{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4UI4ODKCNZN366KHXOJEOLAOUY","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":"8999253f75a6544023e181d0c6c6965af8175a0948c0756bc9b8a76bc09dbac6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-12T15:25:05Z","title_canon_sha256":"4e6a7aca31be6088d447af5dd83dff5dea2d05fb0eef90a9039c1b4d0ba2eda7"},"schema_version":"1.0","source":{"id":"1503.03768","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03768","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03768v2","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03768","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"4UI4ODKCNZN3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4UI4ODKCNZN366KH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4UI4ODKC","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:43f3e408d2a1db1b597678a691ba66aac7abd61ce8517d1bb875fdb24d593edc","target":"graph","created_at":"2026-05-18T00:57:38Z","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":"Following the approach in the book \"Commutative Algebra\", by D. Eisenbud, where the author describes the generic initial ideal by means of a suitable total order on the terms of an exterior power, we introduce first the generic initial extensor of a subset of a Grassmannian and then the double-generic initial ideal of a so-called GL-stable subset of a Hilbert scheme. We discuss the features of these new notions and introduce also a partial order which gives another useful description of them. The double-generic initial ideals turn out to be the appropriate points to understand some geometric p","authors_text":"Cristina Bertone, Francesca Cioffi, Margherita Roggero","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-12T15:25:05Z","title":"Double-Generic Initial Ideal and Hilbert Scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03768","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:d020bffd9fb91e5a0eb2af82fe8266d2e2066ecac679146f4ba9806073ffd6fc","target":"record","created_at":"2026-05-18T00:57:38Z","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":"8999253f75a6544023e181d0c6c6965af8175a0948c0756bc9b8a76bc09dbac6","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-12T15:25:05Z","title_canon_sha256":"4e6a7aca31be6088d447af5dd83dff5dea2d05fb0eef90a9039c1b4d0ba2eda7"},"schema_version":"1.0","source":{"id":"1503.03768","kind":"arxiv","version":2}},"canonical_sha256":"e511c70d426e5bbf7947bb92472c0ea63dbc22b2266c22939ca4b04163148bb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e511c70d426e5bbf7947bb92472c0ea63dbc22b2266c22939ca4b04163148bb1","first_computed_at":"2026-05-18T00:57:38.392696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:38.392696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhiABjhH0EY/ojgiDXLnISDjRSHVYIyXuZpCjV594dt+OoXuNUaGtsDpPwivgLyuBQ7k8n2ztUKvoFCGzpFqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:38.393202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03768","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d020bffd9fb91e5a0eb2af82fe8266d2e2066ecac679146f4ba9806073ffd6fc","sha256:43f3e408d2a1db1b597678a691ba66aac7abd61ce8517d1bb875fdb24d593edc"],"state_sha256":"8e6b33bef2b43846e66e5cbec0cccf0e3b4bca052eaa7daed3fa55a0d79eac60"}