{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OFEZXM4EWN274BVI4UZBANG7Q2","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":"0027cfc6daa33449989ca430e8a0c1285974cc60015ec942fcc2e38e9c2f6673","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2018-04-18T06:50:27Z","title_canon_sha256":"bb8e8bf87e26af833198017c0644224354f2ab94942f0a686f86a1ceffa4914a"},"schema_version":"1.0","source":{"id":"1804.06571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06571","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06571v1","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06571","created_at":"2026-05-18T00:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"OFEZXM4EWN27","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OFEZXM4EWN274BVI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OFEZXM4E","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:cef4dad260d6fa781bbe84549eaf9dc34bec2a2013c80171c48c86c1fb458850","target":"graph","created_at":"2026-05-18T00:17:59Z","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"},"paper":{"abstract_excerpt":"We introduce the notion of \\emph{stab number} and \\emph{exact stab number} of rectangle intersection graphs, otherwise known as graphs of boxicity at most 2. A graph $G$ is said to be a \\emph{$k$-stabbable rectangle intersection graph}, or \\emph{$k$-SRIG} for short, if it has a rectangle intersection representation in which $k$ horizontal lines can be chosen such that each rectangle is intersected by at least one of them. If there exists such a representation with the additional property that each rectangle intersects exactly one of the $k$ horizontal lines, then the graph $G$ is said to be a ","authors_text":"Dibyayan Chakraborty, Mathew C. Francis","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2018-04-18T06:50:27Z","title":"On the stab number of rectangle intersection graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06571","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:d6a0d56a0e01db8e5e1d9ec765e608da532c26b0b7fc9b0d34658e0b38fb04a9","target":"record","created_at":"2026-05-18T00:17:59Z","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":"0027cfc6daa33449989ca430e8a0c1285974cc60015ec942fcc2e38e9c2f6673","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.DM","submitted_at":"2018-04-18T06:50:27Z","title_canon_sha256":"bb8e8bf87e26af833198017c0644224354f2ab94942f0a686f86a1ceffa4914a"},"schema_version":"1.0","source":{"id":"1804.06571","kind":"arxiv","version":1}},"canonical_sha256":"71499bb384b375fe06a8e5321034df86ad45960c92b277e05af526855a448874","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71499bb384b375fe06a8e5321034df86ad45960c92b277e05af526855a448874","first_computed_at":"2026-05-18T00:17:59.306130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:59.306130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sfIRmQtwjxtu7yYlyLcREDa6gSXxYZGm540a4ExtCniwYvKl/FuvU8q9vAhavi+Anp7CGWFM/NpMwKF+I8DyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:59.306733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6a0d56a0e01db8e5e1d9ec765e608da532c26b0b7fc9b0d34658e0b38fb04a9","sha256:cef4dad260d6fa781bbe84549eaf9dc34bec2a2013c80171c48c86c1fb458850"],"state_sha256":"2ad9ae6080dafdb4d94e8b070b39dc77262b0e005e02958ca9afb9910779fc93"}