{"paper":{"title":"Shape Theories. I. Their Diversity is Killing-Based and thus Nongeneric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Edward Anderson","submitted_at":"2018-11-15T18:23:19Z","abstract_excerpt":"Kendall's Shape Theory covers shapes formed by $N$ points in $\\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space. Kendall studied this to build a widely useful Shape Statistics thereupon. The corresponding Shape-and-Scale Theory -- quotienting out the Euclidean transformations -- is useful in Classical Dynamics and Molecular Physics, as well as for the relational `Leibnizian' side of the Absolute versus Relational Motion Debate. Kendall's shape spaces moreover recur withing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06516","kind":"arxiv","version":3},"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"}