# Zipf Distributions from Two-Stage Symbolic Processes: Stability Under Stochastic Lexical Filtering

arXiv: https://arxiv.org/abs/2511.21060 · HTML: https://mlsanity.com/paper/2511.21060/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 9 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 1 of 1)

- [Structural Foundations for Leading Digit Laws: Beyond Probabilistic Mixtures](https://mlsanity.com/paper/2508.13237/) (2025)

## Built on by (most cited first, 2 of 2)

- [A path to natural language through tokenisation and transformers](https://mlsanity.com/paper/2601.03368/) (2026)
- [Phase-Type Variational Autoencoders for Heavy-Tailed Data](https://mlsanity.com/paper/2603.01800/) (2026)

## Abstract (arXiv)

Zipf's law in language lacks a definitive origin, debated across fields. This study explains Zipf-like behavior using geometric mechanisms without linguistic elements. The Full Combinatorial Word Model (FCWM) forms words from a finite alphabet, generating a geometric distribution of word lengths. Interacting exponential forces yield a power-law rank-frequency curve, determined by alphabet size and blank symbol probability. Simulations support predictions, matching English, Russian, and mixed-genre data. The symbolic model suggests Zipf-type laws arise from geometric constraints, not communicative efficiency.