{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5UZPNKHE3MDZY4SBEUHHI4ABCA","short_pith_number":"pith:5UZPNKHE","canonical_record":{"source":{"id":"1412.0681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-01T21:11:40Z","cross_cats_sorted":[],"title_canon_sha256":"1f3b6d2cffb11e08d4933c9c0da58b9ceaf6490efaf00041fdc647456ad38bf7","abstract_canon_sha256":"c9334a94f7c18bac29a1b8b910c558dda2b469a8ad693fd78b66cc159d430186"},"schema_version":"1.0"},"canonical_sha256":"ed32f6a8e4db079c7241250e747001101bc2a9204f640e6ceea6afbd7c8ea6bb","source":{"kind":"arxiv","id":"1412.0681","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0681","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0681v3","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0681","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"5UZPNKHE3MDZ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5UZPNKHE3MDZY4SB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5UZPNKHE","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5UZPNKHE3MDZY4SBEUHHI4ABCA","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0681","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-01T21:11:40Z","cross_cats_sorted":[],"title_canon_sha256":"1f3b6d2cffb11e08d4933c9c0da58b9ceaf6490efaf00041fdc647456ad38bf7","abstract_canon_sha256":"c9334a94f7c18bac29a1b8b910c558dda2b469a8ad693fd78b66cc159d430186"},"schema_version":"1.0"},"canonical_sha256":"ed32f6a8e4db079c7241250e747001101bc2a9204f640e6ceea6afbd7c8ea6bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:55.085123Z","signature_b64":"k+ijAX/MoGzGXV6QtsLbWWAolzoH6wSY4EEzONWoUigeeqlYPsszJ3Ol33EcSWcKZseH4RiErJk+rgxuHZhZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed32f6a8e4db079c7241250e747001101bc2a9204f640e6ceea6afbd7c8ea6bb","last_reissued_at":"2026-05-18T01:39:55.084575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:55.084575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0681","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3WClayttJ9cVsbyXWEN+6jDPF0W9wUCuEQvKakAmcz3aBNP0zG2pIhClwNlmKab5tpJyIj0VMxa5RDvycn3uCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:19:53.960706Z"},"content_sha256":"5544a55885fa20acc9a9a3f0331766610c11d47762db646539afdadf076b2087","schema_version":"1.0","event_id":"sha256:5544a55885fa20acc9a9a3f0331766610c11d47762db646539afdadf076b2087"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5UZPNKHE3MDZY4SBEUHHI4ABCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near Optimal LP Rounding Algorithm for Correlation Clustering on Complete and Complete k-partite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Grigory Yaroslavtsev, Konstantin Makarychev, Shuchi Chawla, Tselil Schramm","submitted_at":"2014-12-01T21:11:40Z","abstract_excerpt":"We give new rounding schemes for the standard linear programming relaxation of the correlation clustering problem, achieving approximation factors almost matching the integrality gaps:\n  - For complete graphs our appoximation is $2.06 - \\varepsilon$ for a fixed constant $\\varepsilon$, which almost matches the previously known integrality gap of $2$.\n  - For complete $k$-partite graphs our approximation is $3$. We also show a matching integrality gap.\n  - For complete graphs with edge weights satisfying triangle inequalities and probability constraints, our approximation is $1.5$, and we show a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0681","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:39:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2OF6kISMOzfkWJX72fki/U49up7sigVe4t8zFphdzxblU8magvZHtgne6joYZ6roiFx8oXxp0JvLHJce5oQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:19:53.961302Z"},"content_sha256":"2199166092cc8687ab1a68c078dabadcfe24d77908580b1196b78799ca9e1b91","schema_version":"1.0","event_id":"sha256:2199166092cc8687ab1a68c078dabadcfe24d77908580b1196b78799ca9e1b91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA/bundle.json","state_url":"https://pith.science/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA/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":"2026-06-05T07:19:53Z","links":{"resolver":"https://pith.science/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA","bundle":"https://pith.science/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA/bundle.json","state":"https://pith.science/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5UZPNKHE3MDZY4SBEUHHI4ABCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5UZPNKHE3MDZY4SBEUHHI4ABCA","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":"c9334a94f7c18bac29a1b8b910c558dda2b469a8ad693fd78b66cc159d430186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-01T21:11:40Z","title_canon_sha256":"1f3b6d2cffb11e08d4933c9c0da58b9ceaf6490efaf00041fdc647456ad38bf7"},"schema_version":"1.0","source":{"id":"1412.0681","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0681","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0681v3","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0681","created_at":"2026-05-18T01:39:55Z"},{"alias_kind":"pith_short_12","alias_value":"5UZPNKHE3MDZ","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"5UZPNKHE3MDZY4SB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"5UZPNKHE","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:2199166092cc8687ab1a68c078dabadcfe24d77908580b1196b78799ca9e1b91","target":"graph","created_at":"2026-05-18T01:39:55Z","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 give new rounding schemes for the standard linear programming relaxation of the correlation clustering problem, achieving approximation factors almost matching the integrality gaps:\n  - For complete graphs our appoximation is $2.06 - \\varepsilon$ for a fixed constant $\\varepsilon$, which almost matches the previously known integrality gap of $2$.\n  - For complete $k$-partite graphs our approximation is $3$. We also show a matching integrality gap.\n  - For complete graphs with edge weights satisfying triangle inequalities and probability constraints, our approximation is $1.5$, and we show a","authors_text":"Grigory Yaroslavtsev, Konstantin Makarychev, Shuchi Chawla, Tselil Schramm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-01T21:11:40Z","title":"Near Optimal LP Rounding Algorithm for Correlation Clustering on Complete and Complete k-partite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0681","kind":"arxiv","version":3},"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":"sha256:5544a55885fa20acc9a9a3f0331766610c11d47762db646539afdadf076b2087","target":"record","created_at":"2026-05-18T01:39:55Z","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":"c9334a94f7c18bac29a1b8b910c558dda2b469a8ad693fd78b66cc159d430186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-12-01T21:11:40Z","title_canon_sha256":"1f3b6d2cffb11e08d4933c9c0da58b9ceaf6490efaf00041fdc647456ad38bf7"},"schema_version":"1.0","source":{"id":"1412.0681","kind":"arxiv","version":3}},"canonical_sha256":"ed32f6a8e4db079c7241250e747001101bc2a9204f640e6ceea6afbd7c8ea6bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed32f6a8e4db079c7241250e747001101bc2a9204f640e6ceea6afbd7c8ea6bb","first_computed_at":"2026-05-18T01:39:55.084575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:55.084575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+ijAX/MoGzGXV6QtsLbWWAolzoH6wSY4EEzONWoUigeeqlYPsszJ3Ol33EcSWcKZseH4RiErJk+rgxuHZhZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:55.085123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0681","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5544a55885fa20acc9a9a3f0331766610c11d47762db646539afdadf076b2087","sha256:2199166092cc8687ab1a68c078dabadcfe24d77908580b1196b78799ca9e1b91"],"state_sha256":"1652ad8db471111c25b6496809bd344881a14ccd7f43621783191c593cca4f5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BPHzrD1yg+qYq0pRnytD4ZonntjkPCebwj93EaB+lTmZYEQDTDeSyY/F3sbGZ1TyPkpW1NOEn8S7HR78GZwkCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:19:53.964524Z","bundle_sha256":"7c053a990ff6e96d59027a05b584a27bb53969dc1a233c794be13cef1ed12e4d"}}