{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TLZZZPDAHR2JSOU65C7L4HZLG4","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":"6d628cd5e38b661d41c04c64208f3593a8b3ac706b66f8b2b5f40414c6a42feb","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-12-05T19:39:52Z","title_canon_sha256":"334068138240aae0ac74b44ceee6060e0c7699070325dab72f5755312f2ae470"},"schema_version":"1.0","source":{"id":"2412.04574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.04574","created_at":"2026-05-25T02:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"2412.04574v2","created_at":"2026-05-25T02:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.04574","created_at":"2026-05-25T02:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"TLZZZPDAHR2J","created_at":"2026-05-25T02:01:01Z"},{"alias_kind":"pith_short_16","alias_value":"TLZZZPDAHR2JSOU6","created_at":"2026-05-25T02:01:01Z"},{"alias_kind":"pith_short_8","alias_value":"TLZZZPDA","created_at":"2026-05-25T02:01:01Z"}],"graph_snapshots":[{"event_id":"sha256:e38988474e54236379fd5eed153f645429e5c2b2fc76804591add89c8a0872af","target":"graph","created_at":"2026-05-25T02:01:01Z","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/2412.04574/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaining as values both the positive and the negative infinity. We prove several properties of gradient flows of $(K,N)$-convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness.","authors_text":"Chiara Rigoni, Lorenzo Dello Schiavo, Mattia Magnabosco","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-12-05T19:39:52Z","title":"Gradient flows of $(K,N)$-convex functions with negative $N$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.04574","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":"sha256:675863d19c2a10eca034942774cd7eebddd1af9ad8a456867f37a9598d6f45b9","target":"record","created_at":"2026-05-25T02:01:01Z","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":"6d628cd5e38b661d41c04c64208f3593a8b3ac706b66f8b2b5f40414c6a42feb","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-12-05T19:39:52Z","title_canon_sha256":"334068138240aae0ac74b44ceee6060e0c7699070325dab72f5755312f2ae470"},"schema_version":"1.0","source":{"id":"2412.04574","kind":"arxiv","version":2}},"canonical_sha256":"9af39cbc603c74993a9ee8bebe1f2b371e1f3e48d28f958abed1ca6c234ac802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9af39cbc603c74993a9ee8bebe1f2b371e1f3e48d28f958abed1ca6c234ac802","first_computed_at":"2026-05-25T02:01:01.952106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:01.952106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"51IbAiIp3hDqcNGPl3MgOJllXP75rqW3G/emtb8ImPHk65UpTSrlgDvXqSWe96JMAtpkhkoQeV/laaBTlspCAw==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:01.952737Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.04574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675863d19c2a10eca034942774cd7eebddd1af9ad8a456867f37a9598d6f45b9","sha256:e38988474e54236379fd5eed153f645429e5c2b2fc76804591add89c8a0872af"],"state_sha256":"aeedf2b0629b395d4273f62b61f174d89e5f29ada11fc89b3e1a4b7d120655e6"}