{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XO5CWAPY2WIZK72OJ6JCZA6MQ3","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":"c9e0b67bea0ff9db8608b4102719361bb2c5e3afd08ab8f22a65f612c58305fc","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-09T01:21:07Z","title_canon_sha256":"ed13236d63a553805120f38390dfd4bb98e8d30de156bb7c8110709ec887a3d7"},"schema_version":"1.0","source":{"id":"2412.06131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.06131","created_at":"2026-07-05T09:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"2412.06131v1","created_at":"2026-07-05T09:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.06131","created_at":"2026-07-05T09:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"XO5CWAPY2WIZ","created_at":"2026-07-05T09:46:15Z"},{"alias_kind":"pith_short_16","alias_value":"XO5CWAPY2WIZK72O","created_at":"2026-07-05T09:46:15Z"},{"alias_kind":"pith_short_8","alias_value":"XO5CWAPY","created_at":"2026-07-05T09:46:15Z"}],"graph_snapshots":[{"event_id":"sha256:67ea8bce98768a18df2f4b4691a21a6bc5063bc1967abc1db264a38ba3956f16","target":"graph","created_at":"2026-07-05T09:46:15Z","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/2412.06131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a RCD$(-(N-1),N)$ space $(X,d,\\mathcal{H}^N)$ with local bounded covering geometry. The first result is related to Gromov's almost flat manifold theorem. Specifically, if for every point $\\tilde{p}$ in the universal cover $\\widetilde{X}$, we have $\\mathcal{H}^N(B_1(\\tilde{p})) \\ge v > 0$ and the diameter of $X$ is sufficiently small, then $X$ is biH\\\"{o}lder homeomorphic to an infranil-manifold. Moreover, if $X$ is a smooth Riemannian $N$-manifold with $\\mathrm{Ric} \\ge -(N-1)$, then $X$ is biH\\\"{o}lder diffeomorphic to an infranil-manifold. An application of our argument is to con","authors_text":"Jikang Wang","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-09T01:21:07Z","title":"On the non-collapsed RCD spaces with local bounded covering geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06131","kind":"arxiv","version":1},"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:a29b8987ff556eee50685b43bca8c759b04408c11a4c973953d076188a1078e6","target":"record","created_at":"2026-07-05T09:46:15Z","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":"c9e0b67bea0ff9db8608b4102719361bb2c5e3afd08ab8f22a65f612c58305fc","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-09T01:21:07Z","title_canon_sha256":"ed13236d63a553805120f38390dfd4bb98e8d30de156bb7c8110709ec887a3d7"},"schema_version":"1.0","source":{"id":"2412.06131","kind":"arxiv","version":1}},"canonical_sha256":"bbba2b01f8d591957f4e4f922c83cc86c1abde96a7b4f9ef4cc305f36ddfcd35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbba2b01f8d591957f4e4f922c83cc86c1abde96a7b4f9ef4cc305f36ddfcd35","first_computed_at":"2026-07-05T09:46:15.924766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:46:15.924766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h6hFRM1DaZhZCMBBdEl9R2rgs/wZnIWGjoBxtWJ48gX9VqdvEC2oU4kxYQw7drT+8CcBYBb3bW5J255YHg24Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:46:15.925171Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.06131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a29b8987ff556eee50685b43bca8c759b04408c11a4c973953d076188a1078e6","sha256:67ea8bce98768a18df2f4b4691a21a6bc5063bc1967abc1db264a38ba3956f16"],"state_sha256":"e75f14691f52f85270b5a6a4b168a73c02ba190aeff3912f04dd882325b306df"}