What question did this study set out to answer?

This volume aims to develop and characterize forward-backward projection layers for path-space compatibility.

June 19, 2026Open Access

Re-Phase Vol.5.1: Forward–Backward Path Compatibility — Reachability, Survivability, and Admissible Path Projections

Key Points

This volume aims to develop and characterize forward-backward projection layers for path-space compatibility.
Introduced backward survivable-compatible sets and combined them with forward reachable-compatible sets.
Characterized admissible path projections through joint compatibility analysis.
Isolated the gluing mechanism and examined implications of insufficient state information.
Defined and characterized new sets of backward survivable-compatible and forward reachable-compatible sets.
Identified conditions under which false gluing can occur with higher-order or memory-dependent constraints.
Provided insight into the mechanisms affecting compatibility projections.

Abstract

This volume develops the forward–backward projection layer of finite-horizon path-space compatibility in the Re-Phase framework. It introduces backward survivable-compatible sets, combines them with forward reachable-compatible sets, and characterizes admissible path projections through their joint compatibility. The note also isolates the gluing mechanism behind this characterization and explains how false gluing can occur when higher-order or memory-dependent constraints are represented with insufficient state information.

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