{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:WTG2V6L43NWFETWSUQRYGEVNFQ","short_pith_number":"pith:WTG2V6L4","canonical_record":{"source":{"id":"0704.0874","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-04-06T11:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"95689d5f4c1c7ee90f5d4f5275d2edf4ce13b3a6a71e401ce97b0ea5302ef031","abstract_canon_sha256":"64149576cf4696f74a44f0b9aca1ba1717a11d23a319ea332e7739b82f8525c9"},"schema_version":"1.0"},"canonical_sha256":"b4cdaaf97cdb6c524ed2a4238312ad2c0aff36c18dad7cfe92714413863d9d02","source":{"kind":"arxiv","id":"0704.0874","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.0874","created_at":"2026-05-18T02:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"0704.0874v3","created_at":"2026-05-18T02:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.0874","created_at":"2026-05-18T02:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"WTG2V6L43NWF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WTG2V6L43NWFETWS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WTG2V6L4","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:WTG2V6L43NWFETWSUQRYGEVNFQ","target":"record","payload":{"canonical_record":{"source":{"id":"0704.0874","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-04-06T11:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"95689d5f4c1c7ee90f5d4f5275d2edf4ce13b3a6a71e401ce97b0ea5302ef031","abstract_canon_sha256":"64149576cf4696f74a44f0b9aca1ba1717a11d23a319ea332e7739b82f8525c9"},"schema_version":"1.0"},"canonical_sha256":"b4cdaaf97cdb6c524ed2a4238312ad2c0aff36c18dad7cfe92714413863d9d02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:32.875726Z","signature_b64":"5r/bwlh0WCEB7VPVX1/27QNOXLFOkY/mkBGoDsR1yFAXXBhO/UczvYO0y491EDcXyG2qBnEj03Lr25WiZOO3DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4cdaaf97cdb6c524ed2a4238312ad2c0aff36c18dad7cfe92714413863d9d02","last_reissued_at":"2026-05-18T02:33:32.875129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:32.875129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.0874","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":"2026-05-18T02:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djcVqVEUflO0Sl2WKuSAgC9RxOI1zXeX5hNqUsX5vY+fzDJA4nqvZyEj5ILwcmU/7w40qHKO9vDdrPYCGV2VDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:54:42.438435Z"},"content_sha256":"8dd42e3ab2a7def0ce3b55730a3f791631787a386f8f925e91a29628342bfe3a","schema_version":"1.0","event_id":"sha256:8dd42e3ab2a7def0ce3b55730a3f791631787a386f8f925e91a29628342bfe3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:WTG2V6L43NWFETWSUQRYGEVNFQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher ramification and varieties of secant divisors on the generic curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gavril Farkas","submitted_at":"2007-04-06T11:07:01Z","abstract_excerpt":"For a smooth projective curve, the cycles of e-secant k-planes are among the most studied objects in classical enumerative geometry and there are well-known formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite various attempts, surprisingly little is known about the enumerative validity of such formulas. The aim of this paper is to completely clarify this problem in the case of the generic curve C of given genus. Using degeneration techniques and a few facts about the birational geometry of moduli spaces of stable pointed curves we determine precisely under which conditio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.0874","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":"2026-05-18T02:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aq63o9mWC0dSoFDebdrCwzDGwCxyhfyrdiyBJJVpAsteF0MJjizJXa1GKNoTY1jezv4/SgCTEsY4DhKcr2qWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:54:42.438774Z"},"content_sha256":"951b04f38da68e23f8ceef2e5577fdbd7b6a7f25415aad0d7c3332f5c4e66754","schema_version":"1.0","event_id":"sha256:951b04f38da68e23f8ceef2e5577fdbd7b6a7f25415aad0d7c3332f5c4e66754"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTG2V6L43NWFETWSUQRYGEVNFQ/bundle.json","state_url":"https://pith.science/pith/WTG2V6L43NWFETWSUQRYGEVNFQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTG2V6L43NWFETWSUQRYGEVNFQ/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":"2026-06-02T15:54:42Z","links":{"resolver":"https://pith.science/pith/WTG2V6L43NWFETWSUQRYGEVNFQ","bundle":"https://pith.science/pith/WTG2V6L43NWFETWSUQRYGEVNFQ/bundle.json","state":"https://pith.science/pith/WTG2V6L43NWFETWSUQRYGEVNFQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTG2V6L43NWFETWSUQRYGEVNFQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:WTG2V6L43NWFETWSUQRYGEVNFQ","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":"64149576cf4696f74a44f0b9aca1ba1717a11d23a319ea332e7739b82f8525c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-04-06T11:07:01Z","title_canon_sha256":"95689d5f4c1c7ee90f5d4f5275d2edf4ce13b3a6a71e401ce97b0ea5302ef031"},"schema_version":"1.0","source":{"id":"0704.0874","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.0874","created_at":"2026-05-18T02:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"0704.0874v3","created_at":"2026-05-18T02:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.0874","created_at":"2026-05-18T02:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"WTG2V6L43NWF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"WTG2V6L43NWFETWS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"WTG2V6L4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:951b04f38da68e23f8ceef2e5577fdbd7b6a7f25415aad0d7c3332f5c4e66754","target":"graph","created_at":"2026-05-18T02:33:32Z","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 smooth projective curve, the cycles of e-secant k-planes are among the most studied objects in classical enumerative geometry and there are well-known formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite various attempts, surprisingly little is known about the enumerative validity of such formulas. The aim of this paper is to completely clarify this problem in the case of the generic curve C of given genus. Using degeneration techniques and a few facts about the birational geometry of moduli spaces of stable pointed curves we determine precisely under which conditio","authors_text":"Gavril Farkas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-04-06T11:07:01Z","title":"Higher ramification and varieties of secant divisors on the generic curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.0874","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":"sha256:8dd42e3ab2a7def0ce3b55730a3f791631787a386f8f925e91a29628342bfe3a","target":"record","created_at":"2026-05-18T02:33:32Z","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":"64149576cf4696f74a44f0b9aca1ba1717a11d23a319ea332e7739b82f8525c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-04-06T11:07:01Z","title_canon_sha256":"95689d5f4c1c7ee90f5d4f5275d2edf4ce13b3a6a71e401ce97b0ea5302ef031"},"schema_version":"1.0","source":{"id":"0704.0874","kind":"arxiv","version":3}},"canonical_sha256":"b4cdaaf97cdb6c524ed2a4238312ad2c0aff36c18dad7cfe92714413863d9d02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4cdaaf97cdb6c524ed2a4238312ad2c0aff36c18dad7cfe92714413863d9d02","first_computed_at":"2026-05-18T02:33:32.875129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:32.875129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5r/bwlh0WCEB7VPVX1/27QNOXLFOkY/mkBGoDsR1yFAXXBhO/UczvYO0y491EDcXyG2qBnEj03Lr25WiZOO3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:32.875726Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.0874","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dd42e3ab2a7def0ce3b55730a3f791631787a386f8f925e91a29628342bfe3a","sha256:951b04f38da68e23f8ceef2e5577fdbd7b6a7f25415aad0d7c3332f5c4e66754"],"state_sha256":"c2277d6f79f2630c2b45b1f5a20a63cbfe71068c8624d9d430d3503a3a684e32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2IIoY+QXLLAiRP4U4prdGasT28wXeXzsuO72XmD+uNm+EQ2xF2q8V/cDTOhGffQWkOaP71OtrJLcFaoS8hUDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:54:42.440650Z","bundle_sha256":"c39055f9627632d3c5539e0e04a1ec233cd68508b71efb6a770f67483b4b48dd"}}