{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:K2F3LQ5E5ULAWBDUIRQSAUYTWS","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":"5ec3319cbef4d8f6106d7d8c10a2ec88279d16ed85709052f6003a4b3b1e5136","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T15:24:38Z","title_canon_sha256":"a93c9e91ec7c538a1e01c860a1d2ac9d4160fa9b56a73179e2c5e39f98a3ce2c"},"schema_version":"1.0","source":{"id":"1309.1072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1072","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1072v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1072","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"K2F3LQ5E5ULA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K2F3LQ5E5ULAWBDU","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K2F3LQ5E","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:2c3e65bf1c16134ee374671b9c79e8d4cfc2b9d09e04fd52ac07b9e7a2c875ba","target":"graph","created_at":"2026-05-18T03:14:09Z","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":"In a recent work, Fouli and Lin generalized a Villarreal's result and showed that if each connected components of the line graph of a squarefree monomial ideal contains at most a unique odd cycle, then this ideal is of linear type. In this short note, we reprove this result with Villarreal's original ideas together with a method of Conca and De Negri. We also propose a class of squarefree monomial ideals of linear type.","authors_text":"Yi-Huang Shen","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T15:24:38Z","title":"On a class of squarefree monomial ideals of linear type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1072","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":"sha256:0cace93b3a9fda7346787ca4d2d528217df59a9988e4eba0fabb422f453049cf","target":"record","created_at":"2026-05-18T03:14:09Z","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":"5ec3319cbef4d8f6106d7d8c10a2ec88279d16ed85709052f6003a4b3b1e5136","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-09-04T15:24:38Z","title_canon_sha256":"a93c9e91ec7c538a1e01c860a1d2ac9d4160fa9b56a73179e2c5e39f98a3ce2c"},"schema_version":"1.0","source":{"id":"1309.1072","kind":"arxiv","version":1}},"canonical_sha256":"568bb5c3a4ed160b04744461205313b4b051092bc9ab0d91e4cfae8861cf4539","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"568bb5c3a4ed160b04744461205313b4b051092bc9ab0d91e4cfae8861cf4539","first_computed_at":"2026-05-18T03:14:09.168776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:09.168776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KIz4S6NPLhRJxx3W4kJtXaGoKrWxo4RPpyUhwLXnKmQAngWWp9ARzUT9MgtW77sk7a+kU4g+rrODoj+G+lO3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:09.169248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cace93b3a9fda7346787ca4d2d528217df59a9988e4eba0fabb422f453049cf","sha256:2c3e65bf1c16134ee374671b9c79e8d4cfc2b9d09e04fd52ac07b9e7a2c875ba"],"state_sha256":"07021ea99552261775bbded334f5fce8e478308342bd0a19e2d526dff47dc25e"}