{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RIUVBUWTTFXAST2YHIHZJUWLAL","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":"a78231935cd951e6ace7abd241f9c4b0f709a13a1f1d0769e2f73451aea5df6e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-08-10T10:28:54Z","title_canon_sha256":"5f160e2a051b4858250530b587cce48fb0db2c9af379c6ccb15b81b48dff4289"},"schema_version":"1.0","source":{"id":"1108.2141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2141","created_at":"2026-05-18T04:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2141v1","created_at":"2026-05-18T04:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2141","created_at":"2026-05-18T04:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"RIUVBUWTTFXA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIUVBUWTTFXAST2Y","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIUVBUWT","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:785e543d8d17f638be78061fe1b2d59a1d1f99a500f42a83f6c56310eabecb31","target":"graph","created_at":"2026-05-18T04:15:49Z","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":"This paper gives a comprehensive treatment of local uniqueness, asymptotics and numerics for intrinsic means on the circle. It turns out that local uniqueness as well as rates of convergence are governed by the distribution near the antipode. In a nutshell, if the distribution there is locally less than uniform, we have local uniqueness and asymptotic normality with a rate of 1 / \\surdn. With increased proximity to the uniform distribution the rate can be arbitrarly slow, and in the limit, local uniqueness is lost. Further, we give general distributional conditions, e.g. unimodality, that ensu","authors_text":"Stephan Huckemann, Thomas Hotz","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-08-10T10:28:54Z","title":"Intrinsic Means on the Circle: Uniqueness, Locus and Asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2141","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":"sha256:629db95c4646016eb2e5b7760325d0504773fbe3e0e4e93d7fbcd00876470d5c","target":"record","created_at":"2026-05-18T04:15:49Z","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":"a78231935cd951e6ace7abd241f9c4b0f709a13a1f1d0769e2f73451aea5df6e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-08-10T10:28:54Z","title_canon_sha256":"5f160e2a051b4858250530b587cce48fb0db2c9af379c6ccb15b81b48dff4289"},"schema_version":"1.0","source":{"id":"1108.2141","kind":"arxiv","version":1}},"canonical_sha256":"8a2950d2d3996e094f583a0f94d2cb02c486f30a29fcc31b71ca2e02535ca7b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a2950d2d3996e094f583a0f94d2cb02c486f30a29fcc31b71ca2e02535ca7b2","first_computed_at":"2026-05-18T04:15:49.287830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:49.287830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GB7Hkro/5MmhVJif/557q231yJBRzgdBG0Dehq8dCreWqQOL7HwzKd8iKBYb9qIP5WNTLfYmn9C0qOuGaUGCDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:49.288508Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:629db95c4646016eb2e5b7760325d0504773fbe3e0e4e93d7fbcd00876470d5c","sha256:785e543d8d17f638be78061fe1b2d59a1d1f99a500f42a83f6c56310eabecb31"],"state_sha256":"b7633cf2e0e9ad45616d6a69bbc19f59978649d13fa767ffd3107a380832e930"}