fc54dd500beeabe9b8faae9f335ec6d9f85aea13e64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a75e6fb3f7cda7ddd5538fc54dd500beeabe9b8faae9f335ec6d9f85aea13e64","first_computed_at":"2026-07-05T06:54:28.725035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:54:28.725035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+5cSs4rwnvphzlli4+EMpjlylFL32JPg4iv6iTEe4jrx0ZfS0ijX9rhugwn8vwmWPrpQ3h3+NZoFPRubrw6Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:54:28.725447Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.14696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18b892d1a57c99595982cd40e503ea1abc24ca78f206c3f84b9b6f1ed158ec74","sha256:96938dcfb4912bef01d028500c94b1ccf41740a375c19b698ded5b10ccf930ed"],"state_sha256":"6e86a56519e6514463d936f23b25e0d180e23fb01dfb006e3f15e9f242ae845a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZuVTyhRZTp18b4xp85xZiyCz+srurjsW6Zja4PNIFZRgg++jK7eeMUI1na38Hurq1naP/rOkfiZfL/gV1dYbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T04:13:21.388347Z","bundle_sha256":"2c83ffb5130b77e7ab71c0b99f5c926c4e0a2becc7f40d0021df1a833e0257f9"}}