{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CGT22OOKBPH5RDBKJFMUNUQAZN","short_pith_number":"pith:CGT22OOK","canonical_record":{"source":{"id":"1309.4079","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-09-16T19:40:31Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7acc7f46a9895333e7600b5c878f68e17b5380e88dca37aad0890a29ed9758ee","abstract_canon_sha256":"4348e2f5f0fcd5890fdb1d652cd9ddc29f18baa730a7c49828086a2c1a20d699"},"schema_version":"1.0"},"canonical_sha256":"11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911","source":{"kind":"arxiv","id":"1309.4079","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4079","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4079v4","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4079","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"CGT22OOKBPH5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGT22OOKBPH5RDBK","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGT22OOK","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CGT22OOKBPH5RDBKJFMUNUQAZN","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4079","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-09-16T19:40:31Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7acc7f46a9895333e7600b5c878f68e17b5380e88dca37aad0890a29ed9758ee","abstract_canon_sha256":"4348e2f5f0fcd5890fdb1d652cd9ddc29f18baa730a7c49828086a2c1a20d699"},"schema_version":"1.0"},"canonical_sha256":"11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:02.289025Z","signature_b64":"t4tmFJyrH3LyH3U9bG91O7i28pkYVVmbJ34CZyPtrtxBQS+uvPvbS+Pjr9g5CGaecIjc3LsJWjaRvqA+CWHTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911","last_reissued_at":"2026-05-18T00:23:02.288552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:02.288552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4079","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lV+hkzEcu87giW801IM87R2tpQp73nnsfkp6C/4R35+sDo6gKqnvTwufmRDpJIscY3ok7npKZgg7dgRbiED0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:32:56.463059Z"},"content_sha256":"50d8bcc70edae02ecb7aa54d31dc9cc5da161332a9b149e2fe6ba1d1bd9cdb65","schema_version":"1.0","event_id":"sha256:50d8bcc70edae02ecb7aa54d31dc9cc5da161332a9b149e2fe6ba1d1bd9cdb65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CGT22OOKBPH5RDBKJFMUNUQAZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration of real curves in CP^{2n-1} and a WDVV relation for real 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, Penka Georgieva","submitted_at":"2013-09-16T19:40:31Z","abstract_excerpt":"We establish a homology relation for the Deligne-Mumford moduli spaces of real curves which lifts to a WDVV-type relation for real Gromov-Witten invariants of real symplectic manifolds; we also obtain a vanishing theorem for these invariants. For many real symplectic manifolds, these results reduce all genus 0 real invariants with conjugate pairs of constraints to genus 0 invariants with a single conjugate pair of constraints. In particular, we give a complete recursion for counts of real rational curves in odd-dimensional projective spaces with conjugate pairs of constraints and specify all c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4079","kind":"arxiv","version":4},"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":"2026-05-18T00:23:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v2yunA0plJ0LAE8wkALYdp1fZCelYn470nNx5y8bCr8f9zMJhq+F+rI8CGpdXAORu0kv2Nic3vLU5EYuj96oCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:32:56.463432Z"},"content_sha256":"6c695cad34e6a6710046498a2bada1bf07bf2ad0ee3b4dc107cff599986340e6","schema_version":"1.0","event_id":"sha256:6c695cad34e6a6710046498a2bada1bf07bf2ad0ee3b4dc107cff599986340e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGT22OOKBPH5RDBKJFMUNUQAZN/bundle.json","state_url":"https://pith.science/pith/CGT22OOKBPH5RDBKJFMUNUQAZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGT22OOKBPH5RDBKJFMUNUQAZN/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":"2026-05-26T16:32:56Z","links":{"resolver":"https://pith.science/pith/CGT22OOKBPH5RDBKJFMUNUQAZN","bundle":"https://pith.science/pith/CGT22OOKBPH5RDBKJFMUNUQAZN/bundle.json","state":"https://pith.science/pith/CGT22OOKBPH5RDBKJFMUNUQAZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGT22OOKBPH5RDBKJFMUNUQAZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CGT22OOKBPH5RDBKJFMUNUQAZN","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":"4348e2f5f0fcd5890fdb1d652cd9ddc29f18baa730a7c49828086a2c1a20d699","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-09-16T19:40:31Z","title_canon_sha256":"7acc7f46a9895333e7600b5c878f68e17b5380e88dca37aad0890a29ed9758ee"},"schema_version":"1.0","source":{"id":"1309.4079","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4079","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4079v4","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4079","created_at":"2026-05-18T00:23:02Z"},{"alias_kind":"pith_short_12","alias_value":"CGT22OOKBPH5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CGT22OOKBPH5RDBK","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CGT22OOK","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:6c695cad34e6a6710046498a2bada1bf07bf2ad0ee3b4dc107cff599986340e6","target":"graph","created_at":"2026-05-18T00:23:02Z","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":"We establish a homology relation for the Deligne-Mumford moduli spaces of real curves which lifts to a WDVV-type relation for real Gromov-Witten invariants of real symplectic manifolds; we also obtain a vanishing theorem for these invariants. For many real symplectic manifolds, these results reduce all genus 0 real invariants with conjugate pairs of constraints to genus 0 invariants with a single conjugate pair of constraints. In particular, we give a complete recursion for counts of real rational curves in odd-dimensional projective spaces with conjugate pairs of constraints and specify all c","authors_text":"Aleksey Zinger, Penka Georgieva","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-09-16T19:40:31Z","title":"Enumeration of real curves in CP^{2n-1} and a WDVV relation for real Gromov-Witten invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4079","kind":"arxiv","version":4},"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":"sha256:50d8bcc70edae02ecb7aa54d31dc9cc5da161332a9b149e2fe6ba1d1bd9cdb65","target":"record","created_at":"2026-05-18T00:23:02Z","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":"4348e2f5f0fcd5890fdb1d652cd9ddc29f18baa730a7c49828086a2c1a20d699","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-09-16T19:40:31Z","title_canon_sha256":"7acc7f46a9895333e7600b5c878f68e17b5380e88dca37aad0890a29ed9758ee"},"schema_version":"1.0","source":{"id":"1309.4079","kind":"arxiv","version":4}},"canonical_sha256":"11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11a7ad39ca0bcfd88c2a495946d200cb6cf26909722e827159f9b484d03a9911","first_computed_at":"2026-05-18T00:23:02.288552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:02.288552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t4tmFJyrH3LyH3U9bG91O7i28pkYVVmbJ34CZyPtrtxBQS+uvPvbS+Pjr9g5CGaecIjc3LsJWjaRvqA+CWHTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:02.289025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4079","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50d8bcc70edae02ecb7aa54d31dc9cc5da161332a9b149e2fe6ba1d1bd9cdb65","sha256:6c695cad34e6a6710046498a2bada1bf07bf2ad0ee3b4dc107cff599986340e6"],"state_sha256":"6c86022d42648afdb6b900c98819a749b31b6e9e349ee13928be0ab2a4d9ec11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agba3+/bfFYNHz75SdOiAteT+hXM4s9aJVyi037DeS5nHPTsE+hosPIMO9T5CuSOcRou/I9eKlmI6gn+wfrcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:32:56.466431Z","bundle_sha256":"8a595be7223a464abf42df1e0963d446504b2bab689ec74c2a42844a6203b267"}}