{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YVQHM3J3WMBKK3MGMZV5V3HYAH","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":"54f11e3cf9e6514e8050013ee58e3d0aab9e026b0eaae13c86594093511619f2","cross_cats_sorted":["math.AC","math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-05-02T15:11:48Z","title_canon_sha256":"abffc23f69d24eb2762a162c0abe312aefe3d6cfedef6a3515f4acd691a24b5c"},"schema_version":"1.0","source":{"id":"1205.0456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0456","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0456v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0456","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"YVQHM3J3WMBK","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YVQHM3J3WMBKK3MG","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YVQHM3J3","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:1af1b93daf5a81ae0303c7bd7e7902f4ede05285e0afc044f0f56b55a2eec2be","target":"graph","created_at":"2026-05-18T03:56:34Z","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":"Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed each component and each intersection of components of a Hilbert scheme contains at least one Borel-fixed point, i.e. a point corresponding to a subscheme defined by a Borel-fixed ideal. Moreover Borel-fixed ideals have good combinatorial properties, which make them very interesting in an algorithmic perspective. In this paper, we propose an implementation of the algorithm computing all the saturated Borel-fixed ideals with number of variables and Hilbert polynomial assigned, introduced from a theoretical point of view i","authors_text":"Paolo Lella","cross_cats":["math.AC","math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-05-02T15:11:48Z","title":"An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0456","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":"sha256:5dbb140aa79fbdd0cff12f6923ce7451ad464d9432fcb7a7cd5993b35c9e0d70","target":"record","created_at":"2026-05-18T03:56:34Z","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":"54f11e3cf9e6514e8050013ee58e3d0aab9e026b0eaae13c86594093511619f2","cross_cats_sorted":["math.AC","math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-05-02T15:11:48Z","title_canon_sha256":"abffc23f69d24eb2762a162c0abe312aefe3d6cfedef6a3515f4acd691a24b5c"},"schema_version":"1.0","source":{"id":"1205.0456","kind":"arxiv","version":1}},"canonical_sha256":"c560766d3bb302a56d86666bdaecf801efd1647836080ac586e6748346df1f7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c560766d3bb302a56d86666bdaecf801efd1647836080ac586e6748346df1f7e","first_computed_at":"2026-05-18T03:56:34.491329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:34.491329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"urQ5vBKfTSiLKhneNBbuhJEISN7wcNnr6Pl5Nw1/FBsJxfnOXm2OvDVg04mP5QpUt4IzPt/ipSJgsxmFTb49DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:34.491904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dbb140aa79fbdd0cff12f6923ce7451ad464d9432fcb7a7cd5993b35c9e0d70","sha256:1af1b93daf5a81ae0303c7bd7e7902f4ede05285e0afc044f0f56b55a2eec2be"],"state_sha256":"08450a775b35ae163725f1f509e173241f33ca8e02ef460f7e966cf294bb2a97"}