{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QRQY26KSPETR2TLRKLTTEQLYPW","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":"c14fe03017912a305894f47f1afba346286d89a79861e553556657f3e826a348","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-08-07T20:52:10Z","title_canon_sha256":"6be5a64db60fe786296d134e80d59082f74445af2ba2aec32272d82729855319"},"schema_version":"1.0","source":{"id":"2308.03909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.03909","created_at":"2026-07-05T10:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"2308.03909v1","created_at":"2026-07-05T10:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.03909","created_at":"2026-07-05T10:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"QRQY26KSPETR","created_at":"2026-07-05T10:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"QRQY26KSPETR2TLR","created_at":"2026-07-05T10:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"QRQY26KS","created_at":"2026-07-05T10:06:27Z"}],"graph_snapshots":[{"event_id":"sha256:f6c84622ae926e61f11f7af221d17e042ff366cd916bcd836d7861357ebacde6","target":"graph","created_at":"2026-07-05T10:06:27Z","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/2308.03909/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is known that a limit $(M^n_j,g_j)\\to (X^k,d)$ of manifolds $M_j$ with uniform lower bounds on Ricci curvature must be $k$-rectifiable for some unique $\\dim X:= k\\leq n = \\dim M_j$. It is also known that if $k=n$, then $X^n$ is a topological manifold on an open dense subset, and it has been an open question as to whether this holds for $k<n$.\n  Consider now any smooth complete $4$-manifold $(X^4,h)$ with $\\text{Ric}>\\lambda$ and $\\lambda\\in \\mathbb{R}$. Then for each $\\epsilon>0$ we construct a complete $4$-rectifiable metric space $(X^4_\\epsilon,d_\\epsilon)$ with $d_{GH}(X^4_\\epsilon,X^4)<","authors_text":"Aaron Naber, Erik Hupp, Kai-Hsiang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-08-07T20:52:10Z","title":"Lower Ricci Curvature and Nonexistence of Manifold Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.03909","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:b1ec29b466477b72c1b3f788ac62db8f0b9b8e23f868729d8f5b5137ea662ea8","target":"record","created_at":"2026-07-05T10:06:27Z","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":"c14fe03017912a305894f47f1afba346286d89a79861e553556657f3e826a348","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-08-07T20:52:10Z","title_canon_sha256":"6be5a64db60fe786296d134e80d59082f74445af2ba2aec32272d82729855319"},"schema_version":"1.0","source":{"id":"2308.03909","kind":"arxiv","version":1}},"canonical_sha256":"84618d795279271d4d7152e73241787d923d269bed9b832f3d57ecc2fea4d836","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84618d795279271d4d7152e73241787d923d269bed9b832f3d57ecc2fea4d836","first_computed_at":"2026-07-05T10:06:27.238041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:27.238041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E19uGG2t1DVXBckAXB/4Femf8mZKvQhu3Zc54S6dP5Z4zYHSdkDsVY4eO85zr2IKyA7TphUZ1y303eRzZyVVBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:27.238470Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.03909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1ec29b466477b72c1b3f788ac62db8f0b9b8e23f868729d8f5b5137ea662ea8","sha256:f6c84622ae926e61f11f7af221d17e042ff366cd916bcd836d7861357ebacde6"],"state_sha256":"4f30f6caabbefb7d2ee9d5032f3c29d7b37298f42125dd8fde5d4e679b8244d2"}