{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TDJ27CA657NALKYFFRREH2P2TM","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":"5b7df057294998fd0229d85bae610c718239d06af955641a2146d8f4e28c3338","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-05-23T15:15:27Z","title_canon_sha256":"68e284d44f8fae8cc3c5ee42b0f94dd316a2e1f4bc8f1419aecf140267fead4a"},"schema_version":"1.0","source":{"id":"2505.18014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.18014","created_at":"2026-07-05T11:08:35Z"},{"alias_kind":"arxiv_version","alias_value":"2505.18014v1","created_at":"2026-07-05T11:08:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.18014","created_at":"2026-07-05T11:08:35Z"},{"alias_kind":"pith_short_12","alias_value":"TDJ27CA657NA","created_at":"2026-07-05T11:08:35Z"},{"alias_kind":"pith_short_16","alias_value":"TDJ27CA657NALKYF","created_at":"2026-07-05T11:08:35Z"},{"alias_kind":"pith_short_8","alias_value":"TDJ27CA6","created_at":"2026-07-05T11:08:35Z"}],"graph_snapshots":[{"event_id":"sha256:f27b70960c42a86d2480e9b4c93deb1eca8eb4198e40e1783d91934a44f75fbf","target":"graph","created_at":"2026-07-05T11:08:35Z","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/2505.18014/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the \\emph{geometric $k$-colored crossing number} of complete graphs $\\overline{\\overline{\\text{cr}}}_k(K_n)$, which is the smallest number of monochromatic crossings in any $k$-edge colored straight-line drawing of $K_n$.\n  We substantially improve asymptotic upper bounds on $\\overline{\\overline{\\text{cr}}}_k(K_n)$ for $k=2,\\ldots, 10$ by developing a procedure for general $k$ that derives $k$-edge colored drawings of $K_n$ for arbitrarily large $n$ from initial drawings with a low number of monochromatic crossings.\n  We obtain the latter by heuristic search, employing a \\textsc{MAX-$","authors_text":"Benedikt Hahn, Bettina Klinz, Birgit Vogtenhuber","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-05-23T15:15:27Z","title":"On the geometric $k$-colored crossing number of $K_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.18014","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:c68111103df181ced466ac5f2ab6e04dceb48806b5d4b514a7cb69b62b98bb2f","target":"record","created_at":"2026-07-05T11:08:35Z","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":"5b7df057294998fd0229d85bae610c718239d06af955641a2146d8f4e28c3338","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2025-05-23T15:15:27Z","title_canon_sha256":"68e284d44f8fae8cc3c5ee42b0f94dd316a2e1f4bc8f1419aecf140267fead4a"},"schema_version":"1.0","source":{"id":"2505.18014","kind":"arxiv","version":1}},"canonical_sha256":"98d3af881eefda05ab052c6243e9fa9b3503d7f81ebf3ba62da68a6b7f6032cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98d3af881eefda05ab052c6243e9fa9b3503d7f81ebf3ba62da68a6b7f6032cd","first_computed_at":"2026-07-05T11:08:35.235927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:08:35.235927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+c2JMz7xb/x314o6RNydriljaJOKVaDuhYKn323jxb3l3rH+IzZxO44W6gWZTYsywVY0hZO2ufCT6s8Y3k6pDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:08:35.236395Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.18014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c68111103df181ced466ac5f2ab6e04dceb48806b5d4b514a7cb69b62b98bb2f","sha256:f27b70960c42a86d2480e9b4c93deb1eca8eb4198e40e1783d91934a44f75fbf"],"state_sha256":"569b130a24284c0db8a75791462e8da1259d9406a6eb57ace4ff21f54b061766"}