{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4KYPZN3WCZ2VIDKWSN7JM76YTW","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":"3fb24b0ffc81f92f92692a2859e3b0763720996aa59de449faf945a3b744d3f2","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-09-07T20:21:18Z","title_canon_sha256":"a5f22f07a68696154b9e113c9f42faa69525060432090116ce2da9573f55a9b9"},"schema_version":"1.0","source":{"id":"1509.02178","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02178","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02178v2","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02178","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"4KYPZN3WCZ2V","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4KYPZN3WCZ2VIDKW","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4KYPZN3W","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:17e1aa85e6344e56d3726db82eca362bb06e0b478c44378d1dc7664a93cec09b","target":"graph","created_at":"2026-05-18T01:27:31Z","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"},"paper":{"abstract_excerpt":"In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study $(\\kappa,N)$-convex functions on metric spaces where $\\kappa$ is a lower semi-continuous function, and gradient flow curves in the sense of a new evolution variational inequality that captures the information that is provided by $\\kappa$. Then, in the spirit of previous work by Erbar, Kuwada and Sturm \\cite{erbarkuwadasturm} we introduce an entropic curvature-dimension condition $CD^e(\\kappa,N)$ for metric measure spaces and lower semi-continuous $\\kappa$. This condition is stabl","authors_text":"Christian Ketterer","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-09-07T20:21:18Z","title":"Evolution variational inequality and Wasserstein control in variable curvature context"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02178","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":"sha256:5135b1d66fb66c3f96dcdc52f6e3c35cd946544dc0d7b611aca07c99208d62c1","target":"record","created_at":"2026-05-18T01:27:31Z","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":"3fb24b0ffc81f92f92692a2859e3b0763720996aa59de449faf945a3b744d3f2","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-09-07T20:21:18Z","title_canon_sha256":"a5f22f07a68696154b9e113c9f42faa69525060432090116ce2da9573f55a9b9"},"schema_version":"1.0","source":{"id":"1509.02178","kind":"arxiv","version":2}},"canonical_sha256":"e2b0fcb7761675540d56937e967fd89db90075830a84b3fb01617687c1eed045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b0fcb7761675540d56937e967fd89db90075830a84b3fb01617687c1eed045","first_computed_at":"2026-05-18T01:27:31.238107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:31.238107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"scpdo/ehhbKxxHRRwI/nAelaPtpak+Kz+2sMUdKq2usitjoA/UL0yHHKHHm0cKFIXlnkOayyNQig/voKAxnHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:31.238515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02178","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5135b1d66fb66c3f96dcdc52f6e3c35cd946544dc0d7b611aca07c99208d62c1","sha256:17e1aa85e6344e56d3726db82eca362bb06e0b478c44378d1dc7664a93cec09b"],"state_sha256":"d13ab9b06535f2ff1079cfad5d13f824bc7134fdd8f8c5fba6d9c0d6569e488e"}