{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZGX2DTHOVN3U2IY4TKMGQPDRGS","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":"df4b47b0e3c1a26782c49918c26c5d986f36980f9d45eed2d961daf065c5b5cf","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T17:32:04Z","title_canon_sha256":"3b086eb3075ef2f698149d6f629973e532baeea1c19c2e3c5d0c1d41554a07d3"},"schema_version":"1.0","source":{"id":"2309.15089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.15089","created_at":"2026-07-05T07:52:59Z"},{"alias_kind":"arxiv_version","alias_value":"2309.15089v2","created_at":"2026-07-05T07:52:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.15089","created_at":"2026-07-05T07:52:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZGX2DTHOVN3U","created_at":"2026-07-05T07:52:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZGX2DTHOVN3U2IY4","created_at":"2026-07-05T07:52:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZGX2DTHO","created_at":"2026-07-05T07:52:59Z"}],"graph_snapshots":[{"event_id":"sha256:9ee2b9ba2a363e0b9059d41dc64dfee78b94f2a13e1fa57985435ccd40e557e0","target":"graph","created_at":"2026-07-05T07:52:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.15089/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize the Cohen-Jones-Segal construction to the Morse-Bott setting. In other words, we define framings for Morse-Bott analogues of flow categories and associate a stable homotopy type to this data. We use this to recover the stable homotopy type of a closed manifold from Morse-Bott theory, and the stable equivariant homotopy type of a closed manifold with the action of a compact Lie group from Morse theory.\n  We use this machinery in Floer theory to construct a genuine circle equivariant model for symplectic cohomology with coefficients in the sphere spectrum. Using the formalism of re","authors_text":"Laurent C\\^ot\\'e, Yusuf Bar{\\i}\\c{s} Kartal","cross_cats":["math.GT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T17:32:04Z","title":"Equivariant Floer homotopy via Morse-Bott theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15089","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:b45ba2e02c02eaf73231cf84deafc0e56220d2202d0f4ad8be4f794eab89e349","target":"record","created_at":"2026-07-05T07:52:59Z","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":"df4b47b0e3c1a26782c49918c26c5d986f36980f9d45eed2d961daf065c5b5cf","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T17:32:04Z","title_canon_sha256":"3b086eb3075ef2f698149d6f629973e532baeea1c19c2e3c5d0c1d41554a07d3"},"schema_version":"1.0","source":{"id":"2309.15089","kind":"arxiv","version":2}},"canonical_sha256":"c9afa1cceeab774d231c9a98683c7134a3a0f2f1d7bc8dd89fdcede2b849fac8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9afa1cceeab774d231c9a98683c7134a3a0f2f1d7bc8dd89fdcede2b849fac8","first_computed_at":"2026-07-05T07:52:59.193544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:52:59.193544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MlK6JIePTyszBS+Pg+M8u6tHpdbjeywT8LS7Fn9u8n99W8hE2wohyoIcpUziEt93GQPmmEWb2sPe9GycyadcDA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:52:59.193960Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.15089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b45ba2e02c02eaf73231cf84deafc0e56220d2202d0f4ad8be4f794eab89e349","sha256:9ee2b9ba2a363e0b9059d41dc64dfee78b94f2a13e1fa57985435ccd40e557e0"],"state_sha256":"48c6dd8e50fabd1c1912f23bbf7f12b06d686a0f62354b55caea0e623f1e31c8"}