{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LHJ6YU7KB7TAV7FDWAMFWEKEYQ","short_pith_number":"pith:LHJ6YU7K","canonical_record":{"source":{"id":"1403.7489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-28T19:11:03Z","cross_cats_sorted":[],"title_canon_sha256":"b2139c6a1f647cd075c713480b8760ecc46d62eb74bc5cef9a1a4ae5b6659a5d","abstract_canon_sha256":"b97923f246138041d290989542014e76640654ebe8b9397b5d9513484d571f0e"},"schema_version":"1.0"},"canonical_sha256":"59d3ec53ea0fe60afca3b0185b1144c43f50193cf493a12a1d8d84e661a7ecdb","source":{"kind":"arxiv","id":"1403.7489","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7489","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7489v2","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7489","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"LHJ6YU7KB7TA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LHJ6YU7KB7TAV7FD","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LHJ6YU7K","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LHJ6YU7KB7TAV7FDWAMFWEKEYQ","target":"record","payload":{"canonical_record":{"source":{"id":"1403.7489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-28T19:11:03Z","cross_cats_sorted":[],"title_canon_sha256":"b2139c6a1f647cd075c713480b8760ecc46d62eb74bc5cef9a1a4ae5b6659a5d","abstract_canon_sha256":"b97923f246138041d290989542014e76640654ebe8b9397b5d9513484d571f0e"},"schema_version":"1.0"},"canonical_sha256":"59d3ec53ea0fe60afca3b0185b1144c43f50193cf493a12a1d8d84e661a7ecdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:03.055224Z","signature_b64":"G7WllVTYf3ngUuGgtWrrLBy3E/Bcm+NSDxeqv8940Y3z/eR9FqnP43RmQ6vNND3BjrOEaYqWNyAMUeDFXhO/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59d3ec53ea0fe60afca3b0185b1144c43f50193cf493a12a1d8d84e661a7ecdb","last_reissued_at":"2026-05-18T02:49:03.054730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:03.054730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.7489","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1Gi4tc7aUB2w4r1E2pV9sUwLdEj3eT8/mlFLkA3QSLQU4mQk0YtvNKXMxctFwxepUs8WvCD91mLKNL4XOTJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:34:54.155385Z"},"content_sha256":"e640632f58672ad0892f15bc4f3b4510e10de0604b0ba82e8250c459def547a8","schema_version":"1.0","event_id":"sha256:e640632f58672ad0892f15bc4f3b4510e10de0604b0ba82e8250c459def547a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LHJ6YU7KB7TAV7FDWAMFWEKEYQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants of the Brill-Noether curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Alberto L\\'opez Mart\\'in, Montserrat Teixidor i Bigas","submitted_at":"2014-03-28T19:11:03Z","abstract_excerpt":"For a projective nonsingular curve of genus $g$, the Brill-Noether locus $W^r_d(C)$ parametrizes line bundles of degree $d$ over $C$ with at least $r+1$ sections. When the curve is generic and the Brill-Noether number $\\rho(g,r,d)$ equals $1$, one can then talk of the \\emph{Brill-Noether curve}. In this paper, we explore the first two invariants of this curve, giving a new way of calculating the genus of this curve and computing its gonality when $C$ has genus 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7489","kind":"arxiv","version":2},"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":"2026-05-18T02:49:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3mngmF9Az/8rAYPucPUFdgyommCdlDixbwYBlXT9SkMYO6t1JI2YVAxIv3GeaTirph01teZ/uDCVLhvVP3vNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:34:54.155781Z"},"content_sha256":"0260d0f6d1433a28c70817efa193ef5b9a3315640b4af810b197e2d4d0351b60","schema_version":"1.0","event_id":"sha256:0260d0f6d1433a28c70817efa193ef5b9a3315640b4af810b197e2d4d0351b60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ/bundle.json","state_url":"https://pith.science/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ/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":"2026-06-03T03:34:54Z","links":{"resolver":"https://pith.science/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ","bundle":"https://pith.science/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ/bundle.json","state":"https://pith.science/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHJ6YU7KB7TAV7FDWAMFWEKEYQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LHJ6YU7KB7TAV7FDWAMFWEKEYQ","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":"b97923f246138041d290989542014e76640654ebe8b9397b5d9513484d571f0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-28T19:11:03Z","title_canon_sha256":"b2139c6a1f647cd075c713480b8760ecc46d62eb74bc5cef9a1a4ae5b6659a5d"},"schema_version":"1.0","source":{"id":"1403.7489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7489","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7489v2","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7489","created_at":"2026-05-18T02:49:03Z"},{"alias_kind":"pith_short_12","alias_value":"LHJ6YU7KB7TA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LHJ6YU7KB7TAV7FD","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LHJ6YU7K","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:0260d0f6d1433a28c70817efa193ef5b9a3315640b4af810b197e2d4d0351b60","target":"graph","created_at":"2026-05-18T02:49:03Z","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":"For a projective nonsingular curve of genus $g$, the Brill-Noether locus $W^r_d(C)$ parametrizes line bundles of degree $d$ over $C$ with at least $r+1$ sections. When the curve is generic and the Brill-Noether number $\\rho(g,r,d)$ equals $1$, one can then talk of the \\emph{Brill-Noether curve}. In this paper, we explore the first two invariants of this curve, giving a new way of calculating the genus of this curve and computing its gonality when $C$ has genus 5.","authors_text":"Abel Castorena, Alberto L\\'opez Mart\\'in, Montserrat Teixidor i Bigas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-28T19:11:03Z","title":"Invariants of the Brill-Noether curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7489","kind":"arxiv","version":2},"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:e640632f58672ad0892f15bc4f3b4510e10de0604b0ba82e8250c459def547a8","target":"record","created_at":"2026-05-18T02:49:03Z","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":"b97923f246138041d290989542014e76640654ebe8b9397b5d9513484d571f0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-28T19:11:03Z","title_canon_sha256":"b2139c6a1f647cd075c713480b8760ecc46d62eb74bc5cef9a1a4ae5b6659a5d"},"schema_version":"1.0","source":{"id":"1403.7489","kind":"arxiv","version":2}},"canonical_sha256":"59d3ec53ea0fe60afca3b0185b1144c43f50193cf493a12a1d8d84e661a7ecdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59d3ec53ea0fe60afca3b0185b1144c43f50193cf493a12a1d8d84e661a7ecdb","first_computed_at":"2026-05-18T02:49:03.054730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:03.054730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G7WllVTYf3ngUuGgtWrrLBy3E/Bcm+NSDxeqv8940Y3z/eR9FqnP43RmQ6vNND3BjrOEaYqWNyAMUeDFXhO/BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:03.055224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e640632f58672ad0892f15bc4f3b4510e10de0604b0ba82e8250c459def547a8","sha256:0260d0f6d1433a28c70817efa193ef5b9a3315640b4af810b197e2d4d0351b60"],"state_sha256":"685bf3148333d3a1d58b42b0c493256c92b292faee0cb7c277e342cc6277c318"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JiFHMJRhvSi/79Y0m9isbF2ig2VyG98nTCuw8DECXomGwJ8mYod+kgXNIyjsJ7fsSDHbTi6MecojuIWEHGpSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:34:54.157778Z","bundle_sha256":"d71dedfb8117b6348a7ce4f643bae5c01df3251756a8e206b7aa61d19217babe"}}