{"paper":{"title":"Quantifying Symmetry: Transformation Information for Planetary Nebulae and Supernova Remnants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.GA","astro-ph.HE"],"primary_cat":"astro-ph.IM","authors_text":"Amir Michaelis, Dmitry Shishkin","submitted_at":"2026-01-12T19:00:01Z","abstract_excerpt":"We present a quantitative symmetry-identification pipeline for astrophysical images based on Transformation Information (TI), an information measure of self-similarity under geometric transformations. TI is expressed as a Kullback-Leibler (cross-entropy) divergence between an image and its rotated or reflected counterpart on the overlapping domain. By scanning rotation angles and reflection axes, we obtain TI curves whose local minima identify symmetry operations. We validate the method on a wind-rose pattern and then apply it to planetary nebulae, where the recovered axes trace bipolar and mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07913","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.07913/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}