Re-Phase Vol.1.7: Observation, Constraint, and Assembly Design — Design Targets, Context Navigation, and Recoverability

This volume formulates observation, constraint, and assembly design in the Re-Phase framework. Vol.1.7 studies design from the viewpoint of a designer who does not initially know the full structure of the context poset. Given a pre-specified design target (s,B), the design problem is to choose, revise, or evaluate observations, constraints, or assembly conditions so that the resulting admissible set remains nonempty and the target feature becomes recoverable. The central success condition is: A_S ≠ ∅ and s(A_S) ⊂ B. The nonemptiness condition prevents collapsed contexts from being counted as successful designs. This volume distinguishes design exploration, adopted design trace, and monotone design path. A design exploration may include refinement, relaxation, replacement, collapse, revision, backtracking, and exploratory evaluation of candidate moves. An adopted design trace records the retained sequence of feasible or successful design states. A monotone design path is treated as a special case of an adopted trace. The volume also extends the interpretation of compatible sets to assembly conditions. The notation K_i(o_i) is retained from earlier volumes, but o_i is read broadly as a given condition at index i, including observations, imposed constraints, geometric conditions, contact conditions, clearance conditions, inspection rules, safety conditions, and assembly requirements. Vol.1.7 works at the Level 0 compatibility-design layer. It does not introduce probabilistic noise, robust relaxation, numerical optimization, control laws, or algorithmic search. Those belong to later layers.