{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZO2HWSH2EVWO2NEGZ6UZ6MY5UI","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":"3343ba85968d91b2f5e729564024f777194ea278f368f6c33a64f3797e89d97b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-06-25T16:24:12Z","title_canon_sha256":"82aef2bf42fe0227fbf1c06e8e536087c2992072162226c385dfe7ab4e294b7d"},"schema_version":"1.0","source":{"id":"1006.5020","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5020","created_at":"2026-05-18T04:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5020v2","created_at":"2026-05-18T04:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5020","created_at":"2026-05-18T04:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZO2HWSH2EVWO","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZO2HWSH2EVWO2NEG","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZO2HWSH2","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ddecf2b842020389b7d71d13e77d306496ba2bcfe5aa0a25b218fbbeac56ae93","target":"graph","created_at":"2026-05-18T04:38:40Z","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 this paper we introduce an effective method to construct rational deformations between couples of Borel-fixed ideals. These deformations are governed by flat families, so that they correspond to rational curves on the Hilbert scheme. Looking globally at all the deformations among Borel-fixed ideals defining points on the same Hilbert scheme, we are able to give a new proof of the connectedness of the Hilbert scheme and to introduce a new criterion to establish whenever a set of points defined by Borel ideals lies on a common component of the Hilbert scheme. The paper contains a detailed alg","authors_text":"Paolo Lella","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-06-25T16:24:12Z","title":"A network of rational curves on the Hilbert scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5020","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":"sha256:67ccd53e6691957646f60616786cfc93182e3b51c9b1356e820c89f19baa261f","target":"record","created_at":"2026-05-18T04:38:40Z","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":"3343ba85968d91b2f5e729564024f777194ea278f368f6c33a64f3797e89d97b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-06-25T16:24:12Z","title_canon_sha256":"82aef2bf42fe0227fbf1c06e8e536087c2992072162226c385dfe7ab4e294b7d"},"schema_version":"1.0","source":{"id":"1006.5020","kind":"arxiv","version":2}},"canonical_sha256":"cbb47b48fa256ced3486cfa99f331da22f4be92e9d42e3ad25792ae30d3181fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbb47b48fa256ced3486cfa99f331da22f4be92e9d42e3ad25792ae30d3181fd","first_computed_at":"2026-05-18T04:38:40.016612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:40.016612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oGzFzwYd4IA8gTkOQeQysoKMJXkUPIV361OIBWP5ahBfG9otNCSAg/IcH4L8nnXPlcopc3i8oQ4igeCb+wkIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:40.017120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5020","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67ccd53e6691957646f60616786cfc93182e3b51c9b1356e820c89f19baa261f","sha256:ddecf2b842020389b7d71d13e77d306496ba2bcfe5aa0a25b218fbbeac56ae93"],"state_sha256":"d82aff457107d4d2443e51c8b1d4a2ae8f880dc1f8f7a7031b6cc505bde8187b"}