Nonlinear Tree-Based Numeration Systems: A Consolidated Synthesis

Abstract

1. **Rofa (Quni-Gudzinas, 2013).** *On Number Representation.* arXiv:2005.10207. `[EXTERNAL-SOURCE]` 2. **Tarau, P. (2013).** *Arithmetic Algorithms for Hereditarily Binary Natural Numbers.* arXiv:1310.8277. `[WEB-SEARCH]` 3. **Akiyama, S., Frougny, C., & Sakarovitch, J. (2008).** On subtrees of the representation tree in rational base numeration systems. *Discrete Mathematics & Theoretical Computer Science.* `[WEB-SEARCH]` 4. **Charlier, E. & Kreczman, S. (2025).** Positional numeration systems and regular languages. `[WEB-SEARCH]` 5. **Lecomte, P. & Rigo, M. (2001).** Abstract numeration systems. In *Words, Languages & Combinatorics III.* `[LLM-INFERRED]` 6. **Chrisomalis, S. (2010).** *Numerical Notation: A Comparative History.* Cambridge. `[WEB-SEARCH]` 7. **Spencer-Brown, G. (1969).** *Laws of Form.* Allen & Unwin. `[established]` 8. **Holly, J. (2001).** Pictures of Ultrametric Spaces, the $p$-adic Numbers, and Valued Fields. *Amer. Math. Monthly*, 108(8), 721-728. `[established]` 9. **QNFO Research Collective (2026).** *The Ultrametric Foundation.* deep.qwav.tech/papers/ultrametric-foundation/. `[EXTERNAL-SOURCE]` 10. **Scholze, P. (2012).** Perfectoid Spaces. *Publ. Math. IHES*, 116, 245-313. `[established]`