{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KCIO2DPABY657DQY23TUSM7KIU","short_pith_number":"pith:KCIO2DPA","canonical_record":{"source":{"id":"1207.5371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-07-23T12:25:50Z","cross_cats_sorted":["cs.CV","math.MG"],"title_canon_sha256":"71c43f501ad40e8c159b4478e4798d6b41bd5fdb2aa15eae97f37fb971c4fef7","abstract_canon_sha256":"83bd7a7a86fb157030e0872b7d39b27a416e1f2470f8165f048e79def0d1b7f8"},"schema_version":"1.0"},"canonical_sha256":"5090ed0de00e3ddf8e18d6e74933ea4516e0a002cfd60405ca803942b528cf60","source":{"kind":"arxiv","id":"1207.5371","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KCIO2DPABY657DQY23TUSM7KIU","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-07-23T12:25:50Z","cross_cats_sorted":["cs.CV","math.MG"],"title_canon_sha256":"71c43f501ad40e8c159b4478e4798d6b41bd5fdb2aa15eae97f37fb971c4fef7","abstract_canon_sha256":"83bd7a7a86fb157030e0872b7d39b27a416e1f2470f8165f048e79def0d1b7f8"},"schema_version":"1.0"},"canonical_sha256":"5090ed0de00e3ddf8e18d6e74933ea4516e0a002cfd60405ca803942b528cf60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:23.725509Z","signature_b64":"d95X93Hi4YXv4hzSBZZWOaGvbAowWRtuLFhXfS+n07WxKs67X60iekgWMwTODo07AOlewfuKjPl0rEb8VqIfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5090ed0de00e3ddf8e18d6e74933ea4516e0a002cfd60405ca803942b528cf60","last_reissued_at":"2026-05-18T03:50:23.724798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:23.724798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5371","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wXLw0c8L/E72VycxKb4Zakp+yTbrEeXMzgzOsoIgudU9XUqv6idkfi+Z8s04GMxgLZxGD++1Nrma2iNSm3rDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:07:58.430074Z"},"content_sha256":"ac1d267e9d3d8e8ddfc8dcf3ac85b7de549741512ecb77e1822cf244f297114b","schema_version":"1.0","event_id":"sha256:ac1d267e9d3d8e8ddfc8dcf3ac85b7de549741512ecb77e1822cf244f297114b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KCIO2DPABY657DQY23TUSM7KIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a theory of statistical tree-shape analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.MG"],"primary_cat":"stat.ME","authors_text":"Aasa Feragen, Francois Lauze, Mads Nielsen, Marleen de Bruijne, Pechin Lo","submitted_at":"2012-07-23T12:25:50Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5371","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XttriQqToz6Dcoe6Ye0rMu4PTDoOGKCv+fphdg8x8/v4Oxwrl/I/Hp1ziGYkJMH+COaFVU5N9bUow+qLdIIRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:07:58.430745Z"},"content_sha256":"20ce5cd6f14c15d0a406148c944d63c1b4c7eee7b83b31be98cf9fc050ce322e","schema_version":"1.0","event_id":"sha256:20ce5cd6f14c15d0a406148c944d63c1b4c7eee7b83b31be98cf9fc050ce322e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCIO2DPABY657DQY23TUSM7KIU/bundle.json","state_url":"https://pith.science/pith/KCIO2DPABY657DQY23TUSM7KIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCIO2DPABY657DQY23TUSM7KIU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T21:07:58Z","links":{"resolver":"https://pith.science/pith/KCIO2DPABY657DQY23TUSM7KIU","bundle":"https://pith.science/pith/KCIO2DPABY657DQY23TUSM7KIU/bundle.json","state":"https://pith.science/pith/KCIO2DPABY657DQY23TUSM7KIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCIO2DPABY657DQY23TUSM7KIU/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GFnz1+wVkqiE0bhn2exAdxOoaXNo/GwZUC10ugZ1jpOeBj3iDh9AJcwruwjNm4NNVDuQaKkNWbmdc+coMyh9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:07:58.435085Z","bundle_sha256":"61977b07d613a6f0c796a05e865b19b1c41c755c242f1ea2adc6997b7a0187e5"}}