{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YUJBBED56YIJME7KDUNDVNZAVK","short_pith_number":"pith:YUJBBED5","canonical_record":{"source":{"id":"1902.01896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-05T20:14:33Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"770356d8888d21eabead51d83d2fcdf50716e3ee903e77bb91eb2b109fe7f708","abstract_canon_sha256":"b1335968531ebacc00e3acb21106a99c11075a1a79a73f0cdb7f4dc1a67eb07f"},"schema_version":"1.0"},"canonical_sha256":"c51210907df6109613ea1d1a3ab720aab4396dc6507c9f2736c60e9e9aab6a64","source":{"kind":"arxiv","id":"1902.01896","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01896","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01896v2","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01896","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"YUJBBED56YIJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YUJBBED56YIJME7K","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YUJBBED5","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YUJBBED56YIJME7KDUNDVNZAVK","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-05T20:14:33Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"770356d8888d21eabead51d83d2fcdf50716e3ee903e77bb91eb2b109fe7f708","abstract_canon_sha256":"b1335968531ebacc00e3acb21106a99c11075a1a79a73f0cdb7f4dc1a67eb07f"},"schema_version":"1.0"},"canonical_sha256":"c51210907df6109613ea1d1a3ab720aab4396dc6507c9f2736c60e9e9aab6a64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:50.680579Z","signature_b64":"PFRTsJmAsGS9+FvrJt57PGlhYG+8er+ESiOC6fcCBRoHulCuohJ4qv7TpvxudqYqpQ6rs5pbhbOYYK7+1kIgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c51210907df6109613ea1d1a3ab720aab4396dc6507c9f2736c60e9e9aab6a64","last_reissued_at":"2026-05-17T23:47:50.680038Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:50.680038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01896","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":"2026-05-17T23:47:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PEkYR9K8CEhy82D3Ql0gRmnB+Wjkm+1ksslRcpoJN31CyZtLaEphEHT2tDOZsbFbRJ8w8ty5Rrvt5KNRd0hDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:05:20.243751Z"},"content_sha256":"aaa565540e4271c2e4a02e51884b40c824719a77d4313d0f9528895ecfa2d673","schema_version":"1.0","event_id":"sha256:aaa565540e4271c2e4a02e51884b40c824719a77d4313d0f9528895ecfa2d673"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YUJBBED56YIJME7KDUNDVNZAVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Composable Coreset for k-Center in Doubling Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Mohammad Ghodsi, Sepideh Aghamolaei","submitted_at":"2019-02-05T20:14:33Z","abstract_excerpt":"A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.\n  Doubling metrics are metric spaces in which for any $r$, a ball of radius $r$ can be covered using a constant number of balls of radius $r/2$. Fixed dimensional Euclidean spaces are doubling metrics. The lower bound on the approximation factor of $k$-center is $1.822$ in Euclidean spaces, however, $(1+\\epsilon)$-approximation algorithms with exponential dependen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01896","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":"2026-05-17T23:47:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7+ZixeXOO4HdzXOmiWeORjiYMTWSIySGpxMdX5VupaBnQyom2Y0e/9w31ePLdwaAV7KrSeVMFwRAns//4xSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:05:20.244105Z"},"content_sha256":"1326b01733037b3f1f4effa6dfd3dcb645229bedb412c01dfaac3f09cd444e5c","schema_version":"1.0","event_id":"sha256:1326b01733037b3f1f4effa6dfd3dcb645229bedb412c01dfaac3f09cd444e5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUJBBED56YIJME7KDUNDVNZAVK/bundle.json","state_url":"https://pith.science/pith/YUJBBED56YIJME7KDUNDVNZAVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUJBBED56YIJME7KDUNDVNZAVK/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":"2026-06-19T23:05:20Z","links":{"resolver":"https://pith.science/pith/YUJBBED56YIJME7KDUNDVNZAVK","bundle":"https://pith.science/pith/YUJBBED56YIJME7KDUNDVNZAVK/bundle.json","state":"https://pith.science/pith/YUJBBED56YIJME7KDUNDVNZAVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUJBBED56YIJME7KDUNDVNZAVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YUJBBED56YIJME7KDUNDVNZAVK","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":"b1335968531ebacc00e3acb21106a99c11075a1a79a73f0cdb7f4dc1a67eb07f","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-05T20:14:33Z","title_canon_sha256":"770356d8888d21eabead51d83d2fcdf50716e3ee903e77bb91eb2b109fe7f708"},"schema_version":"1.0","source":{"id":"1902.01896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01896","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01896v2","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01896","created_at":"2026-05-17T23:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"YUJBBED56YIJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YUJBBED56YIJME7K","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YUJBBED5","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:1326b01733037b3f1f4effa6dfd3dcb645229bedb412c01dfaac3f09cd444e5c","target":"graph","created_at":"2026-05-17T23:47:50Z","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":"A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized.\n  Doubling metrics are metric spaces in which for any $r$, a ball of radius $r$ can be covered using a constant number of balls of radius $r/2$. Fixed dimensional Euclidean spaces are doubling metrics. The lower bound on the approximation factor of $k$-center is $1.822$ in Euclidean spaces, however, $(1+\\epsilon)$-approximation algorithms with exponential dependen","authors_text":"Mohammad Ghodsi, Sepideh Aghamolaei","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-05T20:14:33Z","title":"A Composable Coreset for k-Center in Doubling Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01896","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:aaa565540e4271c2e4a02e51884b40c824719a77d4313d0f9528895ecfa2d673","target":"record","created_at":"2026-05-17T23:47:50Z","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":"b1335968531ebacc00e3acb21106a99c11075a1a79a73f0cdb7f4dc1a67eb07f","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-02-05T20:14:33Z","title_canon_sha256":"770356d8888d21eabead51d83d2fcdf50716e3ee903e77bb91eb2b109fe7f708"},"schema_version":"1.0","source":{"id":"1902.01896","kind":"arxiv","version":2}},"canonical_sha256":"c51210907df6109613ea1d1a3ab720aab4396dc6507c9f2736c60e9e9aab6a64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c51210907df6109613ea1d1a3ab720aab4396dc6507c9f2736c60e9e9aab6a64","first_computed_at":"2026-05-17T23:47:50.680038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:50.680038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFRTsJmAsGS9+FvrJt57PGlhYG+8er+ESiOC6fcCBRoHulCuohJ4qv7TpvxudqYqpQ6rs5pbhbOYYK7+1kIgBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:50.680579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaa565540e4271c2e4a02e51884b40c824719a77d4313d0f9528895ecfa2d673","sha256:1326b01733037b3f1f4effa6dfd3dcb645229bedb412c01dfaac3f09cd444e5c"],"state_sha256":"ed24dc5e7702e12d9678d8eaddbcd2bbf40a6ca587d69e2c22a8fb434d872c14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QfJ7ta+VGBFudwvPt1deU13UHPLKgyrE7zH4xlzl5aWMNhTb4yuYOnCrdZU3JpVB+OPgeNY59I2xd/tnvMAmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:05:20.246058Z","bundle_sha256":"3a8f9ba161ee422fc1ecf5e09e73b665d470d2c30785a040187ff6f28f068306"}}