{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YUMXVL36GS5TG6QVAA66TB7IYG","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":"45bbd2d39ca3a7845f1f45bb915988b4d5ef96962aa968c45688e17594eedff8","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-07-23T10:06:14Z","title_canon_sha256":"34078e42ea63f857d1e1a433bf78d56ece3f812dfcb5c4bf0919879fd6ec809f"},"schema_version":"1.0","source":{"id":"1107.4674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4674","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4674v1","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4674","created_at":"2026-05-18T01:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"YUMXVL36GS5T","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YUMXVL36GS5TG6QV","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YUMXVL36","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:46f0d85d955113d0330e84b9b229d9c5ed31c8cea4c0346d54fc19dc78fc121f","target":"graph","created_at":"2026-05-18T01:22:28Z","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 prove that any closed connected exact Lagrangian manifold L in a connected cotangent bundle T*N is up to a finite covering space lift a homology equivalence. We prove this by constructing a fibrant parametrized family of ring spectra FL parametrized by the manifold N. The homology of FL will be (twisted) symplectic cohomology of T*L. The fibrancy property will imply that there is a Serre spectral sequence converging to the homology of FL and the product combined with intersection product on N induces a product on this spectral sequence. This product structure and its relation to the interse","authors_text":"Thomas Kragh","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-07-23T10:06:14Z","title":"Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4674","kind":"arxiv","version":1},"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:c07de07f40965a0663b1a38692254b5732a27a5447c441ab2dfb84254a9ea62f","target":"record","created_at":"2026-05-18T01:22:28Z","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":"45bbd2d39ca3a7845f1f45bb915988b4d5ef96962aa968c45688e17594eedff8","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-07-23T10:06:14Z","title_canon_sha256":"34078e42ea63f857d1e1a433bf78d56ece3f812dfcb5c4bf0919879fd6ec809f"},"schema_version":"1.0","source":{"id":"1107.4674","kind":"arxiv","version":1}},"canonical_sha256":"c5197aaf7e34bb337a15003de987e8c1959513dec845abb13073e27b4473f102","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5197aaf7e34bb337a15003de987e8c1959513dec845abb13073e27b4473f102","first_computed_at":"2026-05-18T01:22:28.945798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:28.945798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OuRJDV52JK28a+BFwKpX345nXj5ogCogxh0OFL/vXuDxrKT48Bn50duJmg7emo+sRBTTMwwNZiVrx6m00U+lCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:28.946284Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c07de07f40965a0663b1a38692254b5732a27a5447c441ab2dfb84254a9ea62f","sha256:46f0d85d955113d0330e84b9b229d9c5ed31c8cea4c0346d54fc19dc78fc121f"],"state_sha256":"58aa63edefd5c1f0af3a20c4a5a4404f926bba325b1806bce3d0023ad8bc51ca"}