{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:APTSZZ6DVJHD5P5I2ZV3JXHHMQ","short_pith_number":"pith:APTSZZ6D","schema_version":"1.0","canonical_sha256":"03e72ce7c3aa4e3ebfa8d66bb4dce7640cec887c3236a2aa9c14ff8e85cbb51b","source":{"kind":"arxiv","id":"2508.04173","version":2},"attestation_state":"computed","paper":{"title":"Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shuli Chen","submitted_at":"2025-08-06T07:58:32Z","abstract_excerpt":"We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \\frac{2}{3}$, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and $\\mathbb{S}^2\\times \\mathbb{S}^1$ summands. Consequently, $M$ carries a complete Riemannian metric of uniformly positive scalar curvature. The decay constant $\\frac{2}{3}$ is sharp, as demonstrated by metrics on $\\mathbb{R}^2 \\times \\mathbb{S}^1$. This improves a result of Balacheff, Gil Moreno de Mora Sard\\`a, and Sabou"},"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":"2508.04173","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-08-06T07:58:32Z","cross_cats_sorted":[],"title_canon_sha256":"7c498efd6067a577c867788dc83fc4c1a3426866ff0229972090c5ab90ce0518","abstract_canon_sha256":"6442e22c7030ae0b1e8dcfe711eefff849d486b839d95202352675dd4b937fa7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:00:28.695156Z","signature_b64":"X/S3UprkD83PHkZR6yFXNi5BmZwmBhrQbs54R9aBVDDgLM+5Ha6AbMr/ZsGVl8Wwx6GvaTIaH/BLuqgcRSMnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03e72ce7c3aa4e3ebfa8d66bb4dce7640cec887c3236a2aa9c14ff8e85cbb51b","last_reissued_at":"2026-07-05T12:00:28.694674Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:00:28.694674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shuli Chen","submitted_at":"2025-08-06T07:58:32Z","abstract_excerpt":"We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has at most $C$-quadratic decay at infinity for some $C > \\frac{2}{3}$, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and $\\mathbb{S}^2\\times \\mathbb{S}^1$ summands. Consequently, $M$ carries a complete Riemannian metric of uniformly positive scalar curvature. The decay constant $\\frac{2}{3}$ is sharp, as demonstrated by metrics on $\\mathbb{R}^2 \\times \\mathbb{S}^1$. This improves a result of Balacheff, Gil Moreno de Mora Sard\\`a, and Sabou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04173","kind":"arxiv","version":2},"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/2508.04173/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":"2508.04173","created_at":"2026-07-05T12:00:28.694734+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.04173v2","created_at":"2026-07-05T12:00:28.694734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.04173","created_at":"2026-07-05T12:00:28.694734+00:00"},{"alias_kind":"pith_short_12","alias_value":"APTSZZ6DVJHD","created_at":"2026-07-05T12:00:28.694734+00:00"},{"alias_kind":"pith_short_16","alias_value":"APTSZZ6DVJHD5P5I","created_at":"2026-07-05T12:00:28.694734+00:00"},{"alias_kind":"pith_short_8","alias_value":"APTSZZ6D","created_at":"2026-07-05T12:00:28.694734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.06547","citing_title":"Linking at Infinity and Scalar Curvature Decay on Non-Compact Manifolds","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ","json":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ.json","graph_json":"https://pith.science/api/pith-number/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/graph.json","events_json":"https://pith.science/api/pith-number/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/events.json","paper":"https://pith.science/paper/APTSZZ6D"},"agent_actions":{"view_html":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ","download_json":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ.json","view_paper":"https://pith.science/paper/APTSZZ6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.04173&json=true","fetch_graph":"https://pith.science/api/pith-number/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/action/storage_attestation","attest_author":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/action/author_attestation","sign_citation":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/action/citation_signature","submit_replication":"https://pith.science/pith/APTSZZ6DVJHD5P5I2ZV3JXHHMQ/action/replication_record"}},"created_at":"2026-07-05T12:00:28.694734+00:00","updated_at":"2026-07-05T12:00:28.694734+00:00"}