Design the object model and core APIs for a photo album organizer that lets one person group photos into nested albums and browse them in different orders.

Operating context. One user, single in-process service. A library holds photos, each with an id, filename, capture time, and metadata. Albums contain photos and sub-albums, forming a tree. A single photo may belong to several albums at once, held by reference rather than copied. Each album has a display sort order (by capture time, by filename, or manual), and manual order lets the user drag photos into an explicit position. Moving a photo between albums must never duplicate its pixels or metadata.

Out of scope. Image file storage, thumbnail generation, EXIF parsing, face recognition or auto-tagging, cloud upload, and sharing or access permissions.

What to produce. The class hierarchy (library, photo, album, sort strategy), the public API each class exposes, and how album containment is modeled. Be explicit about: the composite structure for nested albums, the many-to-many photo-to-album membership that stores each photo once, how the sort order is a pluggable strategy including a manual order, and how the design prevents an album cycle where an album would contain one of its own ancestors.