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This note aims to clarify the transition to a compatibility-based design perspective within the Re-Phase framework.

June 17, 2026Open Access

Re-Phase Vol.1.10: Orientation Note — From Map/Fiber/Kernel to Compatibility-Based Design

Key Points

This note aims to clarify the transition to a compatibility-based design perspective within the Re-Phase framework.
Describes the shift from map/fiber/kernel to compatibility as the primitive layer in Re-Phase.
Explains the roles of conditions, accumulated conditions, and contexts in defining compatibility.
Outlines separation of condition, configuration/admissible, and feature sides.
Defines compatibility conditions for candidate selection but does not establish a complete index.
Highlights the interaction between condition side and feature side through an admissible configuration.

Abstract

This orientation note explains how to read the Re-Phase framework after the transition from the early map/fiber/kernel viewpoint to the Level 0 compatibility-based design reading.The note clarifies that observation maps, inverse images, fibers, and kernels remain useful special cases, but are not the primitive layer of Re-Phase. The primitive layer is compatibility: conditions leave compatible candidates, accumulated conditions form admissible sets, contexts build order, recoverability sets the target, and indistinguishability organizes compatibility behavior.The note also emphasizes the three-side separation between the condition side, the configuration/admissible side, and the feature side. The condition side and feature side are not directly identified; they are compared through the common configuration/admissible side.This volume is a frozen reader orientation, not a complete volume index. It does not track current series status, planned extensions, or future DOI records.

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