{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RJPA3V4AE3X5KLXGAYM5IRYIUJ","short_pith_number":"pith:RJPA3V4A","canonical_record":{"source":{"id":"1208.4340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T18:54:14Z","cross_cats_sorted":[],"title_canon_sha256":"4869535b51f38aab5e2f054fad6ae75f422388fdcc8a4be0cd25d0839416382e","abstract_canon_sha256":"fe98a7056bf3c4d040c66066fcbdd6c6f485c4d1e1265952e27072b64348b695"},"schema_version":"1.0"},"canonical_sha256":"8a5e0dd78026efd52ee60619d44708a27ee92a32e99234c9bd6b504c9a98a7b6","source":{"kind":"arxiv","id":"1208.4340","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4340","created_at":"2026-05-18T03:48:14Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4340v2","created_at":"2026-05-18T03:48:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4340","created_at":"2026-05-18T03:48:14Z"},{"alias_kind":"pith_short_12","alias_value":"RJPA3V4AE3X5","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RJPA3V4AE3X5KLXG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RJPA3V4A","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RJPA3V4AE3X5KLXGAYM5IRYIUJ","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T18:54:14Z","cross_cats_sorted":[],"title_canon_sha256":"4869535b51f38aab5e2f054fad6ae75f422388fdcc8a4be0cd25d0839416382e","abstract_canon_sha256":"fe98a7056bf3c4d040c66066fcbdd6c6f485c4d1e1265952e27072b64348b695"},"schema_version":"1.0"},"canonical_sha256":"8a5e0dd78026efd52ee60619d44708a27ee92a32e99234c9bd6b504c9a98a7b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:14.412079Z","signature_b64":"2cu/BxaL6OFG8DSgJyhtrqa7W6MOq8zSQAb0FyiMwrQK9ZeNRfKoQQJMAFtun7XtoohmLlD+JoY+8CQOo6O1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a5e0dd78026efd52ee60619d44708a27ee92a32e99234c9bd6b504c9a98a7b6","last_reissued_at":"2026-05-18T03:48:14.411361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:14.411361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4340","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":"2026-05-18T03:48:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47m2X34ouPjH3ZbjQgw4BBf+JlbS5LyYHo9rSxQLC1EsgGbB2YRBFMTAGwyWV4I0YHdZ8iCc0RC1CIlz7L7cBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T19:24:16.070910Z"},"content_sha256":"ee5109460ef41d4ca2f2e33dd0dedface15f9dccd850b01f875232390ad9de3f","schema_version":"1.0","event_id":"sha256:ee5109460ef41d4ca2f2e33dd0dedface15f9dccd850b01f875232390ad9de3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RJPA3V4AE3X5KLXGAYM5IRYIUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards the symplectic Graber-Harris-Starr theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zhiyu Tian","submitted_at":"2012-08-21T18:54:14Z","abstract_excerpt":"A theorem of Graber, Harris, and Starr states that a rationally connected fibration over a curve has a section. We study an analogous question in symplectic geometry. Namely, given a rationally connected fibration over a curve, can one find a section which gives a non-zero Gromov-Witten invariant? We observe that for any fibration, the existence of a section which gives a non-zero Gromov-Witten invariant only depends on the generic fiber, i.e. a variety defined over the function field of a curve. Some examples of rationally connected fibrations with this property are given, including all ratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4340","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":"2026-05-18T03:48:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUI7n4XUrOb0auJ4Rox75JRmY6S2MsrtL/rKg1ZRXKAKz0E998NMhdM824Pbb87wujrGPr6rRGvWgszxOpEGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T19:24:16.071618Z"},"content_sha256":"23bca89557e86f51bced2f22a76746de005f6af8c58555edef6dc649c3ff3681","schema_version":"1.0","event_id":"sha256:23bca89557e86f51bced2f22a76746de005f6af8c58555edef6dc649c3ff3681"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ/bundle.json","state_url":"https://pith.science/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ/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":"2026-05-29T19:24:16Z","links":{"resolver":"https://pith.science/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ","bundle":"https://pith.science/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ/bundle.json","state":"https://pith.science/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJPA3V4AE3X5KLXGAYM5IRYIUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RJPA3V4AE3X5KLXGAYM5IRYIUJ","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":"fe98a7056bf3c4d040c66066fcbdd6c6f485c4d1e1265952e27072b64348b695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T18:54:14Z","title_canon_sha256":"4869535b51f38aab5e2f054fad6ae75f422388fdcc8a4be0cd25d0839416382e"},"schema_version":"1.0","source":{"id":"1208.4340","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4340","created_at":"2026-05-18T03:48:14Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4340v2","created_at":"2026-05-18T03:48:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4340","created_at":"2026-05-18T03:48:14Z"},{"alias_kind":"pith_short_12","alias_value":"RJPA3V4AE3X5","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RJPA3V4AE3X5KLXG","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RJPA3V4A","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:23bca89557e86f51bced2f22a76746de005f6af8c58555edef6dc649c3ff3681","target":"graph","created_at":"2026-05-18T03:48:14Z","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":"A theorem of Graber, Harris, and Starr states that a rationally connected fibration over a curve has a section. We study an analogous question in symplectic geometry. Namely, given a rationally connected fibration over a curve, can one find a section which gives a non-zero Gromov-Witten invariant? We observe that for any fibration, the existence of a section which gives a non-zero Gromov-Witten invariant only depends on the generic fiber, i.e. a variety defined over the function field of a curve. Some examples of rationally connected fibrations with this property are given, including all ratio","authors_text":"Zhiyu Tian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T18:54:14Z","title":"Towards the symplectic Graber-Harris-Starr theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4340","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:ee5109460ef41d4ca2f2e33dd0dedface15f9dccd850b01f875232390ad9de3f","target":"record","created_at":"2026-05-18T03:48:14Z","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":"fe98a7056bf3c4d040c66066fcbdd6c6f485c4d1e1265952e27072b64348b695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-08-21T18:54:14Z","title_canon_sha256":"4869535b51f38aab5e2f054fad6ae75f422388fdcc8a4be0cd25d0839416382e"},"schema_version":"1.0","source":{"id":"1208.4340","kind":"arxiv","version":2}},"canonical_sha256":"8a5e0dd78026efd52ee60619d44708a27ee92a32e99234c9bd6b504c9a98a7b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a5e0dd78026efd52ee60619d44708a27ee92a32e99234c9bd6b504c9a98a7b6","first_computed_at":"2026-05-18T03:48:14.411361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:14.411361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2cu/BxaL6OFG8DSgJyhtrqa7W6MOq8zSQAb0FyiMwrQK9ZeNRfKoQQJMAFtun7XtoohmLlD+JoY+8CQOo6O1Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:14.412079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4340","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee5109460ef41d4ca2f2e33dd0dedface15f9dccd850b01f875232390ad9de3f","sha256:23bca89557e86f51bced2f22a76746de005f6af8c58555edef6dc649c3ff3681"],"state_sha256":"921184bf62c5dd61cb44199906b751290b7316133159f6e76775fb6875830fdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1pLB+vV8xG+3I0g/wWDEYbftDw1bHXKrEZr3WwlUzJS3o1AK0hwXji/6/W4wSDH1UNiOXf7XPyU6uxthinWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T19:24:16.075346Z","bundle_sha256":"76052ccb2de061c6b578f57451b3c47e8743bcab70b9a4c2ef3a9e5552216a11"}}