{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:4BVAFXMZ6YV3B4ISX4GIFPMZDE","short_pith_number":"pith:4BVAFXMZ","canonical_record":{"source":{"id":"0808.2228","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-08-18T15:20:45Z","cross_cats_sorted":[],"title_canon_sha256":"d74377f2b2601c803c1741ddc17a77eb12276debd699d6a850b92142e4a071ef","abstract_canon_sha256":"c92edde013391c10f879db65c900fa8535d366fef56004e4a481abc0d2770f83"},"schema_version":"1.0"},"canonical_sha256":"e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688","source":{"kind":"arxiv","id":"0808.2228","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2228","created_at":"2026-05-18T02:32:55Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2228v6","created_at":"2026-05-18T02:32:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2228","created_at":"2026-05-18T02:32:55Z"},{"alias_kind":"pith_short_12","alias_value":"4BVAFXMZ6YV3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4BVAFXMZ6YV3B4IS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4BVAFXMZ","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:4BVAFXMZ6YV3B4ISX4GIFPMZDE","target":"record","payload":{"canonical_record":{"source":{"id":"0808.2228","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-08-18T15:20:45Z","cross_cats_sorted":[],"title_canon_sha256":"d74377f2b2601c803c1741ddc17a77eb12276debd699d6a850b92142e4a071ef","abstract_canon_sha256":"c92edde013391c10f879db65c900fa8535d366fef56004e4a481abc0d2770f83"},"schema_version":"1.0"},"canonical_sha256":"e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:55.421726Z","signature_b64":"VEhqXw8whJHhHYgNOLNTrKO1xXcNTFaBBB6ea2tds5GV/zl3Ca/wKWn+h/p3cJeX8dJJubH0exLOQDLkm7umAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688","last_reissued_at":"2026-05-18T02:32:55.421138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:55.421138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.2228","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5d6qMtPLKkKcb3g7agJ21X0S8z78bVGoduC9RW+rbQhlarpGDsg3J2RMY2ytO5Kzau0U9s6eTnzKMfIKjMrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:43:05.527012Z"},"content_sha256":"df7fcbb755524601a4917829cc3fdcfdc580959ec93e5b203e22904dc837da2c","schema_version":"1.0","event_id":"sha256:df7fcbb755524601a4917829cc3fdcfdc580959ec93e5b203e22904dc837da2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:4BVAFXMZ6YV3B4ISX4GIFPMZDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relatively Open Gromov-Witten Invariants for Symplectic Manifolds of Lower Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Hai-Long Her","submitted_at":"2008-08-18T15:20:45Z","abstract_excerpt":"Let $(X,\\omega)$ be a compact symplectic manifold, $L$ be a Lagrangian submanifold and $V$ be a codimension 2 symplectic submanifold of $X$, we consider the pseudoholomorphic maps from a Riemann surface with boundary $(\\Sigma,\\partial\\Sigma)$ to the pair $(X,L)$ satisfying Lagrangian boundary conditions and intersecting $V$. In some special cases, for instance, under the semi-positivity condition, we study the stable moduli space of such open pseudoholomorphic maps involving the intersection data. If $L\\cap V=\\emptyset$, we study the problem of orientability of the moduli space. Moreover, assu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2228","kind":"arxiv","version":6},"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":"2026-05-18T02:32:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"loI/fs6bDll9onXXFm8sStMOPCp9jKdByUVeDdnzQwP+gOMwJGEqNJ3sAxoQWWGjp5+HtuaBBcweZySgxJOSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:43:05.527485Z"},"content_sha256":"cb0f1d4b7f9d425bfa5b614465e9be42cdc6024c071d4da69175bd6a4fb36454","schema_version":"1.0","event_id":"sha256:cb0f1d4b7f9d425bfa5b614465e9be42cdc6024c071d4da69175bd6a4fb36454"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE/bundle.json","state_url":"https://pith.science/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE/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":"2026-06-25T20:43:05Z","links":{"resolver":"https://pith.science/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE","bundle":"https://pith.science/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE/bundle.json","state":"https://pith.science/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4BVAFXMZ6YV3B4ISX4GIFPMZDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:4BVAFXMZ6YV3B4ISX4GIFPMZDE","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":"c92edde013391c10f879db65c900fa8535d366fef56004e4a481abc0d2770f83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-08-18T15:20:45Z","title_canon_sha256":"d74377f2b2601c803c1741ddc17a77eb12276debd699d6a850b92142e4a071ef"},"schema_version":"1.0","source":{"id":"0808.2228","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2228","created_at":"2026-05-18T02:32:55Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2228v6","created_at":"2026-05-18T02:32:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2228","created_at":"2026-05-18T02:32:55Z"},{"alias_kind":"pith_short_12","alias_value":"4BVAFXMZ6YV3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4BVAFXMZ6YV3B4IS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4BVAFXMZ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:cb0f1d4b7f9d425bfa5b614465e9be42cdc6024c071d4da69175bd6a4fb36454","target":"graph","created_at":"2026-05-18T02:32:55Z","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 $(X,\\omega)$ be a compact symplectic manifold, $L$ be a Lagrangian submanifold and $V$ be a codimension 2 symplectic submanifold of $X$, we consider the pseudoholomorphic maps from a Riemann surface with boundary $(\\Sigma,\\partial\\Sigma)$ to the pair $(X,L)$ satisfying Lagrangian boundary conditions and intersecting $V$. In some special cases, for instance, under the semi-positivity condition, we study the stable moduli space of such open pseudoholomorphic maps involving the intersection data. If $L\\cap V=\\emptyset$, we study the problem of orientability of the moduli space. Moreover, assu","authors_text":"Hai-Long Her","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-08-18T15:20:45Z","title":"Relatively Open Gromov-Witten Invariants for Symplectic Manifolds of Lower Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2228","kind":"arxiv","version":6},"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:df7fcbb755524601a4917829cc3fdcfdc580959ec93e5b203e22904dc837da2c","target":"record","created_at":"2026-05-18T02:32:55Z","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":"c92edde013391c10f879db65c900fa8535d366fef56004e4a481abc0d2770f83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-08-18T15:20:45Z","title_canon_sha256":"d74377f2b2601c803c1741ddc17a77eb12276debd699d6a850b92142e4a071ef"},"schema_version":"1.0","source":{"id":"0808.2228","kind":"arxiv","version":6}},"canonical_sha256":"e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688","first_computed_at":"2026-05-18T02:32:55.421138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:55.421138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VEhqXw8whJHhHYgNOLNTrKO1xXcNTFaBBB6ea2tds5GV/zl3Ca/wKWn+h/p3cJeX8dJJubH0exLOQDLkm7umAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:55.421726Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2228","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df7fcbb755524601a4917829cc3fdcfdc580959ec93e5b203e22904dc837da2c","sha256:cb0f1d4b7f9d425bfa5b614465e9be42cdc6024c071d4da69175bd6a4fb36454"],"state_sha256":"5495127691f16a6ada33da900f8b1b55708b9efe6ad84c5d5ce1f675c2be9ee4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJ8IajFKvp3raEpeZa4gRgpqT3ATuHjd9N4yqx7tbsoKLLFcbg/e+gAurJyMKgy7e/5j4bjLHKEinIMB49MBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:43:05.530293Z","bundle_sha256":"d8188106d0096df714a67c8c44fb05b2e2a1eebef687d8e86c00e80052b6e46a"}}