Re-Phase Vol.1.1: Compatibility Consistency and Hierarchical Transport

This volume studies observation consistency and hierarchical transport in a set-theoretic framework. Fiberwise determination is formulated as a unique surjective factorization between attained observation images. Joint observations are described through intersections of compatible sets, and feature recoverability is stated with a nonemptiness guard. The framework is motivated by engineering reconstruction problems, distributed observation systems, and hidden-state ambiguity reduction.

Corrected edition dated November 7, 2026. This revision distinguishes transport on attained images from extension to the declared observation codomains, treats empty-set boundary cases explicitly, and clarifies composition, redundancy, inconsistency, and set-valued transport. It includes a revised finite-word example, a correction record, and finite verification scripts. The scripts supplement the mathematical arguments. The original edition remains available at DOI 10.5281/zenodo.20319522.