{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:43F4BWMNSLWD5CVD5KKJPFVPJU","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":"ee60cb89f98c0481e18455e33df04aa9061441a7027258127e93d43c29800879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-06-07T00:57:07Z","title_canon_sha256":"90c03eb918bff13cfb6e729664e5eb7260d63c1487bb385947f9399f415a3045"},"schema_version":"1.0","source":{"id":"2406.04564","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.04564","created_at":"2026-07-05T08:55:36Z"},{"alias_kind":"arxiv_version","alias_value":"2406.04564v2","created_at":"2026-07-05T08:55:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.04564","created_at":"2026-07-05T08:55:36Z"},{"alias_kind":"pith_short_12","alias_value":"43F4BWMNSLWD","created_at":"2026-07-05T08:55:36Z"},{"alias_kind":"pith_short_16","alias_value":"43F4BWMNSLWD5CVD","created_at":"2026-07-05T08:55:36Z"},{"alias_kind":"pith_short_8","alias_value":"43F4BWMN","created_at":"2026-07-05T08:55:36Z"}],"graph_snapshots":[{"event_id":"sha256:537b844061ed218d448fb6a8a68b8e7747d1bdca6c05b632a98ed4e87561597d","target":"graph","created_at":"2026-07-05T08:55:36Z","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/2406.04564/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that any $L^\\infty$ Riemannian metric $g$ on $\\mathbb{R}^n$ that is smooth with nonnegative scalar curvature away from a singular set of finite $(n-\\alpha)$-dimensional Minkowski content, for some $\\alpha>2$, admits an approximation by smooth Riemannian metrics with nonnegative scalar curvature, provided that $g$ is sufficiently close in $L^\\infty$ to the Euclidean metric. The approximation is given by time slices of the Ricci-DeTurck flow, which converge locally in $C^\\infty$ to $g$ away from the singular set. We also identify conditions under which a smooth Ricci-DeTurck flow startin","authors_text":"Paula Burkhardt-Guim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-06-07T00:57:07Z","title":"Smoothing $L^\\infty$ Riemannian metrics with nonnegative scalar curvature outside of a singular set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.04564","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":"sha256:75dddb0a677af3f4a2929b81feae8792dea2da78f2e290c344bb48adb45b3cf3","target":"record","created_at":"2026-07-05T08:55:36Z","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":"ee60cb89f98c0481e18455e33df04aa9061441a7027258127e93d43c29800879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-06-07T00:57:07Z","title_canon_sha256":"90c03eb918bff13cfb6e729664e5eb7260d63c1487bb385947f9399f415a3045"},"schema_version":"1.0","source":{"id":"2406.04564","kind":"arxiv","version":2}},"canonical_sha256":"e6cbc0d98d92ec3e8aa3ea949796af4d170aedb3ce4fe05961809efa1d22afae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6cbc0d98d92ec3e8aa3ea949796af4d170aedb3ce4fe05961809efa1d22afae","first_computed_at":"2026-07-05T08:55:36.527273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:55:36.527273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GFBkEuwK97Sao9QEJEGyIznTfdKj4ZofEg+CMSFt5C23PDd3J08lsWOR0kONzyrX6Ci+iPz+1ImjbZ7reXuzBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:55:36.527725Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.04564","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75dddb0a677af3f4a2929b81feae8792dea2da78f2e290c344bb48adb45b3cf3","sha256:537b844061ed218d448fb6a8a68b8e7747d1bdca6c05b632a98ed4e87561597d"],"state_sha256":"a36499e3a5c2510317d2cb67d5e183a916f970bc05add2b5c48a490a70993e64"}