{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:Z4YE5LN7SXQ2ZDS3G3R2CV56KV","short_pith_number":"pith:Z4YE5LN7","canonical_record":{"source":{"id":"0911.1254","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-06T13:58:18Z","cross_cats_sorted":[],"title_canon_sha256":"39bb2bff30bd91e68ece3791ff1f25f607fe0041816982d14ec9b6ebe058a1b1","abstract_canon_sha256":"476c74c9399ba444c5d5018a06a19e8f41f9c1a427993cf0197fb20057744074"},"schema_version":"1.0"},"canonical_sha256":"cf304eadbf95e1ac8e5b36e3a157be554a0224495761cf75ce4d3cf6ecfc7679","source":{"kind":"arxiv","id":"0911.1254","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1254","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1254v3","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1254","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z4YE5LN7SXQ2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Z4YE5LN7SXQ2ZDS3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Z4YE5LN7","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:Z4YE5LN7SXQ2ZDS3G3R2CV56KV","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1254","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-06T13:58:18Z","cross_cats_sorted":[],"title_canon_sha256":"39bb2bff30bd91e68ece3791ff1f25f607fe0041816982d14ec9b6ebe058a1b1","abstract_canon_sha256":"476c74c9399ba444c5d5018a06a19e8f41f9c1a427993cf0197fb20057744074"},"schema_version":"1.0"},"canonical_sha256":"cf304eadbf95e1ac8e5b36e3a157be554a0224495761cf75ce4d3cf6ecfc7679","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:14.783190Z","signature_b64":"LuI9mvQncL8L+zHkMDG/mpbbuWKwb4OvsFuOkL712MwDOQp6Ht7f7pzDf4uAYN795gt8TvkC5BNBlkOjrwQgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf304eadbf95e1ac8e5b36e3a157be554a0224495761cf75ce4d3cf6ecfc7679","last_reissued_at":"2026-05-18T04:20:14.782745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:14.782745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1254","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v43KIV/Q1BI/88+W6Ismd8aajrDCyCvMzVpOzGa5CTxYAZStjqJwSCLbpTrF4wHDCpPzZQTKaL5glqq2zAkWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:51:44.513333Z"},"content_sha256":"313a325a879d28614dbb69651e2e05f3c3a719e5948cbdcde63cd0f3365ecf01","schema_version":"1.0","event_id":"sha256:313a325a879d28614dbb69651e2e05f3c3a719e5948cbdcde63cd0f3365ecf01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:Z4YE5LN7SXQ2ZDS3G3R2CV56KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonnegatively curved fixed point homogeneous manifolds in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fernando Galaz-Garcia","submitted_at":"2009-11-06T13:58:18Z","abstract_excerpt":"Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1254","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aCmdPiYnDpZMP+J2mAaN4MU6PAETJuUwWGNOov/pQrRxHXDY+J31+3V27JvU8F2sHSEMjmRr4BWcZaX9pEVQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:51:44.514051Z"},"content_sha256":"875f7c2837172de0254f17bbc6027894b1513b92609b3763a2b41ca69150e819","schema_version":"1.0","event_id":"sha256:875f7c2837172de0254f17bbc6027894b1513b92609b3763a2b41ca69150e819"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV/bundle.json","state_url":"https://pith.science/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T20:51:44Z","links":{"resolver":"https://pith.science/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV","bundle":"https://pith.science/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV/bundle.json","state":"https://pith.science/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z4YE5LN7SXQ2ZDS3G3R2CV56KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Z4YE5LN7SXQ2ZDS3G3R2CV56KV","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":"476c74c9399ba444c5d5018a06a19e8f41f9c1a427993cf0197fb20057744074","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-06T13:58:18Z","title_canon_sha256":"39bb2bff30bd91e68ece3791ff1f25f607fe0041816982d14ec9b6ebe058a1b1"},"schema_version":"1.0","source":{"id":"0911.1254","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1254","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1254v3","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1254","created_at":"2026-05-18T04:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z4YE5LN7SXQ2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Z4YE5LN7SXQ2ZDS3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Z4YE5LN7","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:875f7c2837172de0254f17bbc6027894b1513b92609b3763a2b41ca69150e819","target":"graph","created_at":"2026-05-18T04:20:14Z","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":"Let $G$ be a compact Lie group acting isometrically on a compact Riemannian manifold $M$ with nonempty fixed point set $M^G$. We say that $M$ is fixed-point homogeneous if $G$ acts transitively on a normal sphere to some component of $M^G$. Fixed-point homogeneous manifolds with positive sectional curvature have been completely classified. We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure.","authors_text":"Fernando Galaz-Garcia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-06T13:58:18Z","title":"Nonnegatively curved fixed point homogeneous manifolds in low dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1254","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":"sha256:313a325a879d28614dbb69651e2e05f3c3a719e5948cbdcde63cd0f3365ecf01","target":"record","created_at":"2026-05-18T04:20:14Z","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":"476c74c9399ba444c5d5018a06a19e8f41f9c1a427993cf0197fb20057744074","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-06T13:58:18Z","title_canon_sha256":"39bb2bff30bd91e68ece3791ff1f25f607fe0041816982d14ec9b6ebe058a1b1"},"schema_version":"1.0","source":{"id":"0911.1254","kind":"arxiv","version":3}},"canonical_sha256":"cf304eadbf95e1ac8e5b36e3a157be554a0224495761cf75ce4d3cf6ecfc7679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf304eadbf95e1ac8e5b36e3a157be554a0224495761cf75ce4d3cf6ecfc7679","first_computed_at":"2026-05-18T04:20:14.782745Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:14.782745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LuI9mvQncL8L+zHkMDG/mpbbuWKwb4OvsFuOkL712MwDOQp6Ht7f7pzDf4uAYN795gt8TvkC5BNBlkOjrwQgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:14.783190Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1254","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:313a325a879d28614dbb69651e2e05f3c3a719e5948cbdcde63cd0f3365ecf01","sha256:875f7c2837172de0254f17bbc6027894b1513b92609b3763a2b41ca69150e819"],"state_sha256":"710ba00247f093061a8a2cd4755ffab7255a38d7ac3b4b7a3b0f6dccb7d4ac92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVWtV0q9cqKPlS+aAyzdBvJeNYN7kvDRZONOcYnhTaih0LGmRX7bTCfKtc5v6iA47RulnOCqq8sa7x8si7DLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:51:44.518272Z","bundle_sha256":"bedfb1af39885f9406a49263f70cc6e466ce85ca6710a5db23529af5a3b9a161"}}