{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:SOOTYFCH4RWFPQ7LLVQPBYBIME","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":"819aea6c6f3d6bb0162ec61571a45132e8651d216bf2927a7b5f05bd81cc09b5","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2002-11-09T12:59:07Z","title_canon_sha256":"1b59b46f752c15f8b3c21617fcefdf69f503de0194d4ce0623462e1a737bd02a"},"schema_version":"1.0","source":{"id":"math/0211153","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211153","created_at":"2026-07-04T15:04:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211153v3","created_at":"2026-07-04T15:04:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211153","created_at":"2026-07-04T15:04:26Z"},{"alias_kind":"pith_short_12","alias_value":"SOOTYFCH4RWF","created_at":"2026-07-04T15:04:26Z"},{"alias_kind":"pith_short_16","alias_value":"SOOTYFCH4RWFPQ7L","created_at":"2026-07-04T15:04:26Z"},{"alias_kind":"pith_short_8","alias_value":"SOOTYFCH","created_at":"2026-07-04T15:04:26Z"}],"graph_snapshots":[{"event_id":"sha256:50be894f1c0a1e471d469ae5cb14e986a21530564b48caf9741ca157a6868bcf","target":"graph","created_at":"2026-07-04T15:04:26Z","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/math/0211153/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper establishes an equivalence between existence of free involutions on $H{\\Bbb C}P^3$ and existence of involutions on $S^6$ with fixed point set an imbedded $S^3$, then a family of counterexamples of the Smith conjecture for imbeddings of $S^3$ in $S^6$ are given by known result on $H{\\Bbb C}P^3$. In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smooth free involution, which answers an open problem [Pe]. Moreover, the study of existence problem for smooth orientation preserving involutions on $H{\\Bbb C}P^3$ is com","authors_text":"Bang-He Li, Zhi L\\\"u","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2002-11-09T12:59:07Z","title":"Smooth free involution of $H{\\Bbb C}P^3$ and Smith conjecture for imbeddings of $S^3$ in $S^6$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211153","kind":"arxiv","version":3},"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:edaf1f703bdbb84994e7606d52d3acef680af7ed9316e0a52d370538935058dd","target":"record","created_at":"2026-07-04T15:04:26Z","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":"819aea6c6f3d6bb0162ec61571a45132e8651d216bf2927a7b5f05bd81cc09b5","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2002-11-09T12:59:07Z","title_canon_sha256":"1b59b46f752c15f8b3c21617fcefdf69f503de0194d4ce0623462e1a737bd02a"},"schema_version":"1.0","source":{"id":"math/0211153","kind":"arxiv","version":3}},"canonical_sha256":"939d3c1447e46c57c3eb5d60f0e028612d49d75b86d4f12ab628991cf246b8f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"939d3c1447e46c57c3eb5d60f0e028612d49d75b86d4f12ab628991cf246b8f0","first_computed_at":"2026-07-04T15:04:26.162356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:04:26.162356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SMghKKh3KebZ3BcCppJYdPs217HIiJYAk/VwfCSpWs9C0uvyOx6Z2WJgr4Hb1SgIHAKG92Nl/6nlBuSqZmLRCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:04:26.162706Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0211153","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edaf1f703bdbb84994e7606d52d3acef680af7ed9316e0a52d370538935058dd","sha256:50be894f1c0a1e471d469ae5cb14e986a21530564b48caf9741ca157a6868bcf"],"state_sha256":"72fe0bae12768311b2670bcd6ca85650c1c0795567f832c4961c9ffe9ef9615b"}