{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I2EBI4PFFIANCRQDYNP54IKCKN","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":"d84846dfbfb7b41db149ca726920488cf997e36a6f04a7e18774785a7ce36916","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-18T05:23:18Z","title_canon_sha256":"e8efacc26f91db3c45843abb1c88530248efaa187c65896154ec25d0da33603f"},"schema_version":"1.0","source":{"id":"1403.4347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4347","created_at":"2026-05-18T02:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4347v1","created_at":"2026-05-18T02:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4347","created_at":"2026-05-18T02:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"I2EBI4PFFIAN","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I2EBI4PFFIANCRQD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I2EBI4PF","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:c92e7fcfe07deae50dc0fc1ed468d905df73a028b5f3ed1f2e47fc6cad8ae953","target":"graph","created_at":"2026-05-18T02:56:05Z","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":"We specify a result of Yokoi \\cite{yo} by proving that if $G$ is an abelian group and $X$ is a homogeneous metric $ANR$ compactum with $\\dim_GX=n$ and $\\check{H}^n(X;G)\\neq 0$, then $X$ is an $(n,G)$-bubble. This implies that any such space $X$ has the following properties: $\\check{H}^{n-1}(A;G)\\neq 0$ for every closed separator $A$ of $X$, and $X$ is an Alexandroff manifold with respect to the class $D^{n-2}_G$ of all spaces of dimension $\\dim_G\\leq n-2$. We also prove that if $X$ is a homogeneous metric continuum with $\\check{H}^n(X;G)\\neq 0$, then $\\check{H}^{n-1}(C;G)\\neq 0$ for any partit","authors_text":"V. Valov","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-18T05:23:18Z","title":"Homogeneous ANR-spaces and Alexandroff manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4347","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":"sha256:09d00e79583866f57b9089345dde1bc6e91756d9524584d1c4cf46bbafcd9f1d","target":"record","created_at":"2026-05-18T02:56:05Z","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":"d84846dfbfb7b41db149ca726920488cf997e36a6f04a7e18774785a7ce36916","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-18T05:23:18Z","title_canon_sha256":"e8efacc26f91db3c45843abb1c88530248efaa187c65896154ec25d0da33603f"},"schema_version":"1.0","source":{"id":"1403.4347","kind":"arxiv","version":1}},"canonical_sha256":"46881471e52a00d14603c35fde214253440b4ef4b1fe59fe39df0267eb9f4c7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46881471e52a00d14603c35fde214253440b4ef4b1fe59fe39df0267eb9f4c7a","first_computed_at":"2026-05-18T02:56:05.959334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:05.959334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s36SKCyAEq/Sey0piAnio9VMS9Jq1kWgCgErb00tHIw8WEGDKfNCmLCcliWdG1YKMeZa7UqVTZXsis+rN01jBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:05.959759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09d00e79583866f57b9089345dde1bc6e91756d9524584d1c4cf46bbafcd9f1d","sha256:c92e7fcfe07deae50dc0fc1ed468d905df73a028b5f3ed1f2e47fc6cad8ae953"],"state_sha256":"ead8e07012d326a0ee1b3b0427f1da0f1cbbd62856e101687843955eb1225535"}