{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z4QCVK7U2E46OOFJ6U4LSLDR2W","short_pith_number":"pith:Z4QCVK7U","canonical_record":{"source":{"id":"1507.05002","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T15:54:55Z","cross_cats_sorted":[],"title_canon_sha256":"fdd90eaa72cae4e04149edd30fcda91cc92080d267d09031dd3c2f045a7575e2","abstract_canon_sha256":"e9ce93dfc4f9348377f870dd28ac348f0c00e313aac3f04c8d9a00cd5260a663"},"schema_version":"1.0"},"canonical_sha256":"cf202aabf4d139e738a9f538b92c71d595e4e4e76c22b17d5ccaa9ae7f3a9233","source":{"kind":"arxiv","id":"1507.05002","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05002","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05002v3","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05002","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"Z4QCVK7U2E46","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z4QCVK7U2E46OOFJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z4QCVK7U","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z4QCVK7U2E46OOFJ6U4LSLDR2W","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05002","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T15:54:55Z","cross_cats_sorted":[],"title_canon_sha256":"fdd90eaa72cae4e04149edd30fcda91cc92080d267d09031dd3c2f045a7575e2","abstract_canon_sha256":"e9ce93dfc4f9348377f870dd28ac348f0c00e313aac3f04c8d9a00cd5260a663"},"schema_version":"1.0"},"canonical_sha256":"cf202aabf4d139e738a9f538b92c71d595e4e4e76c22b17d5ccaa9ae7f3a9233","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:26.630955Z","signature_b64":"rk7chh3ib0VvKFRkEf8D4LV3a0Vt7mZjnphRc9qZvpACcF3Cypm8vDsCI0C1ETGjOVEyoEv+QkGgLOl0WcYcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf202aabf4d139e738a9f538b92c71d595e4e4e76c22b17d5ccaa9ae7f3a9233","last_reissued_at":"2026-05-18T00:59:26.630380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:26.630380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05002","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qRyW4suaPXzBI7iwiiFxx4NSkYH7wZVgTAQaD1DP9VjhD75/Tf9kObb1Tc2rFLM8q2d9A7MNwPV/UM0ucRVzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:26:12.888238Z"},"content_sha256":"33a189cf7626029214d0720d0f08058869a3ea105e2113a95e3d84f08fc780cd","schema_version":"1.0","event_id":"sha256:33a189cf7626029214d0720d0f08058869a3ea105e2113a95e3d84f08fc780cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z4QCVK7U2E46OOFJ6U4LSLDR2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On hyperplane sections of K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Bruno, Edoardo Sernesi, Enrico Arbarello","submitted_at":"2015-07-17T15:54:55Z","abstract_excerpt":"Let C be a Brill-Noether-Petri curve of genus g\\geq 12. We prove that C lies on a polarized K3 surface, or on a limit thereof, if and only if the Gauss-Wahl map for C is not surjective. The proof is obtained by studying the validity of two conjectures by J. Wahl. Let I_C be the ideal sheaf of a non-hyperelliptic, genus g, canonical curve. The first conjecture states that, if g\\geq 8, and if the Clifford index of C is greater than 2, then H^1(P^{g-1}, I_C^2(k))=0, for k\\geq 3. We prove this conjecture for g\\geq 11. The second conjecture states that a Brill-Noether-Petri curve of genus g\\geq 12 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05002","kind":"arxiv","version":3},"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":"2026-05-18T00:59:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JW4MK4XzpnaIG/ubuaSu+P/QOToBv4YHWjpBqpUCnlv+069xE4PNhF2tOzDVVe0ME2ACmRZLqrMhFCIDv0FtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:26:12.888602Z"},"content_sha256":"57ac1774675b48cf3e740c1c87f4f71de27c7a25fdf99c83236ddd7c0a83e62c","schema_version":"1.0","event_id":"sha256:57ac1774675b48cf3e740c1c87f4f71de27c7a25fdf99c83236ddd7c0a83e62c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/bundle.json","state_url":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/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":"2026-05-27T10:26:12Z","links":{"resolver":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W","bundle":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/bundle.json","state":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z4QCVK7U2E46OOFJ6U4LSLDR2W","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":"e9ce93dfc4f9348377f870dd28ac348f0c00e313aac3f04c8d9a00cd5260a663","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T15:54:55Z","title_canon_sha256":"fdd90eaa72cae4e04149edd30fcda91cc92080d267d09031dd3c2f045a7575e2"},"schema_version":"1.0","source":{"id":"1507.05002","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05002","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05002v3","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05002","created_at":"2026-05-18T00:59:26Z"},{"alias_kind":"pith_short_12","alias_value":"Z4QCVK7U2E46","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z4QCVK7U2E46OOFJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z4QCVK7U","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:57ac1774675b48cf3e740c1c87f4f71de27c7a25fdf99c83236ddd7c0a83e62c","target":"graph","created_at":"2026-05-18T00:59:26Z","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":"Let C be a Brill-Noether-Petri curve of genus g\\geq 12. We prove that C lies on a polarized K3 surface, or on a limit thereof, if and only if the Gauss-Wahl map for C is not surjective. The proof is obtained by studying the validity of two conjectures by J. Wahl. Let I_C be the ideal sheaf of a non-hyperelliptic, genus g, canonical curve. The first conjecture states that, if g\\geq 8, and if the Clifford index of C is greater than 2, then H^1(P^{g-1}, I_C^2(k))=0, for k\\geq 3. We prove this conjecture for g\\geq 11. The second conjecture states that a Brill-Noether-Petri curve of genus g\\geq 12 ","authors_text":"Andrea Bruno, Edoardo Sernesi, Enrico Arbarello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T15:54:55Z","title":"On hyperplane sections of K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05002","kind":"arxiv","version":3},"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":"sha256:33a189cf7626029214d0720d0f08058869a3ea105e2113a95e3d84f08fc780cd","target":"record","created_at":"2026-05-18T00:59:26Z","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":"e9ce93dfc4f9348377f870dd28ac348f0c00e313aac3f04c8d9a00cd5260a663","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T15:54:55Z","title_canon_sha256":"fdd90eaa72cae4e04149edd30fcda91cc92080d267d09031dd3c2f045a7575e2"},"schema_version":"1.0","source":{"id":"1507.05002","kind":"arxiv","version":3}},"canonical_sha256":"cf202aabf4d139e738a9f538b92c71d595e4e4e76c22b17d5ccaa9ae7f3a9233","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf202aabf4d139e738a9f538b92c71d595e4e4e76c22b17d5ccaa9ae7f3a9233","first_computed_at":"2026-05-18T00:59:26.630380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:26.630380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rk7chh3ib0VvKFRkEf8D4LV3a0Vt7mZjnphRc9qZvpACcF3Cypm8vDsCI0C1ETGjOVEyoEv+QkGgLOl0WcYcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:26.630955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05002","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33a189cf7626029214d0720d0f08058869a3ea105e2113a95e3d84f08fc780cd","sha256:57ac1774675b48cf3e740c1c87f4f71de27c7a25fdf99c83236ddd7c0a83e62c"],"state_sha256":"3f27e0ad3fd7f29608447bbad53575952005849c3a3043607cc98986c020b161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaGi5IcIlEKAdmnDU8XHodzXZ4rJqC5BM3/vYZU5HJFClo19Kiw2gFMfXl1PPGaK2MRUF2/0Nl8ixhThzDOKDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:26:12.891023Z","bundle_sha256":"0fc3f2facd84430c68ad1b60bc55c12997e67d1a6f4215539c516f08df09e64c"}}