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We prove that every smooth Riemannian metric $g_0$ with $\\mathrm{Scal}_{g_0}\\geq\\kappa$ is a locally uniform limit of smooth Riemannian metrics $g_i$ with $\\mathrm{Scal}_{g_i}=\\kappa$ that are locally uniformly bounded in $W^{1,\\infty}$. As a corollary, combining this with Gromov's $C^0$-stability theorem, we obtain the perhaps surprising identity \\[ \\overline{\\{g:\\mathrm{Scal}_g=\\kappa\\}}^{\\,C^{0,\\alpha}_{\\mathrm{loc}}}=\\{g:\\mathrm{Scal}_g\\geq\\kappa\\},"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.08707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-09T13:39:46Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"5ebfaf72990c6e42fb871bc42217cc2f19fb8dcce98ea0786559ab92bbbcff08","abstract_canon_sha256":"66307b6e38c7c495d2ff0858ec30c5d31a6daaa07844116ad0167cd1fe323adb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:25:06.376252Z","signature_b64":"4yPp13TlGEk90xgNGQoOE6wvrIRjpWavJTPBVn6H5cIvU9JLiJ76EtIqeFHf5e5oGi5ckiNAKdolU7pheKlJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4575e6c48ccf2281a4750eeb50bc95afc6e2750ad8ababf1736b7c988a3b6f74","last_reissued_at":"2026-08-11T01:25:06.373758Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:25:06.373758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalar Curvature Flexibility in the Riemannian Burnett Compactness Class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jingbo Wan","submitted_at":"2026-08-09T13:39:46Z","abstract_excerpt":"Let $M$ be a connected smooth $n$-manifold without boundary, where $n\\geq3$, and let $\\kappa\\in\\mathbb{R}$, with $\\kappa\\leq0$ if $M$ is open. We prove that every smooth Riemannian metric $g_0$ with $\\mathrm{Scal}_{g_0}\\geq\\kappa$ is a locally uniform limit of smooth Riemannian metrics $g_i$ with $\\mathrm{Scal}_{g_i}=\\kappa$ that are locally uniformly bounded in $W^{1,\\infty}$. As a corollary, combining this with Gromov's $C^0$-stability theorem, we obtain the perhaps surprising identity \\[ \\overline{\\{g:\\mathrm{Scal}_g=\\kappa\\}}^{\\,C^{0,\\alpha}_{\\mathrm{loc}}}=\\{g:\\mathrm{Scal}_g\\geq\\kappa\\},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08707","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08707/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.08707","created_at":"2026-08-11T01:25:06.374691+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.08707v1","created_at":"2026-08-11T01:25:06.374691+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08707","created_at":"2026-08-11T01:25:06.374691+00:00"},{"alias_kind":"pith_short_12","alias_value":"IV26NREMZ4RI","created_at":"2026-08-11T01:25:06.374691+00:00"},{"alias_kind":"pith_short_16","alias_value":"IV26NREMZ4RIDJDV","created_at":"2026-08-11T01:25:06.374691+00:00"},{"alias_kind":"pith_short_8","alias_value":"IV26NREM","created_at":"2026-08-11T01:25:06.374691+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7","json":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7.json","graph_json":"https://pith.science/api/pith-number/IV26NREMZ4RIDJDVB3VVBPEVV7/graph.json","events_json":"https://pith.science/api/pith-number/IV26NREMZ4RIDJDVB3VVBPEVV7/events.json","paper":"https://pith.science/paper/IV26NREM"},"agent_actions":{"view_html":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7","download_json":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7.json","view_paper":"https://pith.science/paper/IV26NREM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.08707&json=true","fetch_graph":"https://pith.science/api/pith-number/IV26NREMZ4RIDJDVB3VVBPEVV7/graph.json","fetch_events":"https://pith.science/api/pith-number/IV26NREMZ4RIDJDVB3VVBPEVV7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7/action/storage_attestation","attest_author":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7/action/author_attestation","sign_citation":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7/action/citation_signature","submit_replication":"https://pith.science/pith/IV26NREMZ4RIDJDVB3VVBPEVV7/action/replication_record"}},"created_at":"2026-08-11T01:25:06.374691+00:00","updated_at":"2026-08-11T01:25:06.374691+00:00"}