CRs as Sheafification: open covers → refinements → global sections

Open cover (scope slices). We represent the project using three overlapping “scope slices”: Approach (A), Foundation (F), and Interior (I). Each slice holds a local specification such as an owner, a material choice, or an inspection status.

Overlaps (interfaces). Where slices overlap (A∩F, F∩I, A∩I), the project has an interface/handoff. For the plan to be coherent, the relevant local specs must agree on these overlaps. When they do, the local specs glue into one consistent project-wide plan.

Global section (integrated plan). A global section is simply a complete set of local choices that are mutually consistent across all overlaps—i.e., an integrated plan.

Change request (refinement). A CR often refines scope: it splits a slice into more detailed pieces (e.g., Approach → Path + Access; Foundation → Footings + Pour). This introduces additional overlaps and therefore more coordination points.

Sheafification (forcing consistency). If the refined overlaps no longer agree, the earlier “global plan” breaks. The failed overlaps show exactly where the CR creates integration risk—interfaces that need negotiation, rework, or a new decision so the plan becomes consistent again.