{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TMHLMXU5GDINYE6HOCRM6RX7OT","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":"56432cd521271a316cddf5b951b4da702e7c8578626de65c421433ed895b04d9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-31T14:44:47Z","title_canon_sha256":"49afdeba074339e6b8c8416309a7de4985f5d647d45f484ecafec5e83796592f"},"schema_version":"1.0","source":{"id":"1503.09068","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09068","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09068v2","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09068","created_at":"2026-05-18T01:55:52Z"},{"alias_kind":"pith_short_12","alias_value":"TMHLMXU5GDIN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TMHLMXU5GDINYE6H","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TMHLMXU5","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:97f54c2864990a9e27ad4e49c14a95fe55958a5496de1686d00e0337fccdf635","target":"graph","created_at":"2026-05-18T01:55:52Z","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 prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the equivariant classification of closed, simply connected cohomogeneity one topological manifolds in dimensions $5$, $6$, and $7$ and obtain topological characterizations of these spaces. In these dimensions, these manifolds are homeomorphic to smooth manifolds.","authors_text":"Fernando Galaz-Garcia, Masoumeh Zarei","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-31T14:44:47Z","title":"Cohomogeneity one topological manifolds revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09068","kind":"arxiv","version":2},"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":"sha256:0f403ae6cdd1b16faff949604c67db7f235d8bf2f8be2b5760396bab1cb1419e","target":"record","created_at":"2026-05-18T01:55:52Z","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":"56432cd521271a316cddf5b951b4da702e7c8578626de65c421433ed895b04d9","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-03-31T14:44:47Z","title_canon_sha256":"49afdeba074339e6b8c8416309a7de4985f5d647d45f484ecafec5e83796592f"},"schema_version":"1.0","source":{"id":"1503.09068","kind":"arxiv","version":2}},"canonical_sha256":"9b0eb65e9d30d0dc13c770a2cf46ff74f0f6dc440488ce440ecb082f7e864a33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b0eb65e9d30d0dc13c770a2cf46ff74f0f6dc440488ce440ecb082f7e864a33","first_computed_at":"2026-05-18T01:55:52.479955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:52.479955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l9JlJl3MNvIF418Ucs1ayjnqo8W62YH+yreIdVqA0y6vS4bpMZTm3XBJvLqQOub7faT9jKaoAez6qTvOMfU6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:52.480386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.09068","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f403ae6cdd1b16faff949604c67db7f235d8bf2f8be2b5760396bab1cb1419e","sha256:97f54c2864990a9e27ad4e49c14a95fe55958a5496de1686d00e0337fccdf635"],"state_sha256":"b1908e9672e0f3f17c62cd4ff39099c161713ff1d21be9013058fd7f32a0bf35"}