{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6KFOHLM6JPJ2AZRRQLH5CSMMOL","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":"1970de4ebd035a10770d44ea036768d2487c0e76241c7138e8cdc4fe1dacd4a5","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-13T21:10:13Z","title_canon_sha256":"6c49c3408f4ee05aac44e7df497b7eecb2155355c125fcbc30d7640f4371d7ec"},"schema_version":"1.0","source":{"id":"1712.05010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05010","created_at":"2026-05-18T00:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05010v2","created_at":"2026-05-18T00:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05010","created_at":"2026-05-18T00:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"6KFOHLM6JPJ2","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6KFOHLM6JPJ2AZRR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6KFOHLM6","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:5aea261c529843a90c9a5af9a486f5019a038e50c0182cf019af907fa938989e","target":"graph","created_at":"2026-05-18T00:22:18Z","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 (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \\textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics '90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show the rather surprising structural result that a disjoint union of cycles is the complement of a disk graph if and only if at most one of those cycles is of odd length. From that, we derive the first QPTAS and subexp","authors_text":"\\'Edouard Bonnet, Eun Jung Kim, Florian Sikora, Panos Giannopoulos, Pawe{\\l} Rz\\k{a}\\.zewski","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-13T21:10:13Z","title":"QPTAS and Subexponential Algorithm for Maximum Clique on Disk Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05010","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":"sha256:4c56b5dee0c70e85e6f85f89b9965a925ff4576a375b7801ef9f0ab2e4ffc159","target":"record","created_at":"2026-05-18T00:22:18Z","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":"1970de4ebd035a10770d44ea036768d2487c0e76241c7138e8cdc4fe1dacd4a5","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-12-13T21:10:13Z","title_canon_sha256":"6c49c3408f4ee05aac44e7df497b7eecb2155355c125fcbc30d7640f4371d7ec"},"schema_version":"1.0","source":{"id":"1712.05010","kind":"arxiv","version":2}},"canonical_sha256":"f28ae3ad9e4bd3a0663182cfd1498c72c2621a3479af701613df3286ec4fcc20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f28ae3ad9e4bd3a0663182cfd1498c72c2621a3479af701613df3286ec4fcc20","first_computed_at":"2026-05-18T00:22:18.422755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:18.422755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gtKn1VJrpCG1vs8eE8+6QUmV+0+5TqCDmD5VBBXxNgx+WiknypM9/eF1GCTJfMMRmVuDXFwK5t7FKRbDZAABDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:18.423178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c56b5dee0c70e85e6f85f89b9965a925ff4576a375b7801ef9f0ab2e4ffc159","sha256:5aea261c529843a90c9a5af9a486f5019a038e50c0182cf019af907fa938989e"],"state_sha256":"89ba00379302978fdfd1e86351e14bc8d7836cd90f13cffa5a40b4bb9566d4cd"}