{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CAITM4G5OLN2ZCUVDFTKOOEAL4","short_pith_number":"pith:CAITM4G5","canonical_record":{"source":{"id":"1303.0097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-01T06:54:25Z","cross_cats_sorted":[],"title_canon_sha256":"61913e5fe4809bbc0140781ccea0d6f3ff037a015a059265a7a49098be8d70b4","abstract_canon_sha256":"48d35597e643e6ab4fb9ef1d147fef421cd51bbbb557e7dbf9a21a7d9b99da69"},"schema_version":"1.0"},"canonical_sha256":"10113670dd72dbac8a951966a738805f387b4e1b8cfe020037421f91d9718c0d","source":{"kind":"arxiv","id":"1303.0097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0097","created_at":"2026-05-18T03:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0097v1","created_at":"2026-05-18T03:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0097","created_at":"2026-05-18T03:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"CAITM4G5OLN2","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CAITM4G5OLN2ZCUV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CAITM4G5","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CAITM4G5OLN2ZCUVDFTKOOEAL4","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-01T06:54:25Z","cross_cats_sorted":[],"title_canon_sha256":"61913e5fe4809bbc0140781ccea0d6f3ff037a015a059265a7a49098be8d70b4","abstract_canon_sha256":"48d35597e643e6ab4fb9ef1d147fef421cd51bbbb557e7dbf9a21a7d9b99da69"},"schema_version":"1.0"},"canonical_sha256":"10113670dd72dbac8a951966a738805f387b4e1b8cfe020037421f91d9718c0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:06.841702Z","signature_b64":"Zq5O24U3EGna53daQ7uZ1+UJrCdLmr6W21egmiOW1aEzyqXinCGEQ4Det0f9SYdX92bfN/ZLR79LYHrXrKIFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10113670dd72dbac8a951966a738805f387b4e1b8cfe020037421f91d9718c0d","last_reissued_at":"2026-05-18T03:32:06.840975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:06.840975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0097","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":"2026-05-18T03:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAAxkmv1Yu4oTn/yc9MsEyQ1tLdkJ9F+cYmej+892E1CiS8IWXIE4afXmnlisBBMMtVk0qdgGR0ZZnVYKiYaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:27.202865Z"},"content_sha256":"259b68d2aab8ff273847b99f0a6f156ad34314f9769dd00281c76ac104f42e83","schema_version":"1.0","event_id":"sha256:259b68d2aab8ff273847b99f0a6f156ad34314f9769dd00281c76ac104f42e83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CAITM4G5OLN2ZCUVDFTKOOEAL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico","submitted_at":"2013-03-01T06:54:25Z","abstract_excerpt":"Let $C$ be a smooth curve of genus $g$. For each positive integer $r$ the $r$-gonality $d_r(C)$ of $C$ is the minimal integer $t$ such that there is $L\\in {Pic}^t(C)$ with $h^0(C,L) =r+1$. In this paper for all $g\\ge 40805$ we construct several examples of smooth curves $C$ of genus $g$ with $d_3(C)/3< d_4(C)/4$, i.e. for which a slope inequality fails."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0097","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":"2026-05-18T03:32:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUNudkXtpoXyCtjLZ6sjnG6TxnCEtuCHtzwPXsfXpIk4apyqC18SI56+pDzMgLWF1Y6E3lmcA/WVieOeymOvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:27.203650Z"},"content_sha256":"4bbd83a0d7492f3820288f39a4935414966b70cedfb8982998ea43612a8e4480","schema_version":"1.0","event_id":"sha256:4bbd83a0d7492f3820288f39a4935414966b70cedfb8982998ea43612a8e4480"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4/bundle.json","state_url":"https://pith.science/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4/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":"2026-05-30T06:15:27Z","links":{"resolver":"https://pith.science/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4","bundle":"https://pith.science/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4/bundle.json","state":"https://pith.science/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CAITM4G5OLN2ZCUVDFTKOOEAL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CAITM4G5OLN2ZCUVDFTKOOEAL4","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":"48d35597e643e6ab4fb9ef1d147fef421cd51bbbb557e7dbf9a21a7d9b99da69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-01T06:54:25Z","title_canon_sha256":"61913e5fe4809bbc0140781ccea0d6f3ff037a015a059265a7a49098be8d70b4"},"schema_version":"1.0","source":{"id":"1303.0097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0097","created_at":"2026-05-18T03:32:06Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0097v1","created_at":"2026-05-18T03:32:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0097","created_at":"2026-05-18T03:32:06Z"},{"alias_kind":"pith_short_12","alias_value":"CAITM4G5OLN2","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CAITM4G5OLN2ZCUV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CAITM4G5","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:4bbd83a0d7492f3820288f39a4935414966b70cedfb8982998ea43612a8e4480","target":"graph","created_at":"2026-05-18T03:32:06Z","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 smooth curve of genus $g$. For each positive integer $r$ the $r$-gonality $d_r(C)$ of $C$ is the minimal integer $t$ such that there is $L\\in {Pic}^t(C)$ with $h^0(C,L) =r+1$. In this paper for all $g\\ge 40805$ we construct several examples of smooth curves $C$ of genus $g$ with $d_3(C)/3< d_4(C)/4$, i.e. for which a slope inequality fails.","authors_text":"Edoardo Ballico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-01T06:54:25Z","title":"On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0097","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":"sha256:259b68d2aab8ff273847b99f0a6f156ad34314f9769dd00281c76ac104f42e83","target":"record","created_at":"2026-05-18T03:32:06Z","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":"48d35597e643e6ab4fb9ef1d147fef421cd51bbbb557e7dbf9a21a7d9b99da69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-01T06:54:25Z","title_canon_sha256":"61913e5fe4809bbc0140781ccea0d6f3ff037a015a059265a7a49098be8d70b4"},"schema_version":"1.0","source":{"id":"1303.0097","kind":"arxiv","version":1}},"canonical_sha256":"10113670dd72dbac8a951966a738805f387b4e1b8cfe020037421f91d9718c0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10113670dd72dbac8a951966a738805f387b4e1b8cfe020037421f91d9718c0d","first_computed_at":"2026-05-18T03:32:06.840975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:06.840975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zq5O24U3EGna53daQ7uZ1+UJrCdLmr6W21egmiOW1aEzyqXinCGEQ4Det0f9SYdX92bfN/ZLR79LYHrXrKIFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:06.841702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:259b68d2aab8ff273847b99f0a6f156ad34314f9769dd00281c76ac104f42e83","sha256:4bbd83a0d7492f3820288f39a4935414966b70cedfb8982998ea43612a8e4480"],"state_sha256":"5eb28b25ff14acfb6ad8d449de879f1880a4e40c8994eab42fafc06877809bce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLBMYHKzM+jbYSlpquroNTFoxByTS67tkQcy7bYqtzyNfZw4WBafoqjzEKDuUaQZyoodcpToDB8WdBREL39+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:15:27.207599Z","bundle_sha256":"a27197e556a99fcc7cf7ad4d99d94d7fa6ea021099aadf31c391347faea180d8"}}