# A Formal Framework for the Definition of 'State': Hierarchical Representation and Meta-Universe Interpretation

arXiv: https://arxiv.org/abs/2508.00853 · HTML: https://mlsanity.com/paper/2508.00853/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 28 references that are in the map.
- First posted on arXiv 14 Jul 2025.

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

- [Toward the Axiomatization of Intelligence: Structure, Time, and Existence](https://mlsanity.com/paper/2504.14596/) (2025)

## Abstract (arXiv)

This study aims to reinforce the theoretical foundation for diverse systems--including the axiomatic definition of intelligence--by introducing a mathematically rigorous and unified formal structure for the concept of 'state,' which has long been used without consensus or formal clarity. First, a 'hierarchical state grid' composed of two axes--state depth and mapping hierarchy--is proposed to provide a unified notational system applicable across mathematical, physical, and linguistic domains. Next, the 'Intermediate Meta-Universe (IMU)' is introduced to enable explicit descriptions of definers (ourselves) and the languages we use, thereby allowing conscious meta-level operations while avoiding self-reference and logical inconsistency. Building on this meta-theoretical foundation, this study expands inter-universal theory beyond mathematics to include linguistic translation and agent integration, introducing the conceptual division between macrocosm-inter-universal and microcosm-inter-universal operations for broader expressivity. Through these contributions, this paper presents a meta-formal logical framework--grounded in the principle of definition = state--that spans time, language, agents, and operations, providing a mathematically robust foundation applicable to the definition of intelligence, formal logic, and scientific theory at large.