{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SDZG5ARG74SGMPHFAGKV4TDMOK","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":"0b7707b74810802a8f21a45d66b77293306f20bf6c04711dc5b7282ce58f7940","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-05T20:46:34Z","title_canon_sha256":"0e5f9f4ea235d75a92f21d8f90496ff4ab2ee65b564c2a2bd9afda9421af77a8"},"schema_version":"1.0","source":{"id":"1602.02146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02146","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02146v2","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02146","created_at":"2026-05-18T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"SDZG5ARG74SG","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SDZG5ARG74SGMPHF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SDZG5ARG","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:b8080a4c7440495463dcd759fa87e9cf3eb7bb0cc0095e4cb59dacc55a980d91","target":"graph","created_at":"2026-05-18T01:19:20Z","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 show that the group of piecewise linear homeomorphisms of any compact PL manifold does not admit a Polish group topology. This uses a) new results on the relationship between topologies on groups of homeomorphisms, their algebraic structure, and the topology of the underlying manifold, and b) new results on the structure of certain subgroups of PL(M). The proof also shows that the group of piecewise projective homeomorphisms of the circle has no Polish group topology.","authors_text":"Kathryn Mann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-05T20:46:34Z","title":"PL(M) admits no Polish group topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02146","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":"sha256:919956bc4effc329502344c18d96bbefda90fb28578e1cd44276c56634332e8d","target":"record","created_at":"2026-05-18T01:19:20Z","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":"0b7707b74810802a8f21a45d66b77293306f20bf6c04711dc5b7282ce58f7940","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-02-05T20:46:34Z","title_canon_sha256":"0e5f9f4ea235d75a92f21d8f90496ff4ab2ee65b564c2a2bd9afda9421af77a8"},"schema_version":"1.0","source":{"id":"1602.02146","kind":"arxiv","version":2}},"canonical_sha256":"90f26e8226ff24663ce501955e4c6c72a87b6213f20e968506c7f3bfe6478203","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90f26e8226ff24663ce501955e4c6c72a87b6213f20e968506c7f3bfe6478203","first_computed_at":"2026-05-18T01:19:20.120292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:20.120292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/oeEtb9yEHCmmhVDtHJrPB0Ld5LKGo7UNyPrabhou9uDMWijB0ona7lcOKjD3r0zfm/eQVEjSp6qU9ju6FF0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:20.120904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:919956bc4effc329502344c18d96bbefda90fb28578e1cd44276c56634332e8d","sha256:b8080a4c7440495463dcd759fa87e9cf3eb7bb0cc0095e4cb59dacc55a980d91"],"state_sha256":"b836d55052ab9019d7e32463462a413721f275980c669075fe02543be88610d8"}