{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XO5CWAPY2WIZK72OJ6JCZA6MQ3","short_pith_number":"pith:XO5CWAPY","schema_version":"1.0","canonical_sha256":"bbba2b01f8d591957f4e4f922c83cc86c1abde96a7b4f9ef4cc305f36ddfcd35","source":{"kind":"arxiv","id":"2412.06131","version":1},"attestation_state":"computed","paper":{"title":"On the non-collapsed RCD spaces with local bounded covering geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Jikang Wang","submitted_at":"2024-12-09T01:21:07Z","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"},"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":"2412.06131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-09T01:21:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"ed13236d63a553805120f38390dfd4bb98e8d30de156bb7c8110709ec887a3d7","abstract_canon_sha256":"c9e0b67bea0ff9db8608b4102719361bb2c5e3afd08ab8f22a65f612c58305fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:46:15.925171Z","signature_b64":"h6hFRM1DaZhZCMBBdEl9R2rgs/wZnIWGjoBxtWJ48gX9VqdvEC2oU4kxYQw7drT+8CcBYBb3bW5J255YHg24Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbba2b01f8d591957f4e4f922c83cc86c1abde96a7b4f9ef4cc305f36ddfcd35","last_reissued_at":"2026-07-05T09:46:15.924766Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:46:15.924766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the non-collapsed RCD spaces with local bounded covering geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Jikang Wang","submitted_at":"2024-12-09T01:21:07Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06131","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/2412.06131/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":"2412.06131","created_at":"2026-07-05T09:46:15.924823+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.06131v1","created_at":"2026-07-05T09:46:15.924823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.06131","created_at":"2026-07-05T09:46:15.924823+00:00"},{"alias_kind":"pith_short_12","alias_value":"XO5CWAPY2WIZ","created_at":"2026-07-05T09:46:15.924823+00:00"},{"alias_kind":"pith_short_16","alias_value":"XO5CWAPY2WIZK72O","created_at":"2026-07-05T09:46:15.924823+00:00"},{"alias_kind":"pith_short_8","alias_value":"XO5CWAPY","created_at":"2026-07-05T09:46:15.924823+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/XO5CWAPY2WIZK72OJ6JCZA6MQ3","json":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3.json","graph_json":"https://pith.science/api/pith-number/XO5CWAPY2WIZK72OJ6JCZA6MQ3/graph.json","events_json":"https://pith.science/api/pith-number/XO5CWAPY2WIZK72OJ6JCZA6MQ3/events.json","paper":"https://pith.science/paper/XO5CWAPY"},"agent_actions":{"view_html":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3","download_json":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3.json","view_paper":"https://pith.science/paper/XO5CWAPY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.06131&json=true","fetch_graph":"https://pith.science/api/pith-number/XO5CWAPY2WIZK72OJ6JCZA6MQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/XO5CWAPY2WIZK72OJ6JCZA6MQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3/action/storage_attestation","attest_author":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3/action/author_attestation","sign_citation":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3/action/citation_signature","submit_replication":"https://pith.science/pith/XO5CWAPY2WIZK72OJ6JCZA6MQ3/action/replication_record"}},"created_at":"2026-07-05T09:46:15.924823+00:00","updated_at":"2026-07-05T09:46:15.924823+00:00"}