{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YR6JDMB53CQTOW5WRMCB7IRUIR","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":"c32b682967b6fdf527fe6203b2ff189fb82e322a9aeb2864cb09eeb4a889d47b","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-01T09:50:36Z","title_canon_sha256":"a176ef67bc79909899160e8093be9e3c3bdb8ae74fddfe82b01d3f0d787a876f"},"schema_version":"1.0","source":{"id":"1107.0174","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0174","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0174v2","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0174","created_at":"2026-05-18T03:52:26Z"},{"alias_kind":"pith_short_12","alias_value":"YR6JDMB53CQT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YR6JDMB53CQTOW5W","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YR6JDMB5","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:2fb32b1e8cb8c2898afa7a93411e39afb1671a0811dfc30e8e717267aa139103","target":"graph","created_at":"2026-05-18T03:52:26Z","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 study smooth projective varieties with small dual variety using methods from symplectic topology. We prove the affine parts of such varieties are subcritical, and that the hyperplane class is invertible in their quantum cohomology. We derive several topological and algebraic geometric consequences from that. The main tool in our work is the Seidel representation associated to Hamiltonian fibrations.","authors_text":"Paul Biran, Yochay Jerby","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-01T09:50:36Z","title":"The symplectic topology of projective manifolds with small dual"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0174","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:e2ea6ed102d5c6ef384535a7a31b0d2f7909d8f8710b76117eee8e025bdcd88f","target":"record","created_at":"2026-05-18T03:52:26Z","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":"c32b682967b6fdf527fe6203b2ff189fb82e322a9aeb2864cb09eeb4a889d47b","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-01T09:50:36Z","title_canon_sha256":"a176ef67bc79909899160e8093be9e3c3bdb8ae74fddfe82b01d3f0d787a876f"},"schema_version":"1.0","source":{"id":"1107.0174","kind":"arxiv","version":2}},"canonical_sha256":"c47c91b03dd8a1375bb68b041fa2344462a440355b239c27689b3245135f64ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c47c91b03dd8a1375bb68b041fa2344462a440355b239c27689b3245135f64ff","first_computed_at":"2026-05-18T03:52:26.465613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:26.465613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HXYTL0EcG9fJs1GzaP0ngKOGNwwgKvbgx2mcF3yA35IJ9jtpbO+J2yRadeW01Gqj4Wdoeox412f1a2Y5UiDPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:26.466306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0174","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2ea6ed102d5c6ef384535a7a31b0d2f7909d8f8710b76117eee8e025bdcd88f","sha256:2fb32b1e8cb8c2898afa7a93411e39afb1671a0811dfc30e8e717267aa139103"],"state_sha256":"8fb0350fb46e2710dba5b6fc6a15da05622e84c7eefd9576f477aebb1a3d17d4"}