{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZXC5O2RO3B66SOYYV74YDFVCVA","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":"11bcc873d53e2d0306e6912af6a5b62be1d3cba5a89c4d93fda17bdd4a611ccc","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-27T19:50:25Z","title_canon_sha256":"2ca51f3c77f7233c7f07528797122e5f2c2318e71288539474bb72afcec42de7"},"schema_version":"1.0","source":{"id":"1005.5156","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5156","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5156v3","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5156","created_at":"2026-05-18T03:42:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZXC5O2RO3B66","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZXC5O2RO3B66SOYY","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZXC5O2RO","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:6851fe46428a311bbf184026bbcb7a3684e9ac29e7ea6325e6d7267a36698890","target":"graph","created_at":"2026-05-18T03:42:34Z","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":"Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the \"dilation\" condition stipulating that the BV operator applied","authors_text":"Jake P. Solomon, Paul Seidel","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-27T19:50:25Z","title":"Symplectic cohomology and q-intersection numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5156","kind":"arxiv","version":3},"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:e402f9b1fb5710c284ba26a1d37447394bc0ab3dd8647201899d172804cc6a8f","target":"record","created_at":"2026-05-18T03:42:34Z","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":"11bcc873d53e2d0306e6912af6a5b62be1d3cba5a89c4d93fda17bdd4a611ccc","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-05-27T19:50:25Z","title_canon_sha256":"2ca51f3c77f7233c7f07528797122e5f2c2318e71288539474bb72afcec42de7"},"schema_version":"1.0","source":{"id":"1005.5156","kind":"arxiv","version":3}},"canonical_sha256":"cdc5d76a2ed87de93b18aff98196a2a8075fbc76dbf59444a07f02a2f63a3ffd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdc5d76a2ed87de93b18aff98196a2a8075fbc76dbf59444a07f02a2f63a3ffd","first_computed_at":"2026-05-18T03:42:34.175521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:34.175521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tX5Zt9IDWENiev9OZUxrwcQqA/llZxbY/4mkA98bGcp+QRiK9pfnwohZbqit8z1VKsRZM7U4SzU4HGLESYBQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:34.176290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5156","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e402f9b1fb5710c284ba26a1d37447394bc0ab3dd8647201899d172804cc6a8f","sha256:6851fe46428a311bbf184026bbcb7a3684e9ac29e7ea6325e6d7267a36698890"],"state_sha256":"44dd94bd43c1ac7780b10af88f0df15eb896743ff34c937d6ae3963234364c72"}