{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GALP3QCFR5NIDJSRA3BJGPAUFJ","short_pith_number":"pith:GALP3QCF","schema_version":"1.0","canonical_sha256":"3016fdc0458f5a81a65106c2933c142a54c8f4bcd8513cd9d08591630be2d1b6","source":{"kind":"arxiv","id":"2404.00619","version":2},"attestation_state":"computed","paper":{"title":"Examples of Ricci limit spaces with infinite holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Shengxuan Zhou","submitted_at":"2024-03-31T09:16:47Z","abstract_excerpt":"Let $n\\geq 3$, $\\lambda \\in \\mathbb{R} $, and $(X,h)$ be an $n$-dimensional smooth complete Riemannian manifold with ${\\rm Ric}_h > \\lambda $.\n  In this paper, we construct, for each given $\\epsilon >0$, a sequence of $(n+2)$-dimensional manifolds $(M_{i} ,g_i ) \\stackrel{GH}{\\longrightarrow} (X_\\epsilon ,d_\\epsilon ) $ with ${\\rm Ric}_{g_i} > \\lambda $, such that $d_{GH} (X,X_\\epsilon ) \\leq \\epsilon $, and $X_\\epsilon $ is homeomorphic to the space obtained by removing an infinite number of balls from $X$. Hence $X_\\epsilon $ has dense boundary with an infinite number of connected components"},"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":"2404.00619","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-31T09:16:47Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"0a2a281dad5d6c68c91131dd8ee09a0b175c86717bdc6a213bdb4ced0ded00c4","abstract_canon_sha256":"34a2b27356295d9830b454b03339cbb7c80c1b23190395212b748b1c51a79fa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:03:51.392292Z","signature_b64":"JEbYugTLinU0U5SsGoWNEZ14E61R6UJznRGZbPqFAXzioonpPb6NvdrqIlQJn348BjqnMx3cTvy+xKYNdzUKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3016fdc0458f5a81a65106c2933c142a54c8f4bcd8513cd9d08591630be2d1b6","last_reissued_at":"2026-07-05T08:03:51.391782Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:03:51.391782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Examples of Ricci limit spaces with infinite holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Shengxuan Zhou","submitted_at":"2024-03-31T09:16:47Z","abstract_excerpt":"Let $n\\geq 3$, $\\lambda \\in \\mathbb{R} $, and $(X,h)$ be an $n$-dimensional smooth complete Riemannian manifold with ${\\rm Ric}_h > \\lambda $.\n  In this paper, we construct, for each given $\\epsilon >0$, a sequence of $(n+2)$-dimensional manifolds $(M_{i} ,g_i ) \\stackrel{GH}{\\longrightarrow} (X_\\epsilon ,d_\\epsilon ) $ with ${\\rm Ric}_{g_i} > \\lambda $, such that $d_{GH} (X,X_\\epsilon ) \\leq \\epsilon $, and $X_\\epsilon $ is homeomorphic to the space obtained by removing an infinite number of balls from $X$. Hence $X_\\epsilon $ has dense boundary with an infinite number of connected components"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00619","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/2404.00619/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":"2404.00619","created_at":"2026-07-05T08:03:51.391840+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.00619v2","created_at":"2026-07-05T08:03:51.391840+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.00619","created_at":"2026-07-05T08:03:51.391840+00:00"},{"alias_kind":"pith_short_12","alias_value":"GALP3QCFR5NI","created_at":"2026-07-05T08:03:51.391840+00:00"},{"alias_kind":"pith_short_16","alias_value":"GALP3QCFR5NIDJSR","created_at":"2026-07-05T08:03:51.391840+00:00"},{"alias_kind":"pith_short_8","alias_value":"GALP3QCF","created_at":"2026-07-05T08:03:51.391840+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.19189","citing_title":"Topology of two-dimensional collapsed spaces with lower Ricci bounds","ref_index":97,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26399","citing_title":"Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature","ref_index":52,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ","json":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ.json","graph_json":"https://pith.science/api/pith-number/GALP3QCFR5NIDJSRA3BJGPAUFJ/graph.json","events_json":"https://pith.science/api/pith-number/GALP3QCFR5NIDJSRA3BJGPAUFJ/events.json","paper":"https://pith.science/paper/GALP3QCF"},"agent_actions":{"view_html":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ","download_json":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ.json","view_paper":"https://pith.science/paper/GALP3QCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.00619&json=true","fetch_graph":"https://pith.science/api/pith-number/GALP3QCFR5NIDJSRA3BJGPAUFJ/graph.json","fetch_events":"https://pith.science/api/pith-number/GALP3QCFR5NIDJSRA3BJGPAUFJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ/action/storage_attestation","attest_author":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ/action/author_attestation","sign_citation":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ/action/citation_signature","submit_replication":"https://pith.science/pith/GALP3QCFR5NIDJSRA3BJGPAUFJ/action/replication_record"}},"created_at":"2026-07-05T08:03:51.391840+00:00","updated_at":"2026-07-05T08:03:51.391840+00:00"}