{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AGQYTUFTUZ335QZPJWLXTUJ362","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":"ce8ff8c8536c93f779f4b1c0de805b9a759fa81518b6012e654b858b355960b6","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-11-03T16:49:58Z","title_canon_sha256":"5113d7a539c12f547df15f93889f7b8580dc0c9270135714b9fa517acda91688"},"schema_version":"1.0","source":{"id":"2411.01631","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.01631","created_at":"2026-07-05T09:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"2411.01631v1","created_at":"2026-07-05T09:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.01631","created_at":"2026-07-05T09:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"AGQYTUFTUZ33","created_at":"2026-07-05T09:30:33Z"},{"alias_kind":"pith_short_16","alias_value":"AGQYTUFTUZ335QZP","created_at":"2026-07-05T09:30:33Z"},{"alias_kind":"pith_short_8","alias_value":"AGQYTUFT","created_at":"2026-07-05T09:30:33Z"}],"graph_snapshots":[{"event_id":"sha256:5ce52d0822cddf7ff9cfa3695ad023bd534610119632aca99279f7f623b843e9","target":"graph","created_at":"2026-07-05T09:30:33Z","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/2411.01631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore analogs of classical centro-affine invariant isoperimetric inequalities, such as the Blaschke--Santal\\'o inequality and the $L_p$-affine isoperimetric inequalities, for convex bodies in spherical space. Specifically, we establish an isoperimetric inequality for the floating area and prove a stability result based on the spherical volume difference.\n  The floating area has previously been studied as a natural extension of classical affine surface area to non-Euclidean convex bodies in spaces of constant curvature. In this work, we introduce the $L_p$-floating areas for spherical conv","authors_text":"Elisabeth M. Werner, Florian Besau","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-11-03T16:49:58Z","title":"The $L_p$-floating area, curvature entropy, and isoperimetric inequalities on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01631","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":"sha256:4a8fd01ad0cc35aca29776a05a7b0d67a864f08a9dc31c76e840a8d25f809e2c","target":"record","created_at":"2026-07-05T09:30:33Z","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":"ce8ff8c8536c93f779f4b1c0de805b9a759fa81518b6012e654b858b355960b6","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-11-03T16:49:58Z","title_canon_sha256":"5113d7a539c12f547df15f93889f7b8580dc0c9270135714b9fa517acda91688"},"schema_version":"1.0","source":{"id":"2411.01631","kind":"arxiv","version":1}},"canonical_sha256":"01a189d0b3a677bec32f4d9779d13bf6afaa3637e9523cfc0427756ad6db749c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01a189d0b3a677bec32f4d9779d13bf6afaa3637e9523cfc0427756ad6db749c","first_computed_at":"2026-07-05T09:30:33.319167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:30:33.319167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOadX/HLvhh8EqQMesV2VhNYzCLJ2cfQqt/M1gQZIUlRNglHtbzLplRdgM771a+jWB18CrPPqeC4HOcNna58Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:30:33.319608Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.01631","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8fd01ad0cc35aca29776a05a7b0d67a864f08a9dc31c76e840a8d25f809e2c","sha256:5ce52d0822cddf7ff9cfa3695ad023bd534610119632aca99279f7f623b843e9"],"state_sha256":"b039f2decc4057820d14d93a53cbc1adb9754ddc0dca1568d0d0215fc282b9f2"}