{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XUE3UDSE3BBSEQJS5UV43LOQZT","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":"1b55f13bab184b363b9b565d8d5f88d149168ec505e1e3e154afc70ba0b30230","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-01-13T12:15:05Z","title_canon_sha256":"cc12611b32c2e6a2ddaef2d67452aaf3db7a233e00f010ddf04eaefd95f66dd4"},"schema_version":"1.0","source":{"id":"2201.04916","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.04916","created_at":"2026-07-05T10:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"2201.04916v3","created_at":"2026-07-05T10:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.04916","created_at":"2026-07-05T10:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"XUE3UDSE3BBS","created_at":"2026-07-05T10:41:43Z"},{"alias_kind":"pith_short_16","alias_value":"XUE3UDSE3BBSEQJS","created_at":"2026-07-05T10:41:43Z"},{"alias_kind":"pith_short_8","alias_value":"XUE3UDSE","created_at":"2026-07-05T10:41:43Z"}],"graph_snapshots":[{"event_id":"sha256:0f68c44eb5892e29a9d9b41b03896a82429046606f12de5b81c4e2c6854d9830","target":"graph","created_at":"2026-07-05T10:41:43Z","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/2201.04916/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies sharp isoperimetric comparison theorems and sharp dimensional concavity properties of the isoperimetric profile for non smooth spaces with lower Ricci curvature bounds, the so-called $N$-dimensional ${\\rm RCD}(K,N)$ spaces $(X,\\mathsf{d},\\mathscr{H}^N)$. The absence of most of the classical tools of Geometric Measure Theory and the possible non existence of isoperimetric regions on non compact spaces are handled via an original argument to estimate first and second variation of the area for isoperimetric sets, avoiding any regularity theory, in combination with an asymptotic","authors_text":"Daniele Semola, Enrico Pasqualetto, Gioacchino Antonelli, Marco Pozzetta","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-01-13T12:15:05Z","title":"Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04916","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":"sha256:5cf70e29d8e660cfcb3f726cd3cc2901f3a47ab0ef5abcff5c64039aaab68a41","target":"record","created_at":"2026-07-05T10:41:43Z","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":"1b55f13bab184b363b9b565d8d5f88d149168ec505e1e3e154afc70ba0b30230","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2022-01-13T12:15:05Z","title_canon_sha256":"cc12611b32c2e6a2ddaef2d67452aaf3db7a233e00f010ddf04eaefd95f66dd4"},"schema_version":"1.0","source":{"id":"2201.04916","kind":"arxiv","version":3}},"canonical_sha256":"bd09ba0e44d843224132ed2bcdadd0ccccd4902acc96a7c7bfa039dafb53768a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd09ba0e44d843224132ed2bcdadd0ccccd4902acc96a7c7bfa039dafb53768a","first_computed_at":"2026-07-05T10:41:43.539679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:43.539679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LmoP1UAoJEYpCGq6rKbCSW7yUg09SIgqcao52JIEwOLG0RcyGBtrQ/gGOIG+h6I4GWFbVbgKsCzVN5mWLulNBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:43.540219Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.04916","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cf70e29d8e660cfcb3f726cd3cc2901f3a47ab0ef5abcff5c64039aaab68a41","sha256:0f68c44eb5892e29a9d9b41b03896a82429046606f12de5b81c4e2c6854d9830"],"state_sha256":"73e578561d3b88948bdeb2c53c9a804ee30678cf518cff2a29bd16dfe3c33c25"}