{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PPFHMX2AI5EBM5PEZ4ICN23FWK","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":"e0548890dc9bf2f276caf2ef1f5faeb3f6c014d7bc7cb967de3adeeb9cad8cfd","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T19:23:43Z","title_canon_sha256":"424a4c33539e761451dfcc259e7d6dfd168a91e6c0de52cbe014215a798ea699"},"schema_version":"1.0","source":{"id":"1908.07036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07036","created_at":"2026-07-05T00:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07036v2","created_at":"2026-07-05T00:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07036","created_at":"2026-07-05T00:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"PPFHMX2AI5EB","created_at":"2026-07-05T00:03:00Z"},{"alias_kind":"pith_short_16","alias_value":"PPFHMX2AI5EBM5PE","created_at":"2026-07-05T00:03:00Z"},{"alias_kind":"pith_short_8","alias_value":"PPFHMX2A","created_at":"2026-07-05T00:03:00Z"}],"graph_snapshots":[{"event_id":"sha256:112d5d21288260998ba36ec29ee707c2921ccdf56776168830ce9b7e0dfc6784","target":"graph","created_at":"2026-07-05T00:03:00Z","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/1908.07036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a structure theory for RCD spaces with curvature bounded above in Alexandrov sense. In particular, we show that any such space is a topological manifold with boundary whose interior is equal to the set of regular points. Further the set of regular points is a smooth manifold and is geodesically convex. Around regular points there are DC coordinates and the distance is induced by a continuous BV Riemannian metric.","authors_text":"Christian Ketterer, Martin Kell, Vitali Kapovitch","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T19:23:43Z","title":"On the structure of RCD spaces with upper curvature bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07036","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":"sha256:153d108923f2c4c8e6a04ad05e1825e9f834c13f002a70e8b21b0c7cd87a55d6","target":"record","created_at":"2026-07-05T00:03:00Z","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":"e0548890dc9bf2f276caf2ef1f5faeb3f6c014d7bc7cb967de3adeeb9cad8cfd","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T19:23:43Z","title_canon_sha256":"424a4c33539e761451dfcc259e7d6dfd168a91e6c0de52cbe014215a798ea699"},"schema_version":"1.0","source":{"id":"1908.07036","kind":"arxiv","version":2}},"canonical_sha256":"7bca765f4047481675e4cf1026eb65b2bba2cf6a8c06344f7f41b4a7a3d20815","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bca765f4047481675e4cf1026eb65b2bba2cf6a8c06344f7f41b4a7a3d20815","first_computed_at":"2026-07-05T00:03:00.879848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:03:00.879848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RSzPiqhjtW9un0/ODBuso7RsKqYBO0IMFZGY76k7dJ0zyQJQmROhC98iirWn0mDYqIt/Y61TjFnC5fYnwHnlAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:03:00.880251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:153d108923f2c4c8e6a04ad05e1825e9f834c13f002a70e8b21b0c7cd87a55d6","sha256:112d5d21288260998ba36ec29ee707c2921ccdf56776168830ce9b7e0dfc6784"],"state_sha256":"b99bdfb169562b15f58045249cdf631ee42740e93b94cf7474fb638d64a6228d"}