Bounded Local Generator Classes for Deterministic State Evolution
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909024616710144 |
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| author | Martin II, R. Jay |
| author_facet | Martin II, R. Jay |
| contents | We define a bounded local generator class (BLGC) for deterministic state evolution on graph-indexed systems. The construction consists of finite-range generators operating on bounded local state under deterministic composition. Each update acts only on a bounded-radius neighborhood and applies a bounded local transformation with projection onto a compact state domain. Under the BLGC constraints, per-step operator work remains independent of total system size M. Specifically, incremental update cost satisfies $W_t = O(1)$ with respect to $M \to \infty$ for fixed interaction radius $r$. The framework admits a Hilbert-space embedding in $\ell^2(V)\otimes \mathbb{R}^d$ and yields bounded operators under composition on admissible subspaces. The result establishes a structural decoupling between global state capacity and incremental computational work. The claims apply specifically to the bounded local generator class defined in this paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_11476 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounded Local Generator Classes for Deterministic State Evolution Martin II, R. Jay Operating Systems Data Structures and Algorithms We define a bounded local generator class (BLGC) for deterministic state evolution on graph-indexed systems. The construction consists of finite-range generators operating on bounded local state under deterministic composition. Each update acts only on a bounded-radius neighborhood and applies a bounded local transformation with projection onto a compact state domain. Under the BLGC constraints, per-step operator work remains independent of total system size M. Specifically, incremental update cost satisfies $W_t = O(1)$ with respect to $M \to \infty$ for fixed interaction radius $r$. The framework admits a Hilbert-space embedding in $\ell^2(V)\otimes \mathbb{R}^d$ and yields bounded operators under composition on admissible subspaces. The result establishes a structural decoupling between global state capacity and incremental computational work. The claims apply specifically to the bounded local generator class defined in this paper. |
| title | Bounded Local Generator Classes for Deterministic State Evolution |
| topic | Operating Systems Data Structures and Algorithms |
| url | https://arxiv.org/abs/2602.11476 |