{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IVFOZ23BKRJ4KYVYNXWPT4CFR4","short_pith_number":"pith:IVFOZ23B","canonical_record":{"source":{"id":"1202.3551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-16T10:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"81c5a90b2b498077f2aba8e08b8204795d4470867189b499f9cfca4f25298d5c","abstract_canon_sha256":"affd1ff629a12839d76ffc651ebbbfc24120b3de13a79a7fff73f12db69955ff"},"schema_version":"1.0"},"canonical_sha256":"454aeceb615453c562b86decf9f0458f0933df41a5a4f5ee31637156c2e1a40c","source":{"kind":"arxiv","id":"1202.3551","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IVFOZ23BKRJ4KYVYNXWPT4CFR4","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-16T10:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"81c5a90b2b498077f2aba8e08b8204795d4470867189b499f9cfca4f25298d5c","abstract_canon_sha256":"affd1ff629a12839d76ffc651ebbbfc24120b3de13a79a7fff73f12db69955ff"},"schema_version":"1.0"},"canonical_sha256":"454aeceb615453c562b86decf9f0458f0933df41a5a4f5ee31637156c2e1a40c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:12.898902Z","signature_b64":"/cQrDNfEXMoSsITg1GylbYp+zUBqd8RzbWbceYME5zDxy7Hxdq2JRUOM1yZ6sQGaL9AnYfjYN1RYbbeQD/ZMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"454aeceb615453c562b86decf9f0458f0933df41a5a4f5ee31637156c2e1a40c","last_reissued_at":"2026-05-18T04:02:12.898218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:12.898218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3551","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uzBfUZZiiDP6aAJ8kthFBShWRIUfPm/bH0V2uJmVmKCxbAeJsQP+jJOBzvJ5lpkXEX56rT8TQzqHa+N9S7D1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:58:20.186769Z"},"content_sha256":"b68b34147408fcb9c832d42251c9a3943d8c5cf32f87025fe0d32c02f7fd8070","schema_version":"1.0","event_id":"sha256:b68b34147408fcb9c832d42251c9a3943d8c5cf32f87025fe0d32c02f7fd8070"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IVFOZ23BKRJ4KYVYNXWPT4CFR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Torsion-free Sheaves and ACM Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"M.L. Spreafico, R. Notari, S. Greco","submitted_at":"2012-02-16T10:04:45Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3551","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/g9MVJ5Cz6rzPh4+UI8XbBMuCodxucftUrFdkvR6yskjSHPu0I1sIy+a8SSwBUqXK7S18PVGLLAh62zIh/+kCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:58:20.187115Z"},"content_sha256":"bc53cccfd66ba7352015fc050a63c7dce7427b0ea52b2011127f17a2bbe5a236","schema_version":"1.0","event_id":"sha256:bc53cccfd66ba7352015fc050a63c7dce7427b0ea52b2011127f17a2bbe5a236"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4/bundle.json","state_url":"https://pith.science/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T22:58:20Z","links":{"resolver":"https://pith.science/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4","bundle":"https://pith.science/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4/bundle.json","state":"https://pith.science/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVFOZ23BKRJ4KYVYNXWPT4CFR4/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZV55yG3KhkzoUJnjsPGxP1X5VVHhu+A7Jx637i2mfzQLQ/TIEEzqCdY6j+GEFrxVtTeB5WDgICnNEY8JrNsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:58:20.189098Z","bundle_sha256":"c38ae435236f2ab4b1219d5e88c9b0835b2f3804e83134a0bfa3b1cf1c889982"}}