{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:STU3QJASNHSJ5MYR7WI6XH7VAM","short_pith_number":"pith:STU3QJAS","canonical_record":{"source":{"id":"2204.12640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-04-27T00:18:17Z","cross_cats_sorted":["cs.DM","math.PR","math.ST","stat.TH"],"title_canon_sha256":"e79786f278e37f9911eeee95873467fefd7967078bef6a81fc57a96113eb0809","abstract_canon_sha256":"6c9d4723ec19e0eb2a1f6f078363f1cf1ee9c85d7a6fabed1f027e697ee7db5c"},"schema_version":"1.0"},"canonical_sha256":"94e9b8241269e49eb311fd91eb9ff503190231778a02f0e75b77eb84226c8795","source":{"kind":"arxiv","id":"2204.12640","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.12640","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"arxiv_version","alias_value":"2204.12640v1","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.12640","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"pith_short_12","alias_value":"STU3QJASNHSJ","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"pith_short_16","alias_value":"STU3QJASNHSJ5MYR","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"pith_short_8","alias_value":"STU3QJAS","created_at":"2026-07-05T04:18:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:STU3QJASNHSJ5MYR7WI6XH7VAM","target":"record","payload":{"canonical_record":{"source":{"id":"2204.12640","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-04-27T00:18:17Z","cross_cats_sorted":["cs.DM","math.PR","math.ST","stat.TH"],"title_canon_sha256":"e79786f278e37f9911eeee95873467fefd7967078bef6a81fc57a96113eb0809","abstract_canon_sha256":"6c9d4723ec19e0eb2a1f6f078363f1cf1ee9c85d7a6fabed1f027e697ee7db5c"},"schema_version":"1.0"},"canonical_sha256":"94e9b8241269e49eb311fd91eb9ff503190231778a02f0e75b77eb84226c8795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:21.045109Z","signature_b64":"sdjoxZjFnflioC4FUfkukMaQTibCE0pDTyuHbmgm0GZRErWoKHVhQJNp4xZp/0tItTYn/2f0ecvX+NT4uYAwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e9b8241269e49eb311fd91eb9ff503190231778a02f0e75b77eb84226c8795","last_reissued_at":"2026-07-05T04:18:21.044712Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:21.044712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.12640","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":"2026-07-05T04:18:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GOoLFtfTCBTDnCXqZrFmjILVtkkcUgAEYqxOw35F18ELWy2N1YwMM31rMYolG0E7NmR+xbARxpMUY03z1kO2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T18:02:30.823437Z"},"content_sha256":"a51ab21a949c8e796b68da6fc346dc0ac234787c6b756183c2302978f7e7be5a","schema_version":"1.0","event_id":"sha256:a51ab21a949c8e796b68da6fc346dc0ac234787c6b756183c2302978f7e7be5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:STU3QJASNHSJ5MYR7WI6XH7VAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Closeness Testing of Discrete Distributions Made (Complex) Simple","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR","math.ST","stat.TH"],"primary_cat":"cs.DS","authors_text":"Cl\\'ement L. Canonne, Yucheng Sun","submitted_at":"2022-04-27T00:18:17Z","abstract_excerpt":"In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables (such as stability and divisibility) nor on any \"clever trick,\" but instead on an identity relating the expectation of the absolute value of any random variable to the integral of its characteristic function:\n  \\[\n  \\mathbb{E}[|X|] = \\frac{2}{\\pi}\\int_0^\\infty \\frac{1-\\Re(\\mathbb{E}[e^{i tX}])}{t^2}\\, dt\n  \\]\n  Our argument, while not devoid of technical aspect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12640","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/2204.12640/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":"2026-07-05T04:18:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRIL4C5Gin76HS/d1nf7CvstvFqAjcHjr6GjuXqS1DclxRsK/WzDdensg+nzRDnCGfOEHQVKOEq+1+U78nKxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T18:02:30.823936Z"},"content_sha256":"2b1435be7dcc6fd1b11521a9cdc9a4064910f3fb212bea3453b779459e04abfc","schema_version":"1.0","event_id":"sha256:2b1435be7dcc6fd1b11521a9cdc9a4064910f3fb212bea3453b779459e04abfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STU3QJASNHSJ5MYR7WI6XH7VAM/bundle.json","state_url":"https://pith.science/pith/STU3QJASNHSJ5MYR7WI6XH7VAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STU3QJASNHSJ5MYR7WI6XH7VAM/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":"2026-08-06T18:02:30Z","links":{"resolver":"https://pith.science/pith/STU3QJASNHSJ5MYR7WI6XH7VAM","bundle":"https://pith.science/pith/STU3QJASNHSJ5MYR7WI6XH7VAM/bundle.json","state":"https://pith.science/pith/STU3QJASNHSJ5MYR7WI6XH7VAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STU3QJASNHSJ5MYR7WI6XH7VAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:STU3QJASNHSJ5MYR7WI6XH7VAM","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":"6c9d4723ec19e0eb2a1f6f078363f1cf1ee9c85d7a6fabed1f027e697ee7db5c","cross_cats_sorted":["cs.DM","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-04-27T00:18:17Z","title_canon_sha256":"e79786f278e37f9911eeee95873467fefd7967078bef6a81fc57a96113eb0809"},"schema_version":"1.0","source":{"id":"2204.12640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.12640","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"arxiv_version","alias_value":"2204.12640v1","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.12640","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"pith_short_12","alias_value":"STU3QJASNHSJ","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"pith_short_16","alias_value":"STU3QJASNHSJ5MYR","created_at":"2026-07-05T04:18:21Z"},{"alias_kind":"pith_short_8","alias_value":"STU3QJAS","created_at":"2026-07-05T04:18:21Z"}],"graph_snapshots":[{"event_id":"sha256:2b1435be7dcc6fd1b11521a9cdc9a4064910f3fb212bea3453b779459e04abfc","target":"graph","created_at":"2026-07-05T04:18:21Z","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/2204.12640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables (such as stability and divisibility) nor on any \"clever trick,\" but instead on an identity relating the expectation of the absolute value of any random variable to the integral of its characteristic function:\n  \\[\n  \\mathbb{E}[|X|] = \\frac{2}{\\pi}\\int_0^\\infty \\frac{1-\\Re(\\mathbb{E}[e^{i tX}])}{t^2}\\, dt\n  \\]\n  Our argument, while not devoid of technical aspect","authors_text":"Cl\\'ement L. Canonne, Yucheng Sun","cross_cats":["cs.DM","math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-04-27T00:18:17Z","title":"Optimal Closeness Testing of Discrete Distributions Made (Complex) Simple"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12640","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:a51ab21a949c8e796b68da6fc346dc0ac234787c6b756183c2302978f7e7be5a","target":"record","created_at":"2026-07-05T04:18:21Z","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":"6c9d4723ec19e0eb2a1f6f078363f1cf1ee9c85d7a6fabed1f027e697ee7db5c","cross_cats_sorted":["cs.DM","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-04-27T00:18:17Z","title_canon_sha256":"e79786f278e37f9911eeee95873467fefd7967078bef6a81fc57a96113eb0809"},"schema_version":"1.0","source":{"id":"2204.12640","kind":"arxiv","version":1}},"canonical_sha256":"94e9b8241269e49eb311fd91eb9ff503190231778a02f0e75b77eb84226c8795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94e9b8241269e49eb311fd91eb9ff503190231778a02f0e75b77eb84226c8795","first_computed_at":"2026-07-05T04:18:21.044712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:21.044712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sdjoxZjFnflioC4FUfkukMaQTibCE0pDTyuHbmgm0GZRErWoKHVhQJNp4xZp/0tItTYn/2f0ecvX+NT4uYAwBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:21.045109Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.12640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a51ab21a949c8e796b68da6fc346dc0ac234787c6b756183c2302978f7e7be5a","sha256:2b1435be7dcc6fd1b11521a9cdc9a4064910f3fb212bea3453b779459e04abfc"],"state_sha256":"7cc1f963366eb57bc648490e02edb6150f213425cf79adfd7cc91bd408624021"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3iJQ+gb1Q2VtSC3tOG9Zb0LEiOUSeGwZpR0JLwEcFZRgohc9bz2XRZ4nU+dZmnh9t59vmnc+C8TdkcqaGqLGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T18:02:30.827668Z","bundle_sha256":"2fb1f87a2e55003e4af74476b4b1de0f6a09cad50ac9710fac8b163d5f3a5686"}}