{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OMOWUIYNF2F4BDOGJNVD35V2XV","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":"fdb595923f83b5c282e33a32378adeceb552464ae7a036c144a7db674c12e247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-14T17:29:30Z","title_canon_sha256":"4593ea138d41cdc156c079b144a215badb00f9c2afcde21a4a89fabadcb508e9"},"schema_version":"1.0","source":{"id":"1101.2866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2866","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2866v2","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2866","created_at":"2026-05-18T03:27:41Z"},{"alias_kind":"pith_short_12","alias_value":"OMOWUIYNF2F4","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OMOWUIYNF2F4BDOG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OMOWUIYN","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:8e0951a29da35396250dc046f98c98f0f63f9669440a2af5f306f32ad0f97168","target":"graph","created_at":"2026-05-18T03:27:41Z","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 J be a strongly stable monomial ideal in S=K[x_1,...,x_n] and let Mf(J) be the family of all homogeneous ideals I in S such that the set of all terms outside J is a K-vector basis of the quotient S/I. We show that an ideal I belongs to Mf(J) if and only if it is generated by a special set of polynomials, the J-marked basis of I, that in some sense generalizes the notion of reduced Groebner basis and its constructive capabilities. Indeed, although not every J-marked basis is a Groebner basis with respect to some term order, a sort of normal form modulo I (with the ideal I in Mf(J)) can be c","authors_text":"Francesca Cioffi, Margherita Roggero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-14T17:29:30Z","title":"Flat families by strongly stable ideals and a generalization of Groebner bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2866","kind":"arxiv","version":2},"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":"sha256:7c60d7d5e016913891bbc73074067367ade6336f4acce4b00026a5812093f8c4","target":"record","created_at":"2026-05-18T03:27:41Z","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":"fdb595923f83b5c282e33a32378adeceb552464ae7a036c144a7db674c12e247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-14T17:29:30Z","title_canon_sha256":"4593ea138d41cdc156c079b144a215badb00f9c2afcde21a4a89fabadcb508e9"},"schema_version":"1.0","source":{"id":"1101.2866","kind":"arxiv","version":2}},"canonical_sha256":"731d6a230d2e8bc08dc64b6a3df6babd49f40f173f386b44ab4788eb5b1cf0dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"731d6a230d2e8bc08dc64b6a3df6babd49f40f173f386b44ab4788eb5b1cf0dc","first_computed_at":"2026-05-18T03:27:41.340027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:41.340027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xPk+9XLsBz58fTAc4QoC9OrSJym+0fijQC/scuiv1p3/P+dq/zw3pxZ8WeWPREX9OVUoFqEoIDXrkMNLkNYiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:41.340545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c60d7d5e016913891bbc73074067367ade6336f4acce4b00026a5812093f8c4","sha256:8e0951a29da35396250dc046f98c98f0f63f9669440a2af5f306f32ad0f97168"],"state_sha256":"a78c8b0d97515b00e39b54ed59305c5f4925f6542c0a35aa8c5f24471cfcd8ec"}