{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3JSAHJ4BUJAYY7CQYYIVHGJ63S","short_pith_number":"pith:3JSAHJ4B","canonical_record":{"source":{"id":"1602.03713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-02-11T13:00:04Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"206b189be1a06ecae67a2e87dac4b900fa19dad79f3c9eb7d0c89043220126f1","abstract_canon_sha256":"7d77e734fa671620a82630d6c92f568cf33d8927ee5e6ae91253d78f1bffd810"},"schema_version":"1.0"},"canonical_sha256":"da6403a781a2418c7c50c61153993edcb14fce26b6fe5b98bce757604423ee6b","source":{"kind":"arxiv","id":"1602.03713","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03713","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03713v2","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03713","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"3JSAHJ4BUJAY","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3JSAHJ4BUJAYY7CQ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3JSAHJ4B","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3JSAHJ4BUJAYY7CQYYIVHGJ63S","target":"record","payload":{"canonical_record":{"source":{"id":"1602.03713","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-02-11T13:00:04Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"206b189be1a06ecae67a2e87dac4b900fa19dad79f3c9eb7d0c89043220126f1","abstract_canon_sha256":"7d77e734fa671620a82630d6c92f568cf33d8927ee5e6ae91253d78f1bffd810"},"schema_version":"1.0"},"canonical_sha256":"da6403a781a2418c7c50c61153993edcb14fce26b6fe5b98bce757604423ee6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:55.265861Z","signature_b64":"XMxnHwOx3QtGLPxkG2CbROgZ37qc0btVh+7ttucga3nCh3cTUs+7WviDLLScY2b4ocMtMiYUYiYPsx1BUtBZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da6403a781a2418c7c50c61153993edcb14fce26b6fe5b98bce757604423ee6b","last_reissued_at":"2026-05-18T01:20:55.265210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:55.265210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.03713","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x1cyVnNhlMIpopUO9VsTXTJBuO0cQNa3jcS5je70B/X5sNfWukCaORUvPYgjeLTAhDc2rNav2QrK/OC1fQENBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:26:02.365354Z"},"content_sha256":"8ef2f1c0208b8c5111c3f09ca8dfdea244751d2e7d7794835d96bfa4ef59ce43","schema_version":"1.0","event_id":"sha256:8ef2f1c0208b8c5111c3f09ca8dfdea244751d2e7d7794835d96bfa4ef59ce43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3JSAHJ4BUJAYY7CQYYIVHGJ63S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Distributed $(2+\\epsilon)$-Approximation for Vertex Cover in $O(\\log{\\Delta}/\\epsilon\\log\\log{\\Delta})$ Rounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Gregory Schwartzman, Keren Censor-Hillel, Reuven Bar-Yehuda","submitted_at":"2016-02-11T13:00:04Z","abstract_excerpt":"We present a simple deterministic distributed $(2+\\epsilon)$-approximation algorithm for minimum weight vertex cover, which completes in $O(\\log{\\Delta}/\\epsilon\\log\\log{\\Delta})$ rounds, where $\\Delta$ is the maximum degree in the graph, for any $\\epsilon>0$ which is at most $O(1)$. For a constant $\\epsilon$, this implies a constant approximation in $O(\\log{\\Delta}/\\log\\log{\\Delta})$ rounds, which contradicts the lower bound of [KMW10]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03713","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":""},"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":"2026-05-18T01:20:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBeCWfs8QSKWPo9B+mxWfnM0QuPwoiS5c5kD0mOtjF8NjJju4KnwLJ+SuwgyRZmwRpb1pOrCEWgIsoelrAvbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:26:02.366032Z"},"content_sha256":"5e91ad8296354f906ae5adb1378219fb930bdad187a8c2a4466152a50bd48922","schema_version":"1.0","event_id":"sha256:5e91ad8296354f906ae5adb1378219fb930bdad187a8c2a4466152a50bd48922"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S/bundle.json","state_url":"https://pith.science/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S/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":"2026-05-27T09:26:02Z","links":{"resolver":"https://pith.science/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S","bundle":"https://pith.science/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S/bundle.json","state":"https://pith.science/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JSAHJ4BUJAYY7CQYYIVHGJ63S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3JSAHJ4BUJAYY7CQYYIVHGJ63S","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":"7d77e734fa671620a82630d6c92f568cf33d8927ee5e6ae91253d78f1bffd810","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-02-11T13:00:04Z","title_canon_sha256":"206b189be1a06ecae67a2e87dac4b900fa19dad79f3c9eb7d0c89043220126f1"},"schema_version":"1.0","source":{"id":"1602.03713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03713","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03713v2","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03713","created_at":"2026-05-18T01:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"3JSAHJ4BUJAY","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3JSAHJ4BUJAYY7CQ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3JSAHJ4B","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:5e91ad8296354f906ae5adb1378219fb930bdad187a8c2a4466152a50bd48922","target":"graph","created_at":"2026-05-18T01:20:55Z","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 present a simple deterministic distributed $(2+\\epsilon)$-approximation algorithm for minimum weight vertex cover, which completes in $O(\\log{\\Delta}/\\epsilon\\log\\log{\\Delta})$ rounds, where $\\Delta$ is the maximum degree in the graph, for any $\\epsilon>0$ which is at most $O(1)$. For a constant $\\epsilon$, this implies a constant approximation in $O(\\log{\\Delta}/\\log\\log{\\Delta})$ rounds, which contradicts the lower bound of [KMW10].","authors_text":"Gregory Schwartzman, Keren Censor-Hillel, Reuven Bar-Yehuda","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-02-11T13:00:04Z","title":"A Distributed $(2+\\epsilon)$-Approximation for Vertex Cover in $O(\\log{\\Delta}/\\epsilon\\log\\log{\\Delta})$ Rounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03713","kind":"arxiv","version":2},"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":"sha256:8ef2f1c0208b8c5111c3f09ca8dfdea244751d2e7d7794835d96bfa4ef59ce43","target":"record","created_at":"2026-05-18T01:20:55Z","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":"7d77e734fa671620a82630d6c92f568cf33d8927ee5e6ae91253d78f1bffd810","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2016-02-11T13:00:04Z","title_canon_sha256":"206b189be1a06ecae67a2e87dac4b900fa19dad79f3c9eb7d0c89043220126f1"},"schema_version":"1.0","source":{"id":"1602.03713","kind":"arxiv","version":2}},"canonical_sha256":"da6403a781a2418c7c50c61153993edcb14fce26b6fe5b98bce757604423ee6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da6403a781a2418c7c50c61153993edcb14fce26b6fe5b98bce757604423ee6b","first_computed_at":"2026-05-18T01:20:55.265210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:55.265210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMxnHwOx3QtGLPxkG2CbROgZ37qc0btVh+7ttucga3nCh3cTUs+7WviDLLScY2b4ocMtMiYUYiYPsx1BUtBZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:55.265861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ef2f1c0208b8c5111c3f09ca8dfdea244751d2e7d7794835d96bfa4ef59ce43","sha256:5e91ad8296354f906ae5adb1378219fb930bdad187a8c2a4466152a50bd48922"],"state_sha256":"a7181d6ee89bde2d8be910e7922702d50f4eb119a80930daa5eb9e9ca408514d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IqUnU6tWFGYmpAQv0cWq3HsXcRRWNKPciqLqj6MVeUCgSpPPJ4mx4yT3eD7w5mSgl2AhUh23hAz/Jm9a6w2/Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:26:02.369466Z","bundle_sha256":"8e5337f598056835abf3010dea50f52b2d35e04af480dfc077f9d3794869955a"}}