{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GXXQFW523DRNAHQQ6VW6U4NULN","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":"4fdbccbba65544f4c74e60994d2d81937ba2227faa5ef26f0865300c0a75594c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-24T17:58:55Z","title_canon_sha256":"767a90bd077a3562d2ccf516dec42729220fa0c9618b4aa93b473f0c4b07897f"},"schema_version":"1.0","source":{"id":"1705.08886","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08886","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08886v3","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08886","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"GXXQFW523DRN","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GXXQFW523DRNAHQQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GXXQFW52","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:f79aeb2710bafcd0e18494c2293a205b6a214d88ed6d65ffd7f3494e1e8b6adb","target":"graph","created_at":"2026-05-18T00:06:26Z","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"},"paper":{"abstract_excerpt":"A closed four dimensional manifold cannot possess a non-flat Ricci soliton metric with arbitrarily small $L^2$-norm of the curvature. In this paper, we localize this fact in the case of shrinking Ricci solitons by proving an $\\varepsilon$-regularity theorem, thus confirming a conjecture of Cheeger-Tian. As applications, we will also derive structural results concerning the degeneration of the metrics on a family of complete non-compact four dimensional shrinking Ricci solitons without a uniform entropy lower bound. In the appendix, we provide a detailed account of the equivariant good chopping","authors_text":"Shaosai Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-24T17:58:55Z","title":"$\\epsilon$-Regularity and Structure of 4-dimensional Shrinking Ricci Solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08886","kind":"arxiv","version":3},"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":"sha256:09e1cbebbb43d0c1128c396b3df24170975c9fda418f243dd44ccd1c5e78f802","target":"record","created_at":"2026-05-18T00:06:26Z","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":"4fdbccbba65544f4c74e60994d2d81937ba2227faa5ef26f0865300c0a75594c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-05-24T17:58:55Z","title_canon_sha256":"767a90bd077a3562d2ccf516dec42729220fa0c9618b4aa93b473f0c4b07897f"},"schema_version":"1.0","source":{"id":"1705.08886","kind":"arxiv","version":3}},"canonical_sha256":"35ef02dbbad8e2d01e10f56dea71b45b5239a9ad382b24c330df0d1c6f73b34f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35ef02dbbad8e2d01e10f56dea71b45b5239a9ad382b24c330df0d1c6f73b34f","first_computed_at":"2026-05-18T00:06:26.559455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:26.559455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5AywPZZVHKGqpDkV+ot4aQELQeukajYWXC6RuUVr6wVFfjavgsakcsYvbaLnpGIRjkOMMDQvZEeh3EJQfR6SBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:26.560165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08886","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09e1cbebbb43d0c1128c396b3df24170975c9fda418f243dd44ccd1c5e78f802","sha256:f79aeb2710bafcd0e18494c2293a205b6a214d88ed6d65ffd7f3494e1e8b6adb"],"state_sha256":"24eddbb89613690fc47cd2a500d925912513d35d62f32a8c987aafc11f0a5770"}