{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OH3YJKFDJ4LFHC2QYDKMGZO6TV","short_pith_number":"pith:OH3YJKFD","canonical_record":{"source":{"id":"1809.02865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T20:02:48Z","cross_cats_sorted":["math.MG","math.RT"],"title_canon_sha256":"e8c1dd7c78e15f745d20b3955548423f59c43765cfe6cf8f8925faef07a93fe3","abstract_canon_sha256":"9cef053d2fbe838d600ec087378ecac57eb434106592e3a940bc0f82d5e23dc6"},"schema_version":"1.0"},"canonical_sha256":"71f784a8a34f16538b50c0d4c365de9d7a03a2b970df2c781f664e372c086778","source":{"kind":"arxiv","id":"1809.02865","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02865","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02865v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02865","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"OH3YJKFDJ4LF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OH3YJKFDJ4LFHC2Q","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OH3YJKFD","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OH3YJKFDJ4LFHC2QYDKMGZO6TV","target":"record","payload":{"canonical_record":{"source":{"id":"1809.02865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T20:02:48Z","cross_cats_sorted":["math.MG","math.RT"],"title_canon_sha256":"e8c1dd7c78e15f745d20b3955548423f59c43765cfe6cf8f8925faef07a93fe3","abstract_canon_sha256":"9cef053d2fbe838d600ec087378ecac57eb434106592e3a940bc0f82d5e23dc6"},"schema_version":"1.0"},"canonical_sha256":"71f784a8a34f16538b50c0d4c365de9d7a03a2b970df2c781f664e372c086778","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:15.073091Z","signature_b64":"m7edeT6nMXHAzTdM+smwTfX0Omfo3TihVVQ4VjM3/lRNL+S3/dX9OZAq0Ai5uABe6EuTJrV2cbF6owi69AtADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f784a8a34f16538b50c0d4c365de9d7a03a2b970df2c781f664e372c086778","last_reissued_at":"2026-05-18T00:06:15.072477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:15.072477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.02865","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FszLSyeGt4OAn/Qlgz4MRFhg4v+WWUzA3RxM01E59kulOiSxyx/wm/iFMfVDX/hxiJHHsoKeNl30Bzv0muwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:02:05.799307Z"},"content_sha256":"9c9ba1039491bc63e624dfbad648890688aa56c74fcbdb5c313d96878ef67960","schema_version":"1.0","event_id":"sha256:9c9ba1039491bc63e624dfbad648890688aa56c74fcbdb5c313d96878ef67960"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OH3YJKFDJ4LFHC2QYDKMGZO6TV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Highly curved orbit spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.RT"],"primary_cat":"math.DG","authors_text":"Claudio Gorodski","submitted_at":"2018-09-08T20:02:48Z","abstract_excerpt":"It is known that the infimum of the sectional curvatures (on the regular part) of orbit spaces of isometric actions on unit spheres in bounded above by $4$. We show that the infimum is $1$ for \"most\" actions, and determine the cases in which it is bigger than $1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02865","kind":"arxiv","version":1},"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":"2026-05-18T00:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xok3DC6PQa4Ob/fn3KvPTC/wWDmOKNWCl5W6yzcwjYBK+dzgX30My8Koe/a7xScwScf1KGBmbraZZjfCywk8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:02:05.799660Z"},"content_sha256":"4a88ce7c7c539d16c7abcfe5956ab8980e5622bcd7accb4953fe856e43f2ee25","schema_version":"1.0","event_id":"sha256:4a88ce7c7c539d16c7abcfe5956ab8980e5622bcd7accb4953fe856e43f2ee25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV/bundle.json","state_url":"https://pith.science/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV/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":"2026-06-20T14:02:05Z","links":{"resolver":"https://pith.science/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV","bundle":"https://pith.science/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV/bundle.json","state":"https://pith.science/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OH3YJKFDJ4LFHC2QYDKMGZO6TV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OH3YJKFDJ4LFHC2QYDKMGZO6TV","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":"9cef053d2fbe838d600ec087378ecac57eb434106592e3a940bc0f82d5e23dc6","cross_cats_sorted":["math.MG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T20:02:48Z","title_canon_sha256":"e8c1dd7c78e15f745d20b3955548423f59c43765cfe6cf8f8925faef07a93fe3"},"schema_version":"1.0","source":{"id":"1809.02865","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02865","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02865v1","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02865","created_at":"2026-05-18T00:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"OH3YJKFDJ4LF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OH3YJKFDJ4LFHC2Q","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OH3YJKFD","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:4a88ce7c7c539d16c7abcfe5956ab8980e5622bcd7accb4953fe856e43f2ee25","target":"graph","created_at":"2026-05-18T00:06:15Z","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":"It is known that the infimum of the sectional curvatures (on the regular part) of orbit spaces of isometric actions on unit spheres in bounded above by $4$. We show that the infimum is $1$ for \"most\" actions, and determine the cases in which it is bigger than $1$.","authors_text":"Claudio Gorodski","cross_cats":["math.MG","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T20:02:48Z","title":"Highly curved orbit spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02865","kind":"arxiv","version":1},"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":"sha256:9c9ba1039491bc63e624dfbad648890688aa56c74fcbdb5c313d96878ef67960","target":"record","created_at":"2026-05-18T00:06:15Z","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":"9cef053d2fbe838d600ec087378ecac57eb434106592e3a940bc0f82d5e23dc6","cross_cats_sorted":["math.MG","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-08T20:02:48Z","title_canon_sha256":"e8c1dd7c78e15f745d20b3955548423f59c43765cfe6cf8f8925faef07a93fe3"},"schema_version":"1.0","source":{"id":"1809.02865","kind":"arxiv","version":1}},"canonical_sha256":"71f784a8a34f16538b50c0d4c365de9d7a03a2b970df2c781f664e372c086778","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f784a8a34f16538b50c0d4c365de9d7a03a2b970df2c781f664e372c086778","first_computed_at":"2026-05-18T00:06:15.072477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:15.072477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m7edeT6nMXHAzTdM+smwTfX0Omfo3TihVVQ4VjM3/lRNL+S3/dX9OZAq0Ai5uABe6EuTJrV2cbF6owi69AtADA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:15.073091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02865","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c9ba1039491bc63e624dfbad648890688aa56c74fcbdb5c313d96878ef67960","sha256:4a88ce7c7c539d16c7abcfe5956ab8980e5622bcd7accb4953fe856e43f2ee25"],"state_sha256":"8054d0ab6a540e88fa6c0eae637e425fe66e8640dd903942f13de53f2fb844cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oD5LNc1MNv97Nm4ni9MKPTLBz1iuUOPhlnkpW6E6pMCJdm8sLspPhcbPxObU1WfqwSLDmrwdjukiEN0uUJ0ZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:02:05.801554Z","bundle_sha256":"75010d47cc77347ff813c3025214381c15c4fc711481b35c418933a04bec80c2"}}