{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IVFOZ23BKRJ4KYVYNXWPT4CFR4","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":"affd1ff629a12839d76ffc651ebbbfc24120b3de13a79a7fff73f12db69955ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-16T10:04:45Z","title_canon_sha256":"81c5a90b2b498077f2aba8e08b8204795d4470867189b499f9cfca4f25298d5c"},"schema_version":"1.0","source":{"id":"1202.3551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3551","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3551v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3551","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"IVFOZ23BKRJ4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IVFOZ23BKRJ4KYVY","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IVFOZ23B","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:bc53cccfd66ba7352015fc050a63c7dce7427b0ea52b2011127f17a2bbe5a236","target":"graph","created_at":"2026-05-18T04:02:12Z","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 study short exact sequences $ 0 \\to \\mathcal P \\to \\mathcal N \\to \\ii_D(k) \\to 0 $ with $ \\mathcal P, \\mathcal N $ torsion--free sheaves and $ D $ closed projective scheme. This is a classical way to construct and study projective schemes (e.g. see \\cite{hart-1974}, \\cite{hart-2}, \\cite{mdp}, \\cite{serre-1960}). In particular, we give homological conditions on $ \\mathcal P $ and $ \\mathcal N $ that force $ D $ to be ACM, without constrains on its codimension. As last result, we prove that if $ \\mathcal N $ is a higher syzygy sheaf of an ACM scheme $ X,$ the scheme $ D $ we get","authors_text":"M.L. Spreafico, R. Notari, S. Greco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-16T10:04:45Z","title":"Torsion-free Sheaves and ACM Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3551","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:b68b34147408fcb9c832d42251c9a3943d8c5cf32f87025fe0d32c02f7fd8070","target":"record","created_at":"2026-05-18T04:02:12Z","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":"affd1ff629a12839d76ffc651ebbbfc24120b3de13a79a7fff73f12db69955ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-16T10:04:45Z","title_canon_sha256":"81c5a90b2b498077f2aba8e08b8204795d4470867189b499f9cfca4f25298d5c"},"schema_version":"1.0","source":{"id":"1202.3551","kind":"arxiv","version":1}},"canonical_sha256":"454aeceb615453c562b86decf9f0458f0933df41a5a4f5ee31637156c2e1a40c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"454aeceb615453c562b86decf9f0458f0933df41a5a4f5ee31637156c2e1a40c","first_computed_at":"2026-05-18T04:02:12.898218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:12.898218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/cQrDNfEXMoSsITg1GylbYp+zUBqd8RzbWbceYME5zDxy7Hxdq2JRUOM1yZ6sQGaL9AnYfjYN1RYbbeQD/ZMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:12.898902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b68b34147408fcb9c832d42251c9a3943d8c5cf32f87025fe0d32c02f7fd8070","sha256:bc53cccfd66ba7352015fc050a63c7dce7427b0ea52b2011127f17a2bbe5a236"],"state_sha256":"2a39b7752f58d0cbcbd423b4874cbf2a8e720916b3853444da685784572f2fb5"}