{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GTWNDTMUM3ANCHR2CUMW3Y2XCE","merge_version":"pith-open-graph-merge-v1","event_count":8,"valid_event_count":8,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5519f36fbabe2eb64df24d318450afd4b014555ca7873cdebbd30bc7b80f9e68","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2026-05-21T17:54:58Z","title_canon_sha256":"ae6c65b8badb08e4ee294a7be251b8a081f472ba41db28c50870cdf626b1223c"},"schema_version":"1.0","source":{"id":"2605.22804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22804","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22804v1","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22804","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"GTWNDTMUM3AN","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"GTWNDTMUM3ANCHR2","created_at":"2026-05-22T02:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"GTWNDTMU","created_at":"2026-05-22T02:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:e9e48e51110f01ef08f06e03e5e900dbd58ce6327a9eb3c900a88b49b6438d1f","target":"graph","created_at":"2026-05-22T02:04:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.22804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the Min-Sum-Radii (MSR) clustering problem, we are given a finite set X of n points in a metric space. The objective is to find at most k clusters centered at a subset of these points such that every point of X is assigned to one of the clusters, minimizing the sum of the radii of the clusters. The problem is known to be NP-hard even on metrics induced by weighted planar graphs and metrics with constant doubling dimension, as shown by Gibson et al. (SWAT 2008). In this work, we investigate the parameterized complexity of MSR on metrics induced by undirected graphs. We distinguish between we","authors_text":"Haiko M\\\"uller, Melanie Schmidt, Pankaj Kumar, Sebastian Ordyniak","cross_cats":["cs.CC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2026-05-21T17:54:58Z","title":"On the Parameterized Complexity of Min-Sum-Radii"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22804","kind":"arxiv","version":1},"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":"sha256:0e5095489fd138d7c3972f61292fe6586d4b198a1481b3e7099dae12e0d82c24","target":"record","created_at":"2026-05-22T02:04:55Z","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":"5519f36fbabe2eb64df24d318450afd4b014555ca7873cdebbd30bc7b80f9e68","cross_cats_sorted":["cs.CC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2026-05-21T17:54:58Z","title_canon_sha256":"ae6c65b8badb08e4ee294a7be251b8a081f472ba41db28c50870cdf626b1223c"},"schema_version":"1.0","source":{"id":"2605.22804","kind":"arxiv","version":1}},"canonical_sha256":"34ecd1cd9466c0d11e3a15196de357113a7564aa744c854c57e73ead3ec5086d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34ecd1cd9466c0d11e3a15196de357113a7564aa744c854c57e73ead3ec5086d","first_computed_at":"2026-05-22T02:04:55.575742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T02:04:55.575742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fyj+1cEOS1K2BLceqda6mk7lQFJhTaQD/PoqJU0QuEickBIXLHGF4w+ldG4IwXP51xS8850zWlN8glmDgT+fCw==","signature_status":"signed_v1","signed_at":"2026-05-22T02:04:55.576267Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22804","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:0744301a5759ec5fac738cb5a2a333cb8e27f25e1c3bfa2820da9152e82c7362","sha256:11fb2f18eb95633aac4f316293a137ddb139a3670704cd167a2076b67113ff8c","sha256:9f939f82b790a6a4aeb7ed0d7e23b05f34d526d52acfef3f712ee2ca6d312b92","sha256:ddb570e69eb60e6d37bb5696fc3a614796b2623cbf93ae3b72e45037b1d15793","sha256:e5d406cbae916dfb0e0b6eb17fbe159449792e8e5998244612c29d5fbe7321db","sha256:e7cfeb0982d35b1cc81c2d331d78bf3747c1fda9ee74485db02ec9e0df24fff3"]}],"invalid_events":[],"applied_event_ids":["sha256:0e5095489fd138d7c3972f61292fe6586d4b198a1481b3e7099dae12e0d82c24","sha256:e9e48e51110f01ef08f06e03e5e900dbd58ce6327a9eb3c900a88b49b6438d1f"],"state_sha256":"c0d0ca5ff3df305fb10cd4d403539ffb7e9d164589807171b0588496801792fd"}