Print Simple Objects With Cycles

Tipalti debugging tools need a deterministic utility that can print a simple object graph. Each object has public properties whose values are JSON primitives or references to other simple objects. Implement a serializer that expands each object once, sorts properties alphabetically, and represents later references, including cycles, as @object_id.

The function should return a string rather than writing directly to standard output so callers can log or test the result.

Formal Specification

Implement print_simple_object(graph, root):

• graph is a dictionary mapping unique object IDs to property dictionaries.
• Each property value is a JSON primitive, or a reference of the form {"$ref": object_id}.
• root is the ID of an object in graph.
• Return the root object in the format {key: value, ...}.
• Sort every object's property names lexicographically.
• Strings use JSON quoting. Booleans and null use JSON-compatible lowercase spellings.
• Expand an object only on its first visit. Any later visit returns @object_id. This includes both shared references and back-edges in cycles.