{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KCIO2DPABY657DQY23TUSM7KIU","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":"83bd7a7a86fb157030e0872b7d39b27a416e1f2470f8165f048e79def0d1b7f8","cross_cats_sorted":["cs.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-07-23T12:25:50Z","title_canon_sha256":"71c43f501ad40e8c159b4478e4798d6b41bd5fdb2aa15eae97f37fb971c4fef7"},"schema_version":"1.0","source":{"id":"1207.5371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5371","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5371v1","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5371","created_at":"2026-05-18T03:50:23Z"},{"alias_kind":"pith_short_12","alias_value":"KCIO2DPABY65","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KCIO2DPABY657DQY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KCIO2DPA","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:20ce5cd6f14c15d0a406148c944d63c1b4c7eee7b83b31be98cf9fc050ce322e","target":"graph","created_at":"2026-05-18T03:50:23Z","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":"In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-like shapes and study metrics on the shape space. This shape space has singularities, corresponding to topological transitions in the represented trees. We study two closely related metrics on the shape space, TED and QED. QED is a quotient Euclidean distance arising naturally from the shape space formulation, while TED is the classical tree edit distance. Using Gromov's metric geometry we gain new insight into the geometries defined by TED and QED. We show that the new metri","authors_text":"Aasa Feragen, Francois Lauze, Mads Nielsen, Marleen de Bruijne, Pechin Lo","cross_cats":["cs.CV","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-07-23T12:25:50Z","title":"Towards a theory of statistical tree-shape analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5371","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:ac1d267e9d3d8e8ddfc8dcf3ac85b7de549741512ecb77e1822cf244f297114b","target":"record","created_at":"2026-05-18T03:50:23Z","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":"83bd7a7a86fb157030e0872b7d39b27a416e1f2470f8165f048e79def0d1b7f8","cross_cats_sorted":["cs.CV","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-07-23T12:25:50Z","title_canon_sha256":"71c43f501ad40e8c159b4478e4798d6b41bd5fdb2aa15eae97f37fb971c4fef7"},"schema_version":"1.0","source":{"id":"1207.5371","kind":"arxiv","version":1}},"canonical_sha256":"5090ed0de00e3ddf8e18d6e74933ea4516e0a002cfd60405ca803942b528cf60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5090ed0de00e3ddf8e18d6e74933ea4516e0a002cfd60405ca803942b528cf60","first_computed_at":"2026-05-18T03:50:23.724798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:23.724798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d95X93Hi4YXv4hzSBZZWOaGvbAowWRtuLFhXfS+n07WxKs67X60iekgWMwTODo07AOlewfuKjPl0rEb8VqIfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:23.725509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac1d267e9d3d8e8ddfc8dcf3ac85b7de549741512ecb77e1822cf244f297114b","sha256:20ce5cd6f14c15d0a406148c944d63c1b4c7eee7b83b31be98cf9fc050ce322e"],"state_sha256":"6569e42f829c89914fca872cb6bd294d29a31e4466c383815c1e43db882bfbf6"}