# Reply to comments arXiv:2512.07881 and arXiv:2601.06104 on quantum structure in human and AI-generated language

arXiv: https://arxiv.org/abs/2609.25797 · HTML: https://mlsanity.com/paper/2609.25797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Quantum Structure in Cognition: Human Language as a Boson Gas of Entangled Words](https://mlsanity.com/paper/1909.06845/) (2019)
- [Towards a Quantum World Wide Web](https://mlsanity.com/paper/1703.06642/) (2017)
- [Quantum entanglement in physical and cognitive systems: a conceptual analysis and a general representation](https://mlsanity.com/paper/1903.09103/) (2019)
- [Spin and Wind Directions II: A Bell State Quantum Model](https://mlsanity.com/paper/1706.01188/) (2017)
- [On Contextuality in Behavioral Data](https://mlsanity.com/paper/1508.04751/) (2015)
- [Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition](https://mlsanity.com/paper/2511.21731/) (2025)
- [The Origin of Quantum Mechanical Statistics: Some Insights from the Research on Human Language](https://mlsanity.com/paper/2407.14924/) (2024)
- [Revised comment on the paper titled "The Origin of Quantum Mechanical Statistics: Insights from Research on Human Language](https://mlsanity.com/paper/2512.07881/) (2025)
- [Comment on arXiv:2511.21731v1: Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition](https://mlsanity.com/paper/2601.06104/) (2026)

## Abstract (arXiv)

We reply to the comments by M. Sienicki and K. Sienicki (arXiv:2512.07881) and by K. Sienicki (arXiv:2601.06104) on our work on quantum-mechanical statistics in human language (arXiv:2407.14924) and on quantum structure in AI-generated language (arXiv:2511.21731). We thank the authors for their careful reading and address what we consider to be the main points of criticism: the exploratory nature of the protocol used in the experiments with large language models; the role of marginal-law violations, and of the Contextuality-by-Default criterion, in the identification of entanglement; the limited diagnostic value of a Bose-Einstein fit taken in isolation; the meaning of assigning the lowest energy levels to the most frequent words; and the relation between the vector spaces used by LLMs and quantum state spaces. We also correct a typographical error in Table 3 of arXiv:2511.21731, which does not affect the reported CHSH value.