{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MQOPEQYGMJQ73LOB24PF3NDRAF","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":"b0890cf6aec7791e3753ef130398f6ad5c679750a76f64b7067f4aceee316594","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-23T04:17:36Z","title_canon_sha256":"8d4511b79b3d726ec160168a5c7898f2864101bcc4580dc2d8b22f1ecc00b749"},"schema_version":"1.0","source":{"id":"1708.06883","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06883","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06883v3","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06883","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"pith_short_12","alias_value":"MQOPEQYGMJQ7","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MQOPEQYGMJQ73LOB","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MQOPEQYG","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:987a76b4bea431d165382a23d037410c3d52bf51b7d201909c05edf4bfb5322b","target":"graph","created_at":"2026-05-17T23:57:07Z","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":"Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a very well-covered graph then for all $s \\geq 2$ the regularity of $I(G)^s$ is exactly $2s+\\nu(G)-1$.","authors_text":"A V Jayanthan, S Selvaraja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-23T04:17:36Z","title":"Linear polynomial for the regularity of powers of edge ideals of very well-covered graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06883","kind":"arxiv","version":3},"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":"sha256:0e2221b5e22b303b295b5b671d680acdeddc1448ba2d90358488b413ecadb132","target":"record","created_at":"2026-05-17T23:57:07Z","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":"b0890cf6aec7791e3753ef130398f6ad5c679750a76f64b7067f4aceee316594","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-08-23T04:17:36Z","title_canon_sha256":"8d4511b79b3d726ec160168a5c7898f2864101bcc4580dc2d8b22f1ecc00b749"},"schema_version":"1.0","source":{"id":"1708.06883","kind":"arxiv","version":3}},"canonical_sha256":"641cf243066261fdadc1d71e5db471016b5257b56e1d043a0d0356921ef07362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"641cf243066261fdadc1d71e5db471016b5257b56e1d043a0d0356921ef07362","first_computed_at":"2026-05-17T23:57:07.802110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:07.802110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tzwXmFpCbTUHLg+b34Eg9/8RTSpy0ZpCId3q7g1H0+npzgkOS3Nk9M3flHlpSzFozk8QM98816uayJRiFduRDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:07.802644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06883","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e2221b5e22b303b295b5b671d680acdeddc1448ba2d90358488b413ecadb132","sha256:987a76b4bea431d165382a23d037410c3d52bf51b7d201909c05edf4bfb5322b"],"state_sha256":"98db8429dc9e28126b1c2589e84791673ce8597943bbf1d2881219d58ef34331"}