{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CYRHZHMYTYXXYRRA5C2YDLFHGJ","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":"3b0ed09d8353e52fadf6a1ccbf7889dc0ec605181feb68f26b01bfe45adddea7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-18T22:32:09Z","title_canon_sha256":"92c2fc2d8f908ebd31b5b63b7dcbfb8b836d05dd9d67656423d4c6871d45a154"},"schema_version":"1.0","source":{"id":"1207.4516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4516","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4516v1","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4516","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"CYRHZHMYTYXX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CYRHZHMYTYXXYRRA","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CYRHZHMY","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:49962eab5c2285b0924f86e8252595e4be6ecc8edd2527f36f4c469858d3554a","target":"graph","created_at":"2026-05-18T02:38:17Z","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":"Given a smooth complex projective variety X, a line bundle L of X an element v of H^1(O_X) and a section s in H^0(L) that deforms to first order in the direction v, we give a sufficient condition on v in terms of Koszul cohomology for this first order deformation to extend to an analytic deformation.\n  We apply this result to improve known results on the paracanonical system of a variety of maximal Albanese dimension, due to Beauville in the case of surfaces and to Lazarsfeld-Popa in higher dimension. In particular, we prove the inequality p_g(X)>=\\chi(K_X)+q(X)-1 for a variety X of maximal Al","authors_text":"Gian Pietro Pirola, Margarida Mendes Lopes, Rita Pardini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-18T22:32:09Z","title":"Continuous families of divisors, paracanonical systems and a new inequality for varieties of maximal Albanese dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4516","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":"sha256:5998c7d869303813cdeb029c52b7ca3febd5e3da178537dc072526fa5d2b1efa","target":"record","created_at":"2026-05-18T02:38:17Z","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":"3b0ed09d8353e52fadf6a1ccbf7889dc0ec605181feb68f26b01bfe45adddea7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-18T22:32:09Z","title_canon_sha256":"92c2fc2d8f908ebd31b5b63b7dcbfb8b836d05dd9d67656423d4c6871d45a154"},"schema_version":"1.0","source":{"id":"1207.4516","kind":"arxiv","version":1}},"canonical_sha256":"16227c9d989e2f7c4620e8b581aca73248917a0716157116f20be76599d2fa1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16227c9d989e2f7c4620e8b581aca73248917a0716157116f20be76599d2fa1d","first_computed_at":"2026-05-18T02:38:17.713166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.713166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qpq5lynFtefiDa2tp+NMKiWqPkJNC22TRZL//REPcqrcjU5wUxyFa9S20kyNFVw9xmHpzMWyU5nsp5+DVVhkAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.713857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5998c7d869303813cdeb029c52b7ca3febd5e3da178537dc072526fa5d2b1efa","sha256:49962eab5c2285b0924f86e8252595e4be6ecc8edd2527f36f4c469858d3554a"],"state_sha256":"f4883004cde1b08d65634e92e2fcdd29f63ee2fa9c9b85779582862d30df6ffb"}