{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6OF7WLIQIK736QF7DGCGHYKTFG","short_pith_number":"pith:6OF7WLIQ","canonical_record":{"source":{"id":"1607.02184","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2016-07-07T22:28:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"fc4e35fe4010abeaeacd63e3f6158c26ce6bd57305712409b9d6c2b5dbc01c47","abstract_canon_sha256":"f8ed3bb839fc3b63fa84f24933961c3785f90c8ee262853ec31869ab5424f483"},"schema_version":"1.0"},"canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","source":{"kind":"arxiv","id":"1607.02184","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02184","created_at":"2026-05-18T00:33:37Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02184v2","created_at":"2026-05-18T00:33:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02184","created_at":"2026-05-18T00:33:37Z"},{"alias_kind":"pith_short_12","alias_value":"6OF7WLIQIK73","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6OF7WLIQIK736QF7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6OF7WLIQ","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6OF7WLIQIK736QF7DGCGHYKTFG","target":"record","payload":{"canonical_record":{"source":{"id":"1607.02184","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2016-07-07T22:28:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"fc4e35fe4010abeaeacd63e3f6158c26ce6bd57305712409b9d6c2b5dbc01c47","abstract_canon_sha256":"f8ed3bb839fc3b63fa84f24933961c3785f90c8ee262853ec31869ab5424f483"},"schema_version":"1.0"},"canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:37.001671Z","signature_b64":"P+fWRa2Mem1Rr2bRI7aoRt28KG47DIQX6zWrydP0R8nYM+elIMbYEUiLH7rbUiQrLa4Q/TDB1XncDuLt7h6jBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","last_reissued_at":"2026-05-18T00:33:37.001198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:37.001198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.02184","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":"2026-05-18T00:33:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xePLd4YQ8532tX2vyX7nZBMuNo3D2rvv1uZbDrJLuzlKF2cTzMoRH2oilH2sUyTSrZhtQf5fxW7LshS0BvWEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:39:08.523334Z"},"content_sha256":"ab94ecd7a3f7f3fb8a66eced90c4b1371a459a20f8f2769459ebfbdc591641c0","schema_version":"1.0","event_id":"sha256:ab94ecd7a3f7f3fb8a66eced90c4b1371a459a20f8f2769459ebfbdc591641c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6OF7WLIQIK736QF7DGCGHYKTFG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximizing the Sum of Radii of Disjoint Balls or Disks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"David Eppstein","submitted_at":"2016-07-07T22:28:34Z","abstract_excerpt":"Finding nonoverlapping balls with given centers in any metric space, maximizing the sum of radii of the balls, can be expressed as a linear program. Its dual linear program expresses the problem of finding a minimum-weight set of cycles (allowing 2-cycles) covering all vertices in a complete geometric graph. For points in a Euclidean space of any finite dimension~$d$, with any convex distance function on this space, this graph can be replaced by a sparse subgraph obeying a separator theorem. This graph structure leads to an algorithm for finding the optimum set of balls in time $O(n^{2-1/d})$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02184","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":"2026-05-18T00:33:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p1nLH/H99bRjZCSIi2uu9x81QUxC297oHJ0QsR5g9c4P14jdH9YJ1rMuUjj/ZF9EfWiv3l5KbYLxUS72kvqnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T21:39:08.523801Z"},"content_sha256":"02031bc343a14b0637db61fbbe0098ff84bfb2392f9e68cd30ef6f62533d9a26","schema_version":"1.0","event_id":"sha256:02031bc343a14b0637db61fbbe0098ff84bfb2392f9e68cd30ef6f62533d9a26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/bundle.json","state_url":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OF7WLIQIK736QF7DGCGHYKTFG/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":"2026-08-13T21:39:08Z","links":{"resolver":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG","bundle":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/bundle.json","state":"https://pith.science/pith/6OF7WLIQIK736QF7DGCGHYKTFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OF7WLIQIK736QF7DGCGHYKTFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6OF7WLIQIK736QF7DGCGHYKTFG","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":"f8ed3bb839fc3b63fa84f24933961c3785f90c8ee262853ec31869ab5424f483","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2016-07-07T22:28:34Z","title_canon_sha256":"fc4e35fe4010abeaeacd63e3f6158c26ce6bd57305712409b9d6c2b5dbc01c47"},"schema_version":"1.0","source":{"id":"1607.02184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02184","created_at":"2026-05-18T00:33:37Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02184v2","created_at":"2026-05-18T00:33:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02184","created_at":"2026-05-18T00:33:37Z"},{"alias_kind":"pith_short_12","alias_value":"6OF7WLIQIK73","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6OF7WLIQIK736QF7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6OF7WLIQ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:02031bc343a14b0637db61fbbe0098ff84bfb2392f9e68cd30ef6f62533d9a26","target":"graph","created_at":"2026-05-18T00:33:37Z","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":"Finding nonoverlapping balls with given centers in any metric space, maximizing the sum of radii of the balls, can be expressed as a linear program. Its dual linear program expresses the problem of finding a minimum-weight set of cycles (allowing 2-cycles) covering all vertices in a complete geometric graph. For points in a Euclidean space of any finite dimension~$d$, with any convex distance function on this space, this graph can be replaced by a sparse subgraph obeying a separator theorem. This graph structure leads to an algorithm for finding the optimum set of balls in time $O(n^{2-1/d})$,","authors_text":"David Eppstein","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2016-07-07T22:28:34Z","title":"Maximizing the Sum of Radii of Disjoint Balls or Disks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02184","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:ab94ecd7a3f7f3fb8a66eced90c4b1371a459a20f8f2769459ebfbdc591641c0","target":"record","created_at":"2026-05-18T00:33:37Z","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":"f8ed3bb839fc3b63fa84f24933961c3785f90c8ee262853ec31869ab5424f483","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2016-07-07T22:28:34Z","title_canon_sha256":"fc4e35fe4010abeaeacd63e3f6158c26ce6bd57305712409b9d6c2b5dbc01c47"},"schema_version":"1.0","source":{"id":"1607.02184","kind":"arxiv","version":2}},"canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f38bfb2d1042bfbf40bf198463e15329b4da2493eaaf73f14451853962ee5ec0","first_computed_at":"2026-05-18T00:33:37.001198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:37.001198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P+fWRa2Mem1Rr2bRI7aoRt28KG47DIQX6zWrydP0R8nYM+elIMbYEUiLH7rbUiQrLa4Q/TDB1XncDuLt7h6jBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:37.001671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab94ecd7a3f7f3fb8a66eced90c4b1371a459a20f8f2769459ebfbdc591641c0","sha256:02031bc343a14b0637db61fbbe0098ff84bfb2392f9e68cd30ef6f62533d9a26"],"state_sha256":"afa950a05711c70014f51a7da95adcf39b6f4f12855b58c11d53414192e36315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mC47vH0+7Zo6XuQfsfM2RUaNYlqyfeMXNmSEGrFj1snq1CiqWq/eSE4fMP81r81lnAspWo3aT6pbWFIZi/bYBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T21:39:08.529901Z","bundle_sha256":"4bf624af99d4d5baa5a64bc8da7cb71000fef17ac9d1aa32d29f483b057f3ca1"}}