{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z5LDU6LFCM5CLNYYF3RYJ3J4XN","short_pith_number":"pith:Z5LDU6LF","canonical_record":{"source":{"id":"1512.07726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-24T06:38:04Z","cross_cats_sorted":[],"title_canon_sha256":"431163ea92d183dd7c9780d62a8513d189e115f5b3314d196f9d652a6fc5827e","abstract_canon_sha256":"a96716cefcf1829cfeb17553631d0904c075fef4fbd2ca227c259b359ff19037"},"schema_version":"1.0"},"canonical_sha256":"cf563a7965133a25b7182ee384ed3cbb520c4588be3108749ea72b77e82b454c","source":{"kind":"arxiv","id":"1512.07726","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07726","created_at":"2026-05-18T00:29:47Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07726v2","created_at":"2026-05-18T00:29:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07726","created_at":"2026-05-18T00:29:47Z"},{"alias_kind":"pith_short_12","alias_value":"Z5LDU6LFCM5C","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z5LDU6LFCM5CLNYY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z5LDU6LF","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z5LDU6LFCM5CLNYYF3RYJ3J4XN","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-24T06:38:04Z","cross_cats_sorted":[],"title_canon_sha256":"431163ea92d183dd7c9780d62a8513d189e115f5b3314d196f9d652a6fc5827e","abstract_canon_sha256":"a96716cefcf1829cfeb17553631d0904c075fef4fbd2ca227c259b359ff19037"},"schema_version":"1.0"},"canonical_sha256":"cf563a7965133a25b7182ee384ed3cbb520c4588be3108749ea72b77e82b454c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:47.164271Z","signature_b64":"tBmYZ8KQvJWRQ3yWXmiBAGQaiafmtx0DOpeVX7G9z5/3AkR+ZtcoeER88NXhe14+6e0IuxkQ6Y6lH7LXOsQXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf563a7965133a25b7182ee384ed3cbb520c4588be3108749ea72b77e82b454c","last_reissued_at":"2026-05-18T00:29:47.163585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:47.163585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07726","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":"2026-05-18T00:29:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INa+meMHMi4IS2xlOCMuf8xVyZ5idalxRuuKYbLf+t0Si4k6u4HQADMfQQrSaRbWlr/w+xzAUlSNdpG9v+4YCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:24:30.695896Z"},"content_sha256":"5946571f92423bc7f1c23840468ee25a25a46425113912a3fe3a72d12f92337b","schema_version":"1.0","event_id":"sha256:5946571f92423bc7f1c23840468ee25a25a46425113912a3fe3a72d12f92337b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z5LDU6LFCM5CLNYYF3RYJ3J4XN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable maps of genus zero in the space of stable vector bundles on a curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kiryong Chung, Sanghyeon Lee","submitted_at":"2015-12-24T06:38:04Z","abstract_excerpt":"Let $X$ be a smooth projective curve with genus $g\\geq3$. Let $\\mathcal{N}$ be the moduli space of stable rank two vector bundles on $X$ with a fixed determinant $\\mathcal{O}_X(-x)$ for $x\\in X$. In this paper, as a generalization of Kiem and Castravet's works, we study the stable maps in $\\mathcal{N}$ with genus $0$ and degree $3$. Let $P$ be a natural closed subvariety of $\\mathcal{N}$ which parametrizes stable vector bundles with a fixed subbundle $L^{-1}(-x)$ for a line bundle $L$ on $X$. We describe the stable map space $\\mathbf{M}_0(P,3)$. It turns out that the space $\\mathbf{M}_0(P,3)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07726","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":"2026-05-18T00:29:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ci8YJFD9fyrGrHKmqm91fiey49HIL+VPAoJ5z8W9SGHI292FDmzJRVlBOtWok/pggDaBJ45rpsTOWdowJN4jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:24:30.696234Z"},"content_sha256":"df127e0ee72a8dc8055d0980a0d308773ba023d3eececadecf1b040d0da73468","schema_version":"1.0","event_id":"sha256:df127e0ee72a8dc8055d0980a0d308773ba023d3eececadecf1b040d0da73468"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN/bundle.json","state_url":"https://pith.science/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN/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":"2026-06-02T01:24:30Z","links":{"resolver":"https://pith.science/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN","bundle":"https://pith.science/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN/bundle.json","state":"https://pith.science/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5LDU6LFCM5CLNYYF3RYJ3J4XN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z5LDU6LFCM5CLNYYF3RYJ3J4XN","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":"a96716cefcf1829cfeb17553631d0904c075fef4fbd2ca227c259b359ff19037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-24T06:38:04Z","title_canon_sha256":"431163ea92d183dd7c9780d62a8513d189e115f5b3314d196f9d652a6fc5827e"},"schema_version":"1.0","source":{"id":"1512.07726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07726","created_at":"2026-05-18T00:29:47Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07726v2","created_at":"2026-05-18T00:29:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07726","created_at":"2026-05-18T00:29:47Z"},{"alias_kind":"pith_short_12","alias_value":"Z5LDU6LFCM5C","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z5LDU6LFCM5CLNYY","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z5LDU6LF","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:df127e0ee72a8dc8055d0980a0d308773ba023d3eececadecf1b040d0da73468","target":"graph","created_at":"2026-05-18T00:29:47Z","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 $X$ be a smooth projective curve with genus $g\\geq3$. Let $\\mathcal{N}$ be the moduli space of stable rank two vector bundles on $X$ with a fixed determinant $\\mathcal{O}_X(-x)$ for $x\\in X$. In this paper, as a generalization of Kiem and Castravet's works, we study the stable maps in $\\mathcal{N}$ with genus $0$ and degree $3$. Let $P$ be a natural closed subvariety of $\\mathcal{N}$ which parametrizes stable vector bundles with a fixed subbundle $L^{-1}(-x)$ for a line bundle $L$ on $X$. We describe the stable map space $\\mathbf{M}_0(P,3)$. It turns out that the space $\\mathbf{M}_0(P,3)$ ","authors_text":"Kiryong Chung, Sanghyeon Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-24T06:38:04Z","title":"Stable maps of genus zero in the space of stable vector bundles on a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07726","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":"sha256:5946571f92423bc7f1c23840468ee25a25a46425113912a3fe3a72d12f92337b","target":"record","created_at":"2026-05-18T00:29:47Z","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":"a96716cefcf1829cfeb17553631d0904c075fef4fbd2ca227c259b359ff19037","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-24T06:38:04Z","title_canon_sha256":"431163ea92d183dd7c9780d62a8513d189e115f5b3314d196f9d652a6fc5827e"},"schema_version":"1.0","source":{"id":"1512.07726","kind":"arxiv","version":2}},"canonical_sha256":"cf563a7965133a25b7182ee384ed3cbb520c4588be3108749ea72b77e82b454c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf563a7965133a25b7182ee384ed3cbb520c4588be3108749ea72b77e82b454c","first_computed_at":"2026-05-18T00:29:47.163585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:47.163585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tBmYZ8KQvJWRQ3yWXmiBAGQaiafmtx0DOpeVX7G9z5/3AkR+ZtcoeER88NXhe14+6e0IuxkQ6Y6lH7LXOsQXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:47.164271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5946571f92423bc7f1c23840468ee25a25a46425113912a3fe3a72d12f92337b","sha256:df127e0ee72a8dc8055d0980a0d308773ba023d3eececadecf1b040d0da73468"],"state_sha256":"cfeb7eccc067e755fb8c0f655e389c04f32e1686f1e42d8659f475ff5ecd3536"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+Q0McGlrOyXq7Gk2hX4PcvQqyZFQWsFYCx7z08FjdJLA7ZgLhiiUFWkf4GD6EDkBcIeObZBiUMgRSC4Kgs1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:24:30.698096Z","bundle_sha256":"87fd5d0bf8d2e0c86454f9f9b2e2f670bd117edc4a46f55382de9aa21f4ecea0"}}