Centered Remainder Representation for Ring Buffer Correction in System-Level Code

This paper presents a practical, implementation-oriented reformulation of ring buffer index correction based on a centered remainder representation. Ring buffers are a fundamental data structure in system-level software and are commonly implemented using modulo-based correction, which constrains indices to a non-negative remainder interval. While functionally correct, this approach introduces an implicit asymmetry at the wrap boundary and separates state evolution from its correction logic. The contribution of this work is not a new data structure or algorithm, but a reinterpretation of index correction as a signed, symmetric adjustment within a centered remainder interval. This formulation preserves the original ring buffer semantics, memory layout, and access patterns, while providing a more uniform and locally bounded representation of deviations. The paper illustrates the approach using realistic production-style code patterns and contrasts classical modulo-based correction with centered correction logic. The benefits of the centered formulation are conceptual clarity, symmetric error handling, and reduced boundary special cases, without relying on performance benchmarks or architecture-specific optimizations. This work serves as a concrete application of the centered remainder framework introduced in REIST Division, demonstrating how the formalism can be applied directly to real system-level code. The presented example is intended to improve reasoning, maintainability, and robustness in cyclic state updates commonly found in operating systems, drivers, and real-time processing pipelines.