{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LWJIJNZH5GROCMACAJV2EERP4V","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":"5afd54844f94662b75580f5c19aafd3680543f6b21c9c6833adb15082f7952e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2023-09-21T09:18:00Z","title_canon_sha256":"d88050d72374551834ab44530a7238d2959776999f432411f2d227f5ebcaf338"},"schema_version":"1.0","source":{"id":"2309.11908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.11908","created_at":"2026-07-05T06:52:56Z"},{"alias_kind":"arxiv_version","alias_value":"2309.11908v1","created_at":"2026-07-05T06:52:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.11908","created_at":"2026-07-05T06:52:56Z"},{"alias_kind":"pith_short_12","alias_value":"LWJIJNZH5GRO","created_at":"2026-07-05T06:52:56Z"},{"alias_kind":"pith_short_16","alias_value":"LWJIJNZH5GROCMAC","created_at":"2026-07-05T06:52:56Z"},{"alias_kind":"pith_short_8","alias_value":"LWJIJNZH","created_at":"2026-07-05T06:52:56Z"}],"graph_snapshots":[{"event_id":"sha256:cef2a1f92d5933e932407c74a537eac3bf1a7a595b6304d09ef239c8dd8db034","target":"graph","created_at":"2026-07-05T06:52:56Z","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/2309.11908/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Multiple interval graphs are a well-known generalization of interval graphs introduced in the 1970s to deal with situations arising naturally in scheduling and allocation. A $d$-interval is the union of $d$ intervals on the real line, and a graph is a $d$-interval graph if it is the intersection graph of $d$-intervals. In particular, it is a unit $d$-interval graph if it admits a $d$-interval representation where every interval has unit length.\n  Whereas it has been known for a long time that recognizing 2-interval graphs and other related classes such as 2-track interval graphs is NP-complete","authors_text":"Florian Sikora, Romeo Rizzi, St\\'ephane Vialette, Virginia Ard\\'evol Mart\\'inez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2023-09-21T09:18:00Z","title":"Recognizing unit multiple intervals is hard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.11908","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":"sha256:195c8c99a42eaeca56368c64e6bdc374dd46f8207c2f6d10e98546e0e810ae02","target":"record","created_at":"2026-07-05T06:52:56Z","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":"5afd54844f94662b75580f5c19aafd3680543f6b21c9c6833adb15082f7952e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2023-09-21T09:18:00Z","title_canon_sha256":"d88050d72374551834ab44530a7238d2959776999f432411f2d227f5ebcaf338"},"schema_version":"1.0","source":{"id":"2309.11908","kind":"arxiv","version":1}},"canonical_sha256":"5d9284b727e9a2e13002026ba2122fe55fc2dcdc39e33cd92ef041cf15ad9cdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d9284b727e9a2e13002026ba2122fe55fc2dcdc39e33cd92ef041cf15ad9cdc","first_computed_at":"2026-07-05T06:52:56.103014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:52:56.103014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j3eJ580V4GQdEo5kxJ16uGAB8V1CBSFhKnDeSt5hRPVAvX2cupg+JzsUXtcWUf1sg6usr1CigANOncBHg4+TAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:52:56.103515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.11908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:195c8c99a42eaeca56368c64e6bdc374dd46f8207c2f6d10e98546e0e810ae02","sha256:cef2a1f92d5933e932407c74a537eac3bf1a7a595b6304d09ef239c8dd8db034"],"state_sha256":"2b1c6ff9bb0a63c3b1369c445499d655dcfb6ddc879448a3b90d2679065ed2d1"}