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Publications Mathématiques de l'IHÉS , year =. doi:10.1007/s10240-025-00145-3 , url =","work_id":"8128ac8d-2823-4987-b435-4f63db7f7119","year":null}],"snapshot_sha256":"f6a22bacae997b2281267a6a5083360035faabfc4eb710670e7449bfe358505d"},"source":{"id":"2605.17001","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:42:34.010833Z","id":"876e60da-1760-4443-98f0-fc1e81ab8c37","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves Lojasiewicz inequality for W-entropy near generalized cylinders in Ricci flow, yielding strong uniqueness of tangent flows and horizontal parabolic k-rectifiability of the corresponding singularity set.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A Lojasiewicz inequality for the pointed W-entropy establishes strong uniqueness of generalized cylindrical tangent flows in Ricci flow.","strongest_claim":"We establish a Lojasiewicz inequality for the pointed W-entropy in Ricci flow under the assumption that the geometry near the base point is close to a generalized cylinder R^k × N^{n-k}, where N is an Einstein manifold with obstruction of order three satisfying a suitable spectral condition. As an application, we prove the strong uniqueness of generalized cylindrical tangent flows. Furthermore, we show that the subset S^k_qc(N) is horizontally parabolic k-rectifiable.","weakest_assumption":"The geometry near the base point is close to a generalized cylinder R^k × N^{n-k}, where N is an Einstein manifold with obstruction of order three satisfying a suitable spectral condition (invoked in the statement of the Lojasiewicz inequality and its applications to uniqueness and rectifiability)."}},"verdict_id":"876e60da-1760-4443-98f0-fc1e81ab8c37"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9e463890cd831331e8a1da9aac2efabe94f4419194093b7498ad910c9e87f7ea","target":"record","created_at":"2026-05-20T00:03:35Z","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":"7aef4169569e4e9192d17365255e19dcbf98131f70bcd66b53ce4fe3c39a6e1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-16T13:54:24Z","title_canon_sha256":"5da0dd1ee21e10f6a935ac6440ba5bf5abdb6ae35bbbf1c7d102fb12614c86f4"},"schema_version":"1.0","source":{"id":"2605.17001","kind":"arxiv","version":1}},"canonical_sha256":"dfb2ebd74c59b21af5f4d9cf7b4cd6fa8806176a7324feb5346eebc016ef2599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfb2ebd74c59b21af5f4d9cf7b4cd6fa8806176a7324feb5346eebc016ef2599","first_computed_at":"2026-05-20T00:03:35.377161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:35.377161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SVn0j1fvjYBu1VV/od7+x9qL8gZsqMe8XBOWlHLbWvbD6eRqF4S/ZEPoE+SzqDerMIeMK7XTjX7upmHdFEnMCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:35.377981Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3398a35e8a9190a1434d3f45370e8c0fa7dc21fa61cf7e972c56b53812fc0d5a","sha256:9e463890cd831331e8a1da9aac2efabe94f4419194093b7498ad910c9e87f7ea","sha256:fed0bc67fc9709ba3411cfbfe222897c81d75193b306a7b4874ce806a940ab5c"],"state_sha256":"f9f3c64379efc17a0d0fd40d370ca1057b9138538d04b3f9011c94b483af1167"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4sj5HKkuRTDMqz2d4oopO4A2ArcL1O+su3ngrSJZd3hl5PIUoSFVuYvbiG8WvbB7I58Kk7tyQiwNes54t9TNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T20:31:34.705239Z","bundle_sha256":"2f342f2248d8f3eda157ab0b6422b529d3375b2292e4639961996591310c08a8"}}