Declare structural model categories explicitly

[isPANN]

Background

The repository exposes five coarse structural model categories through pred list --category:

• algebraic
• formula
• graph
• misc
• set

These categories intentionally match the implementation-oriented catalog organization. They are not an academic taxonomy of NP-hard problems, and the existing model directories do not need to move.

Today the category is inferred by parsing ProblemSchemaEntry.module_path. That makes a user-visible catalog property depend implicitly on Rust source placement. Moving or re-exporting a model can therefore change its category without changing its registered contract, while malformed paths produce inconsistent caller-side fallbacks such as other and uncategorized.

Objective

Keep exactly the existing five categories and directory layout, but declare each model's category explicitly in its model-owned schema registration. Category must be closed and strongly typed, required at compile time, and independent of module_path!().

Interface (Input → Output)

Each ProblemSchemaEntry supplies one required value:

category: ProblemCategory::Graph,

The public/display spellings remain exactly:

algebraic
formula
graph
misc
set

ProblemType, reduction graph export, schema/JSON output, pred list, and pred list --category consume this declared value. There is no inferred or fallback category.

Required changes

• Add a closed ProblemCategory enum to the core registry with the five existing values and one canonical display/CLI spelling.
• Add required category: ProblemCategory metadata to ProblemSchemaEntry.
• Migrate every schema registration to declare its current structural category explicitly.
• Make all category consumers use the declared typed value.
• Delete module-path category parsing and caller-side other/uncategorized fallbacks.
• Update the model-development instructions so a new model must select one of the five categories in its schema registration.
• Do not introduce a central canonical-model-name match table.

Verification

Run:

cargo test -p problemreductions problem_category
cargo test -p problemreductions-cli list_category
cargo run -q -p problemreductions-cli -- list

The tests and command must demonstrate that:

1. representative explicitly registered models report their declared values:
   • QUBO -> algebraic
   • KSatisfiability -> formula
   • MaximumClique -> graph
   • JobShopScheduling -> misc
   • MinimumSetCovering -> set;
2. the summary contains exactly the five established spellings and still totals the full registered model count;
3. text and JSON category output use the same typed metadata;
4. pred list --category unknown exits non-zero and lists the five valid values.

Negative controls:

• A compile-fail macro/unit fixture that constructs a ProblemSchemaEntry without category must fail to compile, proving new models cannot silently omit it.
• A test-only registered model whose module path suggests one category but whose schema explicitly declares another must report the declared category, proving source location is not consulted.
• Restoring module-path parsing or any other/uncategorized fallback must make the focused tests fail.

Scope

This is an intentionally mechanical full-catalog migration and will touch more than 20 model files. It must land as one replacement PR so no mixed explicit/inferred state exists.

Out of scope

• Introducing an academic or domain taxonomy
• Expanding beyond the existing five categories
• Multi-category models or tags
• Moving or renaming model files/directories
• Registry indexing or random-generation changes