{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LVM2OM3GK3CCMVJWAXQGZTBCL4","short_pith_number":"pith:LVM2OM3G","schema_version":"1.0","canonical_sha256":"5d59a7336656c426553605e06ccc225f1c39232728fc78f7f70a86f9d78d911c","source":{"kind":"arxiv","id":"1510.03998","version":2},"attestation_state":"computed","paper":{"title":"On the Classes of Interval Graphs of Limited Nesting and Count of Lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Ji\\v{r}\\'i \\v{S}ejnoha, Pavel Klav\\'ik, Yota Otachi","submitted_at":"2015-10-14T08:26:50Z","abstract_excerpt":"In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called $k$-length interval graphs were considered in which the number of different lengths of intervals is limited by $k$. Even after decades of research, no insight into their structure is known and the complexity of recognition is open even for $k=2$. We propose generalizations of proper interval graphs called $k$-nested interval graphs in which there are no chains of $k+1$ intervals nested in each other. It is easy to see that $k$-nested interv"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.03998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-10-14T08:26:50Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9d7997a613e49270e6e1f60627aab9cc6000243744a3ae4c45dfadc4b36ce111","abstract_canon_sha256":"d2eac7fedac528fa7af4115f1d46a880d7c54cb249c718d436189d3118fb8161"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:32.139361Z","signature_b64":"wqq151GP8X8Av+ZbCg2T1qdnEtBzy4CWPAdIJH+Rt9slKNfBLbfMy1fdxonGKn92rwPco3KjSSh0IoT2Y51/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d59a7336656c426553605e06ccc225f1c39232728fc78f7f70a86f9d78d911c","last_reissued_at":"2026-05-18T00:46:32.138588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:32.138588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Classes of Interval Graphs of Limited Nesting and Count of Lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Ji\\v{r}\\'i \\v{S}ejnoha, Pavel Klav\\'ik, Yota Otachi","submitted_at":"2015-10-14T08:26:50Z","abstract_excerpt":"In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called $k$-length interval graphs were considered in which the number of different lengths of intervals is limited by $k$. Even after decades of research, no insight into their structure is known and the complexity of recognition is open even for $k=2$. We propose generalizations of proper interval graphs called $k$-nested interval graphs in which there are no chains of $k+1$ intervals nested in each other. It is easy to see that $k$-nested interv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03998","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.03998","created_at":"2026-05-18T00:46:32.138702+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03998v2","created_at":"2026-05-18T00:46:32.138702+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03998","created_at":"2026-05-18T00:46:32.138702+00:00"},{"alias_kind":"pith_short_12","alias_value":"LVM2OM3GK3CC","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LVM2OM3GK3CCMVJW","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LVM2OM3G","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4","json":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4.json","graph_json":"https://pith.science/api/pith-number/LVM2OM3GK3CCMVJWAXQGZTBCL4/graph.json","events_json":"https://pith.science/api/pith-number/LVM2OM3GK3CCMVJWAXQGZTBCL4/events.json","paper":"https://pith.science/paper/LVM2OM3G"},"agent_actions":{"view_html":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4","download_json":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4.json","view_paper":"https://pith.science/paper/LVM2OM3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03998&json=true","fetch_graph":"https://pith.science/api/pith-number/LVM2OM3GK3CCMVJWAXQGZTBCL4/graph.json","fetch_events":"https://pith.science/api/pith-number/LVM2OM3GK3CCMVJWAXQGZTBCL4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4/action/storage_attestation","attest_author":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4/action/author_attestation","sign_citation":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4/action/citation_signature","submit_replication":"https://pith.science/pith/LVM2OM3GK3CCMVJWAXQGZTBCL4/action/replication_record"}},"created_at":"2026-05-18T00:46:32.138702+00:00","updated_at":"2026-05-18T00:46:32.138702+00:00"}