{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5FATG7WKLA3FXU2TGLLC722V44","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a9efd4d9999dae146db378dca41798f001397de37fb40675271b1207ff00ba57","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-07-27T12:51:47Z","title_canon_sha256":"990f37ae6f0161d14f1aac57d33ca069a7cbe379e41bedc61bfdf38a4e84cd43"},"schema_version":"1.0","source":{"id":"2607.24375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.24375","created_at":"2026-07-28T02:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.24375v1","created_at":"2026-07-28T02:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24375","created_at":"2026-07-28T02:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"5FATG7WKLA3F","created_at":"2026-07-28T02:23:59Z"},{"alias_kind":"pith_short_16","alias_value":"5FATG7WKLA3FXU2T","created_at":"2026-07-28T02:23:59Z"},{"alias_kind":"pith_short_8","alias_value":"5FATG7WK","created_at":"2026-07-28T02:23:59Z"}],"graph_snapshots":[{"event_id":"sha256:a9a6f481cfb2c0dbffe4b120cca2630b3bad8f344f3530ba3b1fa056130bb131","target":"graph","created_at":"2026-07-28T02:23:59Z","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/2607.24375/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study the weighted book thickness of graphs. A $k$-page book embedding of a graph $G=(V,E)$ is defined by a spanning cycle $C$ for $V$ (which does not need to be part of $G$) and a partition $E=\\bigcup_{i=1}^{k}E_i$ such that $E\\cap C\\subseteq E_1$ and each graph $G_i=(V,E_i\\cup C)$, for $1 \\le i \\le k$, is outerplane with outer cycle $C$. If $e\\in E_i$, we say that $e$ appears on Page $i$. The classical book thickness of a graph $G$ is the minimum $k$ such that there exists a $k$-page book embedding of $G$, that is, the minimum (over all book embeddings of $G$) achievable max","authors_text":"Alexandra Weinberger, Henry F\\\"orster, Johannes Zink, Maria Eleni Pavlidi, Michael Hoffmann, Stephen Kobourov","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-07-27T12:51:47Z","title":"Weighted Book Thickness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24375","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":"sha256:644f1b7b1388a4c209e357cd587d193af816dad70dee2bc7b371351cf338e392","target":"record","created_at":"2026-07-28T02:23:59Z","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":"a9efd4d9999dae146db378dca41798f001397de37fb40675271b1207ff00ba57","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-07-27T12:51:47Z","title_canon_sha256":"990f37ae6f0161d14f1aac57d33ca069a7cbe379e41bedc61bfdf38a4e84cd43"},"schema_version":"1.0","source":{"id":"2607.24375","kind":"arxiv","version":1}},"canonical_sha256":"e941337eca58365bd35332d62feb55e70853e5ba74752b9f6e064d924d331976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e941337eca58365bd35332d62feb55e70853e5ba74752b9f6e064d924d331976","first_computed_at":"2026-07-28T02:23:59.879559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T02:23:59.879559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ALFMhFgoqoaA+q+MCL2U0Wk4H5wf9gVrdmQvvi4jkqPYjDjVOc9mJThPy7B/+tTfYjjtvFXctP/6AVg8iGhDg==","signature_status":"signed_v1","signed_at":"2026-07-28T02:23:59.880408Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.24375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:644f1b7b1388a4c209e357cd587d193af816dad70dee2bc7b371351cf338e392","sha256:a9a6f481cfb2c0dbffe4b120cca2630b3bad8f344f3530ba3b1fa056130bb131","sha256:e9cace6733ac07a14480655e1536c407da9068670bb94eee765942d9f00132f8"],"state_sha256":"fbfdda728bbc1a3895d01d18018882ca1b543d191fcdd2357ead16c87d76f602"}