How do building privileges and build zones work?
Every cupboard creates a build-zone around the structural elements of the building it's in. Inside that zone:
Only players authorized by the cupboard can place new structures, doors, deployables, or another cupboard
Unauthorized players get "Cupboard privilege required to build here" when they try to place something
Decay is paused as long as the cupboard is stocked with upkeep resources
The shape of the zone. The zone isn't a circle around the cupboard — it's built around every structural element of the building. Each foundation, wall and floor extends it around itself, so the zone follows the shape of your base: a long base has a long zone.
How to see where it ends. Watch the building status indicator on your HUD as you walk: it switches between "building allowed" and "building blocked" and shows you the edge of the zone directly. That's more reliable than measuring, because the zone depends on where your structures actually are.
If the zones of several protected buildings overlap, the oldest building wins — the one containing the oldest structural piece is what decides whether you may build there. Being authorized on a nearby cupboard doesn't help if the dominant building is a different one. This is the usual reason for "I'm authorized here but it still won't let me build".
If your building splits, each separated part keeps its own build-zone only if it has its own cupboard. Parts without one are unprotected — decay starts, and others can build nearby.
→ See also: Why did my base split into multiple buildings? · Why can't I place a Tool Cupboard?