Spherical Grid Storage (SGS): A Universal Spatio-Temporal Coordinate System for Data Layout

Description Foundational Coordinate System for Spatio‑Temporal Data Spherical Grid Storage (SGS) introduces a universal coordinate system for organizing spatio‑temporal data across modern computational domains. Instead of flattening multi‑dimensional structures into linear byte streams, SGS represents data in explicit (r, θ, φ) coordinates, where r encodes temporal distance, and θ and φ encode structural dimensions whose meaning is domain‑specific. This coordinate system preserves the relationships that hardware already exploits—temporal recency and structural locality—while remaining independent of traversal strategy, execution model, or hardware implementation. SGS is not a layout, runtime, or optimization technique. It is the address space that makes geometry‑native storage possible. The coordinate system degenerates gracefully when axes collapse, handles both static and dynamic data, and provides a universal substrate for axis‑aware traversal strategies. A synthetic benchmark across seven spatio‑temporal domains demonstrates that axis‑aware traversals over SGS coordinates outperform generic space‑filling curves in six of seven domains, with one domain revealing the boundary condition where general‑purpose curves are superior. This work is the first paper in the NSI Core Series, a coordinated research program exploring geometry‑aware execution for large language models and other spatio‑temporal systems. While later papers define layouts, temporal semantics, execution frameworks, and hardware proposals, this paper focuses exclusively on the coordinate system itself—its definition, properties, degeneracy behavior, and universality. Abstract Spherical Grid Storage (SGS) formalizes a universal coordinate system for spatio‑temporal data using (r, θ, φ) axes. The radial axis r encodes temporal distance from the present, mapping naturally onto tiered storage hierarchies, while structural axes θ and φ encode domain‑specific organization such as layers and heads in LLMs, rows and columns in video, or sensors and metrics in time‑series databases. SGS preserves temporal and structural relationships that linear address spaces discard, enabling traversal strategies to exploit locality without reconstructing structure at runtime. A synthetic benchmark across seven domains—LLM inference, long‑context attention, video streaming, scientific simulation, time‑series databases, OS page caches, and LSM‑tree databases—demonstrates that axis‑aware traversals over SGS coordinates outperform generic space‑filling curves in six of seven domains, with improvements ranging from 1.2× to 791.3× (mean 136.0×). One domain exhibits bimodal radial access where Hilbert curves outperform axis‑aware strategies, establishing the boundary condition where temporal asymmetry disappears. SGS is universal for spatio‑temporal data; traversal strategies remain domain‑specific. This paper defines the coordinate system and its properties, independent of layout or execution semantics. Background This work is the first entry in the NSI Core Series, and provides the coordinate foundation for all subsequent papers: 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 the (r, θ, φ) coordinate system for spatio‑temporal data Demonstration of graceful degeneration when temporal or structural axes collapse Separation of coordinate system from traversal strategy, enabling universality Synthetic benchmark across seven domains and two negative controls Empirical demonstration that axis‑aware traversals outperform generic curves in 6/7 domains Identification of boundary conditions where generic curves (Hilbert) are superior Retroactive unification of patterns found in LSM Trees, Generational GC, and time‑series databases Research Impact This work contributes to storage systems, data layout research, and AI execution frameworks by: Providing a universal coordinate system for spatio‑temporal data Enabling geometry‑native storage independent of hardware or traversal strategy Offering a principled alternative to linear address spaces Supporting domain‑specific optimization without sacrificing generality Establishing the theoretical foundation for NSI’s execution model Clarifying when axis‑aware strategies succeed—and when they do not 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