{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QOUCEKSECZCJJOABEVBREOAHTZ","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":"3ac13a034e692e75e0d06281b5deef9a0af2745f19d9cce53be3814a24db2254","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-30T01:44:52Z","title_canon_sha256":"7f38134f0e7ee148886fedbe571ecc6369c41461d29e39b780df8f36ea19f4b7"},"schema_version":"1.0","source":{"id":"1708.09078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09078","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09078v1","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09078","created_at":"2026-05-18T00:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"QOUCEKSECZCJ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOUCEKSECZCJJOAB","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOUCEKSE","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:60e08a7c6f5099dadf6cbab5056fd46317f27ffe54f4ea98aad79c3227779cd6","target":"graph","created_at":"2026-05-18T00:36:21Z","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 every effective action of a compact Lie group $K$ on a unit sphere $S^n$ admits an explicit orbit whose principal curvatures are bounded from above by $4\\sqrt{14}$.","authors_text":"Artur B. Saturnino, Claudio Gorodski","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-30T01:44:52Z","title":"Focal radii of orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09078","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":"sha256:14116e91594b4d7e9215114b240aa5b617859ff098cb1952b5deaf3abea4fbee","target":"record","created_at":"2026-05-18T00:36:21Z","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":"3ac13a034e692e75e0d06281b5deef9a0af2745f19d9cce53be3814a24db2254","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-30T01:44:52Z","title_canon_sha256":"7f38134f0e7ee148886fedbe571ecc6369c41461d29e39b780df8f36ea19f4b7"},"schema_version":"1.0","source":{"id":"1708.09078","kind":"arxiv","version":1}},"canonical_sha256":"83a8222a44164494b80125431238079e642dec5986fe40137f6e6f7752e0d6db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83a8222a44164494b80125431238079e642dec5986fe40137f6e6f7752e0d6db","first_computed_at":"2026-05-18T00:36:21.074110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:21.074110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VK/FyUh9QxmovhympBqPSDjhi128TEer5+YesV1LfpKY4fSA+mNbZgIfthLHjlkBrCg4mRYk/WhISbkvb04QBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:21.074782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14116e91594b4d7e9215114b240aa5b617859ff098cb1952b5deaf3abea4fbee","sha256:60e08a7c6f5099dadf6cbab5056fd46317f27ffe54f4ea98aad79c3227779cd6"],"state_sha256":"5dae51f125af9feff2e71d2e44f6d8a3c64da4277ef709db98ffa03499b05158"}