Axis-Aware Layouts: Domain-Specific Traversal Strategies over Spherical Grids

Description Traversal Strategies for Geometry‑Native Storage Axis‑Aware Layouts formalizes the traversal layer of the NSI architecture. Building on the SGS coordinate system, this paper defines layouts as bijective functions that map logical (r, θ, φ) coordinates to linear physical addresses. While SGS provides a universal spatio‑temporal address space, layouts determine how that space is physically ordered, which in turn governs locality, prefetch efficiency, and cache behavior across storage tiers. The central insight is that the coordinate system is universal, but traversal is domain‑specific: different workloads exhibit different access signatures, and no single layout dominates across all spatio‑temporal domains. Through synthetic benchmarking across seven domains, this paper analyzes three baseline layouts—Linear (θ‑major), Strided (r‑major), and LogR (logarithmic radial compression)—and demonstrates why each emerges naturally from specific workload geometries. Linear wins when layer‑sequential access dominates. Strided wins when temporal sweeps define the workload. LogR is a theoretically motivated response to bimodal radial access, even though it did not win empirically in the SGS benchmark. The analysis also identifies a layout gap in LSM‑Tree compaction workloads, motivating future compaction‑aware designs. This work is part of the NSI Core Series, which develops geometry‑native execution for LLMs and other spatio‑temporal systems. While SGS defines the coordinate system, this paper defines the traversal strategies that operate over it, establishing the design principles that guide layout selection and future layout innovation. Abstract Axis‑Aware Layouts explores the design space of traversal strategies over the Spherical Grid Storage (SGS) coordinate system. Synthetic benchmarking in S1 demonstrated that axis‑aware traversals outperform generic space‑filling curves in six of seven spatio‑temporal domains, but also revealed that no single traversal strategy is universally optimal. This paper formalizes layouts as bijective functions from (r, θ, φ) to physical addresses and frames layout design as a locality optimization problem: minimizing expected address distance under a domain’s characteristic access signature. We analyze three baseline layouts—Linear (θ‑major), Strided (r‑major), and LogR (logarithmic radial compression)—and show how each arises naturally from specific workload geometries. Linear is optimal for layer‑sequential access (LLM inference, time‑series dashboards). Strided is optimal for temporal sweeps (video streaming, scientific simulation, OS page caches). LogR addresses bimodal radial access theoretically, though synthetic benchmarks favored Hilbert in that domain. We identify a layout gap in LSM‑Tree compaction workloads and propose compaction‑aware layouts as a direction for future research. The coordinate system is universal; traversal is the domain‑specific variable. This paper formalizes that architectural separation. Background This work is the second entry in the NSI Core Series, and builds directly on the coordinate system defined in S1: Spherical Grid Storage (SGS) — 10.5281/zenodo.18665189 Axis‑Aware Layouts — 10.5281/zenodo.18665191 Frozen Onion: Temporal Reference Frames for Zero‑Copy Memory Systems — 10.5281/zenodo.18665193 Neuron Smart Inference (NSI) — 10.5281/zenodo.18665206 Spatially‑Aware NVMe Devices for AI Workloads — 10.5281/zenodo.18665227 Methodological foundations are documented in: Intuitive‑Theoretic Synthesis (ITS) — 10.5281/zenodo.17633100 The Practice of Human‑AI Synthesis — 10.5281/zenodo.17763521 The Minimal Knowledge Paradox — 10.5281/zenodo.17931472 Design as Epistemological Pathway — 10.5281/zenodo.18067554 Key Contributions Formal definition of layouts as bijective traversal functions over SGS coordinates The Coordinate‑Traversal Separation Principle, distinguishing address space from physical ordering The Traversal Matching Principle, linking workload progression to optimal axis ordering Analysis of three baseline layouts (Linear, Strided, LogR) with synthetic benchmark validation Identification of layout gaps in LSM‑Tree compaction workloads Design guidelines for creating domain‑specific layouts Demonstration that layout diversity is architectural, not a limitation of SGS Research Impact This work advances storage architecture, systems design, and AI execution research by: Establishing a principled framework for designing traversal strategies Demonstrating why no single layout can dominate across all spatio‑temporal domains Providing a theoretical foundation for adaptive mapper switching in NSI Highlighting the importance of workload geometry in physical data ordering Identifying new research directions for compaction‑aware and hybrid layouts Strengthening the conceptual bridge between coordinate systems and execution frameworks Access and Documentation ORCID: https://orcid.org/0009-0003-4876-9273 Academia.edu: https://independent.academia.edu/MarceloTeixeira214 LinkedIn: https://www.linkedin.com/in/marcelo-emanuel-paradela-teixeira-702082382/ Email: marcelo.soul.ai@gmail.com License: CC BY-NC 4.0 © Marcelo Emanuel Paradela Teixeira 2026