{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:6JSAQA4KZ7ZFATZ2LH3CKCNOCH","short_pith_number":"pith:6JSAQA4K","canonical_record":{"source":{"id":"math/0507103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2005-07-05T18:45:04Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"427050d6971ba4d9ce54757d0620ad3352d15066e64a2c65c41a69c2342910f2","abstract_canon_sha256":"220ef518a7de013d837fb6e2bc61a9df14375e3ffd00680d2e5db3d4df70d499"},"schema_version":"1.0"},"canonical_sha256":"f26408038acff2504f3a59f62509ae11e0e74a66cb943b3728df37d1736c3534","source":{"kind":"arxiv","id":"math/0507103","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0507103","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0507103v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507103","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"6JSAQA4KZ7ZF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6JSAQA4KZ7ZFATZ2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6JSAQA4K","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:6JSAQA4KZ7ZFATZ2LH3CKCNOCH","target":"record","payload":{"canonical_record":{"source":{"id":"math/0507103","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2005-07-05T18:45:04Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"427050d6971ba4d9ce54757d0620ad3352d15066e64a2c65c41a69c2342910f2","abstract_canon_sha256":"220ef518a7de013d837fb6e2bc61a9df14375e3ffd00680d2e5db3d4df70d499"},"schema_version":"1.0"},"canonical_sha256":"f26408038acff2504f3a59f62509ae11e0e74a66cb943b3728df37d1736c3534","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:29.541094Z","signature_b64":"t546u53uE1jrHzpXivxqLcPYmowT2MWO4EEk5LB9M+IbDmqJhE0SbveGlFWxRfa5Pw5u6ZQhf6Ab95vKmJmXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f26408038acff2504f3a59f62509ae11e0e74a66cb943b3728df37d1736c3534","last_reissued_at":"2026-05-18T04:07:29.540598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:29.540598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0507103","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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KETcWV2Hn0oX9Qkohu24pWa2HxtkfjokTOzcetzapdIU63BZKGmYm7GE2AF4MuHDpIB1+Af1YHB5kGv9dJ8UCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:34:46.560381Z"},"content_sha256":"15c81c403ff5e27371158a65c857054327ab4109b9e71b9db28eb32bf4591918","schema_version":"1.0","event_id":"sha256:15c81c403ff5e27371158a65c857054327ab4109b9e71b9db28eb32bf4591918"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:6JSAQA4KZ7ZFATZ2LH3CKCNOCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduced Genus-One Gromov-Witten Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Aleksey Zinger","submitted_at":"2005-07-05T18:45:04Z","abstract_excerpt":"In a previous paper we described a natural closed subset of the moduli space of stable genus-one J-holomorphic maps into a symplectic manifold X. In this paper we generalize the definition of the main component to moduli spaces of perturbed, in a restricted way, J-holomorphic maps. This generalization implies that the main component, just like the entire moduli space, carries a virtual fundamental class and can be used to define symplectic invariants. These truly genus-one invariants constitute part of the standard genus-one Gromov-Witten invariants, which arise from the entire moduli space. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507103","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":"2026-05-18T04:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A30y/ar5cZb9ZQ9C6f1elgUT8Nv9zLotM1yMsqHh7KI/r2nl0o4Cv61hDLbpRuVwPeFlWJSB2h2VMb7mgJ8nCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:34:46.561120Z"},"content_sha256":"0c1f014dc4bb26c6b83f2a4077fc3bed1cd976e122c70f6a19eb279d5f824679","schema_version":"1.0","event_id":"sha256:0c1f014dc4bb26c6b83f2a4077fc3bed1cd976e122c70f6a19eb279d5f824679"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH/bundle.json","state_url":"https://pith.science/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH/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":"2026-05-26T16:34:46Z","links":{"resolver":"https://pith.science/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH","bundle":"https://pith.science/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH/bundle.json","state":"https://pith.science/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6JSAQA4KZ7ZFATZ2LH3CKCNOCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:6JSAQA4KZ7ZFATZ2LH3CKCNOCH","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":"220ef518a7de013d837fb6e2bc61a9df14375e3ffd00680d2e5db3d4df70d499","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2005-07-05T18:45:04Z","title_canon_sha256":"427050d6971ba4d9ce54757d0620ad3352d15066e64a2c65c41a69c2342910f2"},"schema_version":"1.0","source":{"id":"math/0507103","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0507103","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0507103v2","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507103","created_at":"2026-05-18T04:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"6JSAQA4KZ7ZF","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6JSAQA4KZ7ZFATZ2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6JSAQA4K","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:0c1f014dc4bb26c6b83f2a4077fc3bed1cd976e122c70f6a19eb279d5f824679","target":"graph","created_at":"2026-05-18T04:07:29Z","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":"In a previous paper we described a natural closed subset of the moduli space of stable genus-one J-holomorphic maps into a symplectic manifold X. In this paper we generalize the definition of the main component to moduli spaces of perturbed, in a restricted way, J-holomorphic maps. This generalization implies that the main component, just like the entire moduli space, carries a virtual fundamental class and can be used to define symplectic invariants. These truly genus-one invariants constitute part of the standard genus-one Gromov-Witten invariants, which arise from the entire moduli space. T","authors_text":"Aleksey Zinger","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2005-07-05T18:45:04Z","title":"Reduced Genus-One Gromov-Witten Invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507103","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":"sha256:15c81c403ff5e27371158a65c857054327ab4109b9e71b9db28eb32bf4591918","target":"record","created_at":"2026-05-18T04:07:29Z","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":"220ef518a7de013d837fb6e2bc61a9df14375e3ffd00680d2e5db3d4df70d499","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2005-07-05T18:45:04Z","title_canon_sha256":"427050d6971ba4d9ce54757d0620ad3352d15066e64a2c65c41a69c2342910f2"},"schema_version":"1.0","source":{"id":"math/0507103","kind":"arxiv","version":2}},"canonical_sha256":"f26408038acff2504f3a59f62509ae11e0e74a66cb943b3728df37d1736c3534","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f26408038acff2504f3a59f62509ae11e0e74a66cb943b3728df37d1736c3534","first_computed_at":"2026-05-18T04:07:29.540598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:29.540598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t546u53uE1jrHzpXivxqLcPYmowT2MWO4EEk5LB9M+IbDmqJhE0SbveGlFWxRfa5Pw5u6ZQhf6Ab95vKmJmXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:29.541094Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0507103","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15c81c403ff5e27371158a65c857054327ab4109b9e71b9db28eb32bf4591918","sha256:0c1f014dc4bb26c6b83f2a4077fc3bed1cd976e122c70f6a19eb279d5f824679"],"state_sha256":"b2525c5ed5227d288f49249b4239e674d273af587ca33af87fd8426a117941fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNGxFyVugQ4fAO0rD5KFWiN2R9JEqzgooc3pKrslFHEcagGdmOyii689TecII83aQ1xTWay5/8rCHYOngNjpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:34:46.565110Z","bundle_sha256":"2ef5bd3be41a396e91d776b23e79f9e541cf72debea98834d9ac2f377a8749c5"}}