{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QGQLY5RGALVKKRDK4UC77G4ZVL","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":"4a8ac29b9355a8e27cdedf4d72a392b8b805f020484c478a3e81cb467d97334b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-07-08T15:22:38Z","title_canon_sha256":"d89b8a0c6bd8be81913c5deffa8026cd1e47d6e068046bb01b6839ba83675fa7"},"schema_version":"1.0","source":{"id":"2507.06084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.06084","created_at":"2026-07-05T11:33:41Z"},{"alias_kind":"arxiv_version","alias_value":"2507.06084v1","created_at":"2026-07-05T11:33:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.06084","created_at":"2026-07-05T11:33:41Z"},{"alias_kind":"pith_short_12","alias_value":"QGQLY5RGALVK","created_at":"2026-07-05T11:33:41Z"},{"alias_kind":"pith_short_16","alias_value":"QGQLY5RGALVKKRDK","created_at":"2026-07-05T11:33:41Z"},{"alias_kind":"pith_short_8","alias_value":"QGQLY5RG","created_at":"2026-07-05T11:33:41Z"}],"graph_snapshots":[{"event_id":"sha256:c1e5f02ecd19a07af93a5db92f705354ac7794ce5bd5ac772289f4a669e72bcb","target":"graph","created_at":"2026-07-05T11:33:41Z","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/2507.06084/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a new Floer homology for periodic Reeb orbits on the boundaries of Liouville domains. The construction of this Constrained Floer Homology (CFH) is based on the symplectic area functional, restricted to loops satisfying a vanishing Hamiltonian mean value condition. While CFH shares its chain groups with Rabinowitz Floer homology (RFH), it avoids the use of a Lagrange multiplier, enabling a more intrinsic product structure. Our first main result shows that the Fredholm theory for CFH reduces to that of RFH: in particular, the standard Morse-Bott condition is sufficient. We ","authors_text":"Emilia Konrad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-07-08T15:22:38Z","title":"The Constrained Symplectic Area Functional and its Floer Homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.06084","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:eebb3a14f8a73308e1a5e1f86a884195ef904f4207cff6bc99302207acaed62b","target":"record","created_at":"2026-07-05T11:33:41Z","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":"4a8ac29b9355a8e27cdedf4d72a392b8b805f020484c478a3e81cb467d97334b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2025-07-08T15:22:38Z","title_canon_sha256":"d89b8a0c6bd8be81913c5deffa8026cd1e47d6e068046bb01b6839ba83675fa7"},"schema_version":"1.0","source":{"id":"2507.06084","kind":"arxiv","version":1}},"canonical_sha256":"81a0bc762602eaa5446ae505ff9b99aacd8aa51d5d4d334798288fd18922556a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a0bc762602eaa5446ae505ff9b99aacd8aa51d5d4d334798288fd18922556a","first_computed_at":"2026-07-05T11:33:41.077555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:41.077555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kFaRdRq3+d1jS22ANTdDXnKw8tATyrdSdjT1zuIh5JkZfyJH54PBSXg9+eqHnMsiVr8wrWzd836FaLMtb3hBBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:41.077907Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.06084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eebb3a14f8a73308e1a5e1f86a884195ef904f4207cff6bc99302207acaed62b","sha256:c1e5f02ecd19a07af93a5db92f705354ac7794ce5bd5ac772289f4a669e72bcb"],"state_sha256":"c9ecb13049a45a34a51a93f12bd3474dd35fe4d882c33626e9d87ae280935e05"}