{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EFD6ULLKU5O7FPOOYWLP5IIJZH","short_pith_number":"pith:EFD6ULLK","canonical_record":{"source":{"id":"2507.04902","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-07T11:40:22Z","cross_cats_sorted":[],"title_canon_sha256":"5902de92b537758c51c2869f507a68eba320a8a0cb5a1ceaf841fdb0542c5682","abstract_canon_sha256":"c0d86029b9ae7b5074d9a4cd160f627d68403a21eb182a8a497098c7f2e2f0c0"},"schema_version":"1.0"},"canonical_sha256":"2147ea2d6aa75df2bdcec596fea109c9f98789c4af168d6cf3b19ee8c61632eb","source":{"kind":"arxiv","id":"2507.04902","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04902","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04902v2","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04902","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"EFD6ULLKU5O7","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"EFD6ULLKU5O7FPOO","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"EFD6ULLK","created_at":"2026-07-05T11:39:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EFD6ULLKU5O7FPOOYWLP5IIJZH","target":"record","payload":{"canonical_record":{"source":{"id":"2507.04902","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-07T11:40:22Z","cross_cats_sorted":[],"title_canon_sha256":"5902de92b537758c51c2869f507a68eba320a8a0cb5a1ceaf841fdb0542c5682","abstract_canon_sha256":"c0d86029b9ae7b5074d9a4cd160f627d68403a21eb182a8a497098c7f2e2f0c0"},"schema_version":"1.0"},"canonical_sha256":"2147ea2d6aa75df2bdcec596fea109c9f98789c4af168d6cf3b19ee8c61632eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:13.104423Z","signature_b64":"n3UgRuSvingM7HKgGbPW3QLaYZkxiFEeAY5cjfZIsKH99qFVVrNSfgbSDWgCCbV0Oegm4IQDEIvXIqCsTtxoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2147ea2d6aa75df2bdcec596fea109c9f98789c4af168d6cf3b19ee8c61632eb","last_reissued_at":"2026-07-05T11:39:13.104003Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:13.104003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.04902","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":"2026-07-05T11:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AUyDVOdiPvJsvMMqGAxUj1pSTh7H7oTDtnV7kNiJJwAmHJMTbHS6p9GJm1eLOv7frvXT72N2FFnQl0/qgeCaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:25:40.375902Z"},"content_sha256":"0012614ee53f5bf1edd32801db04230fd64ea3b0472fa86e00acefb73aa08315","schema_version":"1.0","event_id":"sha256:0012614ee53f5bf1edd32801db04230fd64ea3b0472fa86e00acefb73aa08315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EFD6ULLKU5O7FPOOYWLP5IIJZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brill--Noether loci in genus $\\leq 12$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Richard Haburcak","submitted_at":"2025-07-07T11:40:22Z","abstract_excerpt":"A refined Brill--Noether theory seeks to determine which linear series are admitted by a ``general'' curve in a particular Brill--Noether locus. However, as Brill--Noether loci are not irreducible in general, a coarse answer is given by the relative positions of Brill--Noether loci. Via an analysis of unstable Lazarsfeld--Mukai bundles on K3 surfaces, we distinguish Brill--Noether loci and provide expectations for the relative positions of Brill--Noether loci in general. Together with classical results, the refined Brill--Noether theory for curves of fixed gonality and on Hirzebruch surfaces, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04902","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.04902/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:39:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMHf9RfMQAQrQjQmi9HNUmbR791PtTAM8OikR12TaN/kh4/hzuHXwpIdQwuAhv2vTr/Jp2SqL5drHuHWrhc6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T20:25:40.376448Z"},"content_sha256":"364dde87345704ae16ac1191769a17d66b401b917fcfb9e64e9be47245bd4281","schema_version":"1.0","event_id":"sha256:364dde87345704ae16ac1191769a17d66b401b917fcfb9e64e9be47245bd4281"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH/bundle.json","state_url":"https://pith.science/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH/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":"2026-08-12T20:25:40Z","links":{"resolver":"https://pith.science/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH","bundle":"https://pith.science/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH/bundle.json","state":"https://pith.science/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFD6ULLKU5O7FPOOYWLP5IIJZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EFD6ULLKU5O7FPOOYWLP5IIJZH","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":"c0d86029b9ae7b5074d9a4cd160f627d68403a21eb182a8a497098c7f2e2f0c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-07T11:40:22Z","title_canon_sha256":"5902de92b537758c51c2869f507a68eba320a8a0cb5a1ceaf841fdb0542c5682"},"schema_version":"1.0","source":{"id":"2507.04902","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04902","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04902v2","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04902","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"pith_short_12","alias_value":"EFD6ULLKU5O7","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"pith_short_16","alias_value":"EFD6ULLKU5O7FPOO","created_at":"2026-07-05T11:39:13Z"},{"alias_kind":"pith_short_8","alias_value":"EFD6ULLK","created_at":"2026-07-05T11:39:13Z"}],"graph_snapshots":[{"event_id":"sha256:364dde87345704ae16ac1191769a17d66b401b917fcfb9e64e9be47245bd4281","target":"graph","created_at":"2026-07-05T11:39:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.04902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A refined Brill--Noether theory seeks to determine which linear series are admitted by a ``general'' curve in a particular Brill--Noether locus. However, as Brill--Noether loci are not irreducible in general, a coarse answer is given by the relative positions of Brill--Noether loci. Via an analysis of unstable Lazarsfeld--Mukai bundles on K3 surfaces, we distinguish Brill--Noether loci and provide expectations for the relative positions of Brill--Noether loci in general. Together with classical results, the refined Brill--Noether theory for curves of fixed gonality and on Hirzebruch surfaces, ","authors_text":"Richard Haburcak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-07T11:40:22Z","title":"Brill--Noether loci in genus $\\leq 12$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04902","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":"sha256:0012614ee53f5bf1edd32801db04230fd64ea3b0472fa86e00acefb73aa08315","target":"record","created_at":"2026-07-05T11:39:13Z","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":"c0d86029b9ae7b5074d9a4cd160f627d68403a21eb182a8a497098c7f2e2f0c0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-07-07T11:40:22Z","title_canon_sha256":"5902de92b537758c51c2869f507a68eba320a8a0cb5a1ceaf841fdb0542c5682"},"schema_version":"1.0","source":{"id":"2507.04902","kind":"arxiv","version":2}},"canonical_sha256":"2147ea2d6aa75df2bdcec596fea109c9f98789c4af168d6cf3b19ee8c61632eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2147ea2d6aa75df2bdcec596fea109c9f98789c4af168d6cf3b19ee8c61632eb","first_computed_at":"2026-07-05T11:39:13.104003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:13.104003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3UgRuSvingM7HKgGbPW3QLaYZkxiFEeAY5cjfZIsKH99qFVVrNSfgbSDWgCCbV0Oegm4IQDEIvXIqCsTtxoDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:13.104423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.04902","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0012614ee53f5bf1edd32801db04230fd64ea3b0472fa86e00acefb73aa08315","sha256:364dde87345704ae16ac1191769a17d66b401b917fcfb9e64e9be47245bd4281"],"state_sha256":"7ed3dabfa4900ad0a418bfb9adfb0e21c651d2f0c5291b9dac9dda5e7c4dcf06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxRm+aV1ptpm6zbWjX2SAcqfdz9nZ/RaBE0AhrOSIUiCjNdYTkYHYbG+j6nSbcXBBnJ3X4P5eV1eRWgdrplLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T20:25:40.380566Z","bundle_sha256":"10dc4024bd7b9a5c3e73dc20e7273e05fd447452a97292b167a372b51951a3df"}}