{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QO6NAKHEFGAELLSX634M5LI5UB","short_pith_number":"pith:QO6NAKHE","schema_version":"1.0","canonical_sha256":"83bcd028e4298045ae57f6f8cead1da0517023a01552e7bd37ed2a4902a25b07","source":{"kind":"arxiv","id":"1602.08965","version":2},"attestation_state":"computed","paper":{"title":"On 132-representable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice L.L. Gao, Philip B. Zhang, Sergey Kitaev","submitted_at":"2016-02-29T14:07:08Z","abstract_excerpt":"A graph $G = (V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy$ is an edge in $E$. Word-representable graphs are the subject of a long research line in the literature initiated in \\cite{KP}, and they are the main focus in the recently published book \\cite{KL}. A word $w=w_1\\cdots w_{n}$ avoids the pattern $132$ if there are no $1\\leq i_1<i_2<i_3\\leq n$ such that $w_{i_1}<w_{i_3}<w_{i_2}$. The theory of patterns in words and permutations is a fast growing area discussed in \\cite{HM,Kit}.\n  A research d"},"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":"1602.08965","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-29T14:07:08Z","cross_cats_sorted":[],"title_canon_sha256":"b41c6e6735a74ef3264ed5d2fc9a7faea0df5adb58f37f7640f937ec5b89a88b","abstract_canon_sha256":"c178318b759f77659bd003ed18b6a3e11149e565075b2b92d7c7b04ad85d4179"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:28.024849Z","signature_b64":"1FHY2IS/XUK56YIHDGJ99rpiZLkgbSCWq8Dv9sWhmFDppy4A1PfRz2a/SxXfTChfvZI+Fc/M4zKP9P1UkCDVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83bcd028e4298045ae57f6f8cead1da0517023a01552e7bd37ed2a4902a25b07","last_reissued_at":"2026-05-18T01:04:28.024247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:28.024247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 132-representable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice L.L. Gao, Philip B. Zhang, Sergey Kitaev","submitted_at":"2016-02-29T14:07:08Z","abstract_excerpt":"A graph $G = (V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $w$ if and only if $xy$ is an edge in $E$. Word-representable graphs are the subject of a long research line in the literature initiated in \\cite{KP}, and they are the main focus in the recently published book \\cite{KL}. A word $w=w_1\\cdots w_{n}$ avoids the pattern $132$ if there are no $1\\leq i_1<i_2<i_3\\leq n$ such that $w_{i_1}<w_{i_3}<w_{i_2}$. The theory of patterns in words and permutations is a fast growing area discussed in \\cite{HM,Kit}.\n  A research d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08965","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":"1602.08965","created_at":"2026-05-18T01:04:28.024362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.08965v2","created_at":"2026-05-18T01:04:28.024362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08965","created_at":"2026-05-18T01:04:28.024362+00:00"},{"alias_kind":"pith_short_12","alias_value":"QO6NAKHEFGAE","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QO6NAKHEFGAELLSX","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QO6NAKHE","created_at":"2026-05-18T12:30:39.010887+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/QO6NAKHEFGAELLSX634M5LI5UB","json":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB.json","graph_json":"https://pith.science/api/pith-number/QO6NAKHEFGAELLSX634M5LI5UB/graph.json","events_json":"https://pith.science/api/pith-number/QO6NAKHEFGAELLSX634M5LI5UB/events.json","paper":"https://pith.science/paper/QO6NAKHE"},"agent_actions":{"view_html":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB","download_json":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB.json","view_paper":"https://pith.science/paper/QO6NAKHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.08965&json=true","fetch_graph":"https://pith.science/api/pith-number/QO6NAKHEFGAELLSX634M5LI5UB/graph.json","fetch_events":"https://pith.science/api/pith-number/QO6NAKHEFGAELLSX634M5LI5UB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB/action/storage_attestation","attest_author":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB/action/author_attestation","sign_citation":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB/action/citation_signature","submit_replication":"https://pith.science/pith/QO6NAKHEFGAELLSX634M5LI5UB/action/replication_record"}},"created_at":"2026-05-18T01:04:28.024362+00:00","updated_at":"2026-05-18T01:04:28.024362+00:00"}