{"paper":{"title":"Tokunaga self-similarity arises naturally from time invariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","nlin.AO","nlin.CD"],"primary_cat":"math.DS","authors_text":"Ilya Zaliapin, Yevgeniy Kovchegov","submitted_at":"2018-03-10T02:18:43Z","abstract_excerpt":"The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching processes $\\mathcal{G}(s)$ that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of $\\mathcal{G}(s)$ with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03741","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":""},"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"}