{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:77SG3XHMJ4DFNMAA44RVZSFJA5","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":"6d26270d5dac66710186a6697a35a3933a7b83d073f5245e7e1de20cce27da9b","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2010-02-03T17:09:01Z","title_canon_sha256":"c27dee8b646de6dd090e42133657090c5d3960a1d71e88e619fd377bad944cbc"},"schema_version":"1.0","source":{"id":"1002.0795","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0795","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0795v2","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0795","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"77SG3XHMJ4DF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"77SG3XHMJ4DFNMAA","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"77SG3XHM","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:85cfb430b20498b0003ee5ffee96d81d2193c819f30e55121c90fdaf84aab21c","target":"graph","created_at":"2026-05-18T04:22:11Z","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":"Various concepts of mean shape previously unrelated in the literature are brought into relation. In particular for non-manifolds such as Kendall's 3D shape space, this paper answers the question, for which means one may apply a two-sample test. The answer is positive if intrinsic or Ziezold means are used. The underlying general result of manifold stability of a mean on a shape space, the quotient due to an isometric action of a compact Lie group on a Riemannian manifold, blends the Slice Theorem from differential geometry with the statistics of shape. For 3D Procrustes means, however, a count","authors_text":"Stephan Huckemann","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2010-02-03T17:09:01Z","title":"On the meaning of mean shape"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0795","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":"sha256:997e1148d74c2e84fa6679db2b0d2dbb0b0717980b573647f51eea8a7b3d4746","target":"record","created_at":"2026-05-18T04:22:11Z","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":"6d26270d5dac66710186a6697a35a3933a7b83d073f5245e7e1de20cce27da9b","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2010-02-03T17:09:01Z","title_canon_sha256":"c27dee8b646de6dd090e42133657090c5d3960a1d71e88e619fd377bad944cbc"},"schema_version":"1.0","source":{"id":"1002.0795","kind":"arxiv","version":2}},"canonical_sha256":"ffe46ddcec4f0656b000e7235cc8a90766796fe5e1ecfd7d0297a1ba8569bce8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffe46ddcec4f0656b000e7235cc8a90766796fe5e1ecfd7d0297a1ba8569bce8","first_computed_at":"2026-05-18T04:22:11.542355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:11.542355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pk+ZUMLJO7yer2FY7sC5ee9z+w0NQSxKHZeZlcdjAtnZzbkeHcIzIMbIvTmBGptqWrHLPXN35LkVvQGZckaKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:11.542751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0795","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:997e1148d74c2e84fa6679db2b0d2dbb0b0717980b573647f51eea8a7b3d4746","sha256:85cfb430b20498b0003ee5ffee96d81d2193c819f30e55121c90fdaf84aab21c"],"state_sha256":"f6d192432627dd7f753fe763685d9b22d787b70f9a8a1d78c2423de10908aed2"}