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R. Jay Martin II

Publications and source records attributed to R. Jay Martin II.

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The Compute ICE-AGE: Invariant Compute Envelope under Addressable Graph Evolution

This paper presents empirical results from a production-grade C++ implementation of a deterministic semantic state substrate operating under bounded local state evolution. The system was realized as a CPU-resident persistent semantic graph engine designed to preserve semantic continuity structurally rather than repeatedly reconstructing it through probabilistic inference. Contemporary inference-driven AI systems repeatedly recompute semantic state through context replay and probabilistic recomposition. In contrast, the substrate described here evolves semantic continuity incrementally through locality-preserving traversal and bounded local mutation over persistent graph topology. Empirical measurements on Apple Silicon M2-class hardware demonstrated locality-constrained traversal behavior across scaling regimes ranging from 1 million to 25 million persistent semantic nodes. Traversal latency remained within low microsecond ranges (P50 approximately 0.0014 ms) under sustained workloads, while steady-state CPU utilization remained approximately 17.2% with no measurable scale-correlated thermal amplification observed during sustained operation. Measured persistent node density averaged approximately 687 bytes per node under compressed Float32 storage regimes, corresponding to a projected capacity of approximately 1.6 billion persistent semantic nodes within a 1 TiB memory envelope. Under hostile ingress conditions including stochastic perturbation, malformed topology, fragmented adjacency, and active paging pressure, deterministic replay integrity remained stable while degradation localized into bounded orphan structures rather than propagating catastrophic global divergence.

cs.OS

Bounded Local Generator Classes for Deterministic State Evolution

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.

cs.OS