{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HJACSVDAWNPOEDINXHD3V647ZX","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":"ff71d3aadb9b2e5814231fe3ccc22dd435c340e33776d1d149db4dfdad04b2d8","cross_cats_sorted":["math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-18T07:46:25Z","title_canon_sha256":"dcb989cf68fb7b5ba2b4137f1e6d0c64a9ecc95c1a579f87a55b8a39af567a77"},"schema_version":"1.0","source":{"id":"1110.3899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3899","created_at":"2026-05-18T04:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3899v2","created_at":"2026-05-18T04:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3899","created_at":"2026-05-18T04:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"HJACSVDAWNPO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HJACSVDAWNPOEDIN","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HJACSVDA","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:f2f9f05e7ce7aa687f97f75b29417afb31600fa4768195bf5fe65505fcc71ccb","target":"graph","created_at":"2026-05-18T04:06:56Z","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":"The consistency of Fr\\'echet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fr\\'echet medians are estimated. It is also shown that, in compact Riemannian manifolds, the Fr\\'echet sample medians of generic data points are always unique.","authors_text":"Le Yang (LMA)","cross_cats":["math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-18T07:46:25Z","title":"Some properties of Fr\\'echet medians in Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3899","kind":"arxiv","version":2},"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:d8956b84cbb60ccf16432f56ff42f94195a5618c4b76ed9f029641e2ed43574d","target":"record","created_at":"2026-05-18T04:06:56Z","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":"ff71d3aadb9b2e5814231fe3ccc22dd435c340e33776d1d149db4dfdad04b2d8","cross_cats_sorted":["math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-18T07:46:25Z","title_canon_sha256":"dcb989cf68fb7b5ba2b4137f1e6d0c64a9ecc95c1a579f87a55b8a39af567a77"},"schema_version":"1.0","source":{"id":"1110.3899","kind":"arxiv","version":2}},"canonical_sha256":"3a40295460b35ee20d0db9c7bafb9fcdc01f3221ac781cdda4cfc15e16818b19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a40295460b35ee20d0db9c7bafb9fcdc01f3221ac781cdda4cfc15e16818b19","first_computed_at":"2026-05-18T04:06:56.522287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:56.522287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"29I8jYlGANz61GzxTMvSW4ZeIAuLIscKl24SEd4GRpDrhMHkYedrYavjvtvoU29UDaLJ9uSZFUpFiuFGstr6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:56.523059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8956b84cbb60ccf16432f56ff42f94195a5618c4b76ed9f029641e2ed43574d","sha256:f2f9f05e7ce7aa687f97f75b29417afb31600fa4768195bf5fe65505fcc71ccb"],"state_sha256":"efa59769f594ce5f8488cd20f0c63e0696e539d320662817225d174f0096d837"}