{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MNRPKD72MRLISQU7R6NSB4B6DW","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":"10bba7ee66a6452cbad5ee2f01657d24aded5d3dba12049033c3bd4200dce16c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-12T18:34:57Z","title_canon_sha256":"79ec418c04f687cdd7287c08c8995e3b7fefb155f5ae27a98f720084dea9feb7"},"schema_version":"1.0","source":{"id":"1602.04152","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04152","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04152v3","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04152","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"MNRPKD72MRLI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MNRPKD72MRLISQU7","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MNRPKD72","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:6b4bc972e9591f6c02e4e31af59dca43122d8e1c356617bdfd6537026a14e859","target":"graph","created_at":"2026-05-18T00:50:40Z","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":"In the metric multi-cover problem (MMC), we are given two point sets $Y$ (servers) and $X$ (clients) in an arbitrary metric space $(X \\cup Y, d)$, a positive integer $k$ that represents the coverage demand of each client, and a constant $\\alpha \\geq 1$. Each server can have a single ball of arbitrary radius centered on it. Each client $x \\in X$ needs to be covered by at least $k$ such balls centered on servers. The objective function that we wish to minimize is the sum of the $\\alpha$-th powers of the radii of the balls.\n  In this article, we consider the MMC problem as well as some non-trivia","authors_text":"Kasturi Varadarajan, Santanu Bhowmick, Tanmay Inamdar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-12T18:34:57Z","title":"On Metric Multi-Covering Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04152","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":"sha256:32c6347c63052f74f5b7981a3ee36e4514f429fcf0c4e45ab009a2e09ac48e2c","target":"record","created_at":"2026-05-18T00:50:40Z","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":"10bba7ee66a6452cbad5ee2f01657d24aded5d3dba12049033c3bd4200dce16c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-02-12T18:34:57Z","title_canon_sha256":"79ec418c04f687cdd7287c08c8995e3b7fefb155f5ae27a98f720084dea9feb7"},"schema_version":"1.0","source":{"id":"1602.04152","kind":"arxiv","version":3}},"canonical_sha256":"6362f50ffa645689429f8f9b20f03e1da91a43b86d586d417427e3a68922a0d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6362f50ffa645689429f8f9b20f03e1da91a43b86d586d417427e3a68922a0d7","first_computed_at":"2026-05-18T00:50:40.398335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:40.398335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87VXNJhkx3MkVxiROx5VzxD/G80UNKgMS8QmjtXgeOogHtJ3tEotwjAIvDUlx6IS5SRFQw75/aaSF89PaZ+WAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:40.399080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04152","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32c6347c63052f74f5b7981a3ee36e4514f429fcf0c4e45ab009a2e09ac48e2c","sha256:6b4bc972e9591f6c02e4e31af59dca43122d8e1c356617bdfd6537026a14e859"],"state_sha256":"094b3fa3690d834fb48788f2546fe3538b3289aebd7d32367965bf758addb301"}