{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HRFNJY52NWPKJFYQXSUBWTGEAS","short_pith_number":"pith:HRFNJY52","schema_version":"1.0","canonical_sha256":"3c4ad4e3ba6d9ea49710bca81b4cc4049ed669a4c274b8b82f44dc381a1d4905","source":{"kind":"arxiv","id":"1606.07626","version":2},"attestation_state":"computed","paper":{"title":"On topological actions of finite groups on S^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bruno P. Zimmermann","submitted_at":"2016-06-24T10:11:30Z","abstract_excerpt":"We consider orientation-preserving actions of a finite group G on the 3-sphere S^3 (and also on Euclidean space R^3). By the geometrization of finite group actions on 3-manifolds, if such an action is smooth then it is conjugate to an orthogonal action, and in particular G is isomorphic to a subgroup of the orthogonal group SO(4) (or of SO(3) in the case of R^3). On the other hand, there are topological actions with wildly embedded fixed point sets; such actions are not conjugate to smooth actions but one would still expect that the corresponding groups G are isomorphic to subgroups of the ort"},"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":"1606.07626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-06-24T10:11:30Z","cross_cats_sorted":[],"title_canon_sha256":"90ef3596b582f1f36d455b86dded4e94776737b6e6246998e50164b02bf3d7a3","abstract_canon_sha256":"06017d991082800233a63c471a04e16678b11bf14009cc3a863a1fdca49dd47f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:28.522663Z","signature_b64":"iucH5c3eBAwR7qi0MxnG078j7ab6gvrVpgZEYfKkTP50OG59G/d01Sjp4ePYHWRh/hzBD2VviklpF4AI/8XYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c4ad4e3ba6d9ea49710bca81b4cc4049ed669a4c274b8b82f44dc381a1d4905","last_reissued_at":"2026-05-18T01:06:28.522123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:28.522123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On topological actions of finite groups on S^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bruno P. Zimmermann","submitted_at":"2016-06-24T10:11:30Z","abstract_excerpt":"We consider orientation-preserving actions of a finite group G on the 3-sphere S^3 (and also on Euclidean space R^3). By the geometrization of finite group actions on 3-manifolds, if such an action is smooth then it is conjugate to an orthogonal action, and in particular G is isomorphic to a subgroup of the orthogonal group SO(4) (or of SO(3) in the case of R^3). On the other hand, there are topological actions with wildly embedded fixed point sets; such actions are not conjugate to smooth actions but one would still expect that the corresponding groups G are isomorphic to subgroups of the ort"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07626","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":""},"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":"1606.07626","created_at":"2026-05-18T01:06:28.522213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.07626v2","created_at":"2026-05-18T01:06:28.522213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07626","created_at":"2026-05-18T01:06:28.522213+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRFNJY52NWPK","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRFNJY52NWPKJFYQ","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRFNJY52","created_at":"2026-05-18T12:30:19.053100+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS","json":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS.json","graph_json":"https://pith.science/api/pith-number/HRFNJY52NWPKJFYQXSUBWTGEAS/graph.json","events_json":"https://pith.science/api/pith-number/HRFNJY52NWPKJFYQXSUBWTGEAS/events.json","paper":"https://pith.science/paper/HRFNJY52"},"agent_actions":{"view_html":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS","download_json":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS.json","view_paper":"https://pith.science/paper/HRFNJY52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.07626&json=true","fetch_graph":"https://pith.science/api/pith-number/HRFNJY52NWPKJFYQXSUBWTGEAS/graph.json","fetch_events":"https://pith.science/api/pith-number/HRFNJY52NWPKJFYQXSUBWTGEAS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS/action/storage_attestation","attest_author":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS/action/author_attestation","sign_citation":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS/action/citation_signature","submit_replication":"https://pith.science/pith/HRFNJY52NWPKJFYQXSUBWTGEAS/action/replication_record"}},"created_at":"2026-05-18T01:06:28.522213+00:00","updated_at":"2026-05-18T01:06:28.522213+00:00"}