CodingThrust
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@@ -10,6 +10,7 @@ make clippy        # Lint
 make export-graph  # Regenerate reduction graph
 make paper         # Build Typst paper
 make coverage      # Generate coverage report (>95% required)
+make qubo-testdata # Regenerate QUBO ground truth JSON
 ```
 
 ## Verify Changes
@@ -28,6 +29,9 @@ make test clippy export-graph  # Must pass before PR
 - `src/registry/` - Compile-time reduction metadata collection
 - `src/unit_tests/` - Unit test files (mirroring `src/` structure, referenced via `#[path]`)
 - `tests/main.rs` - Integration tests (modules in `tests/suites/`)
+- `tests/data/` - Ground truth JSON for integration tests
+- `scripts/` - Python test data generation scripts (managed with `uv`)
+- `docs/plans/` - Implementation plans
 
 ### Trait Hierarchy
 
 
@@ -5,19 +5,59 @@ paths:
 
 # Adding a Reduction Rule (A → B)
 
+## 0. Brainstorm & Generate Test Data First
+
+Before writing any Rust code, follow this workflow:
+
+1. **Brainstorm the reduction** — use `superpowers:brainstorming` to discuss with the user:
+   - Research the mathematical formulation (paper, textbook, or derive it)
+   - Understand the variable mapping and constraint encoding
+   - Discuss implementation approach: penalty values, matrix construction, solution extraction
+   - Read reference implementations in the codebase (e.g., `src/rules/spinglass_qubo.rs`) to understand conventions
+   - Agree on scope (weighted vs unweighted, specific graph types, const generics)
+2. **Generate ground truth test data** — use an existing library (e.g., Python with qubogen, qubovert, or networkx) to create small instances, reduce them, brute-force solve both sides, and export as JSON to `tests/data/<target>/`. It is recommended to download the relevant package and check the existing tests to understand how to construct tests. To generate the test data, you can use the following command:
+   ```bash
+   # Example: generate QUBO test data
+   cd scripts && uv run python generate_qubo_tests.py
+   ```
+3. **Create a practical example** — design a small, explainable instance for `examples/` (e.g., "wireless tower placement" for IndependentSet, "map coloring" for Coloring). This example will also appear in the `docs/paper/reductions.typ`.
+4. **Write the implementation plan** — save to `docs/plans/` using `superpowers:writing-plans`. The plan must include implementation details from the brainstorming session (formulas, penalty terms, matrix construction, variable indexing).
+
 ## 1. Implementation
-Create `src/rules/<source>_<target>.rs`:
+
+Create `src/rules/<source>_<target>.rs` following the pattern in `src/rules/spinglass_qubo.rs`:
 
 ```rust
-use problemreductions::reduction;
+use crate::reduction;
+
+#[derive(Debug, Clone)]
+pub struct ReductionSourceToTarget {
+    target: TargetProblem<...>,
+    source_size: ProblemSize,
+    // + any metadata needed for extract_solution
+}
+
+impl ReductionResult for ReductionSourceToTarget {
+    type Source = SourceProblem<...>;
+    type Target = TargetProblem<...>;
+
+    fn target_problem(&self) -> &Self::Target { &self.target }
+    fn extract_solution(&self, target_solution: &[usize]) -> Vec<usize> { ... }
+    fn source_size(&self) -> ProblemSize { self.source_size.clone() }
+    fn target_size(&self) -> ProblemSize { self.target.problem_size() }
+}
 
 #[reduction(
     overhead = { ReductionOverhead::new(vec![...]) }
 )]
-impl ReduceTo<TargetProblem<Unweighted>> for SourceProblem<Unweighted> {
+impl ReduceTo<TargetProblem<...>> for SourceProblem<...> {
     type Result = ReductionSourceToTarget;
     fn reduce_to(&self) -> Self::Result { ... }
 }
+
+#[cfg(test)]
+#[path = "../unit_tests/rules/<source>_<target>.rs"]
+mod tests;
 ```
 
 The `#[reduction]` macro auto-generates the `inventory::submit!` call. Optional attributes: `source_graph`, `target_graph`, `source_weighted`, `target_weighted`.
@@ -28,25 +68,39 @@ mod source_target;
 pub use source_target::ReductionSourceToTarget;
 ```
 
-## 2. Closed-Loop Test (Required)
+## 2. Tests (Required)
+
+- **Unit tests** in `src/unit_tests/rules/<source>_<target>.rs` — closed-loop + edge cases. See `rules/testing.md`.
+- **Integration tests** in `tests/suites/reductions.rs` — compare against JSON ground truth from step 0.
+- Test name: `test_<source>_to_<target>_closed_loop`
 
-See `rules/testing.md` for the full pattern. Test name: `test_<source>_to_<target>_closed_loop`.
+## 3. Example Program
+
+Add a round-trip demo to `examples/` showing a practical, explainable instance:
+1. Create source problem with a real-world story
+2. Reduce to target, solve, extract solution
+3. Print human-readable explanation
+
+## 4. Documentation
 
-## 3. Documentation
 Update `docs/paper/reductions.typ` (see `rules/documentation.md` for the pattern):
 - Add theorem + proof sketch
-- Add code example
+- Add Rust code example from the example program
 - Add to summary table with overhead and citation
 
+The goal is to 1. prove the correctness of the reduction to human beings. 2. provide a minimal working example to the readers.
+
 Citations must be verifiable. Use `[Folklore]` or `—` for trivial reductions.
 
-## 4. Regenerate Reduction Graph
+## 5. Regenerate Reduction Graph
 ```bash
 make export-graph
 ```
 
 ## Anti-patterns
+- Don't write Rust code before understanding the math and having test data
 - Don't create reductions without closed-loop tests
 - Don't forget `inventory::submit!` registration (reduction graph won't update)
 - Don't hardcode weights - use generic `W` parameter
 - Don't skip overhead polynomial specification
+- Don't skip the example program — every reduction needs an explainable demo
@@ -19,13 +19,15 @@ Convert a GitHub issue into an actionable PR with a plan that auto-triggers Clau
 digraph issue_to_pr {
     "Receive issue number" [shape=box];
     "Fetch issue with gh" [shape=box];
+    "Check the rules to follow" [shape=box];
     "Brainstorm with user" [shape=box];
     "Write plan file" [shape=box];
     "Create branch and PR" [shape=box];
     "PR triggers [action]" [shape=doublecircle];
 
     "Receive issue number" -> "Fetch issue with gh";
-    "Fetch issue with gh" -> "Brainstorm with user";
+    "Fetch issue with gh" -> "Check the rules to follow";
+    "Check the rules to follow" -> "Brainstorm with user";
     "Brainstorm with user" -> "Write plan file";
     "Write plan file" -> "Create branch and PR";
     "Create branch and PR" -> "PR triggers [action]";
@@ -53,45 +55,27 @@ Present issue summary to user.
 
 **REQUIRED:** Invoke `superpowers:brainstorming` skill with the issue context (if superpowers plugin is available). Otherwise, conduct a manual brainstorming discussion with the user.
 
-This ensures:
-- User intent is clarified
-- Multiple approaches are explored
-- Requirements are understood before planning
+Brainstorming must cover:
+- **User intent** — clarify what the issue is asking for
+- **Multiple approaches** — explore 2-3 different implementation strategies
+- **Implementation details** — discuss the mathematical formulation, data structures, variable mappings, constraint encodings, and any non-obvious design choices
+- **Existing patterns** — read reference implementations in the codebase (e.g., `spinglass_qubo.rs` for reductions) to understand the conventions
+- **Scope** — agree on which variants to implement (e.g., unweighted only, specific K values)
 
 Do NOT skip brainstorming. Do NOT write a plan without user discussion.
 
 ### 4. Write Plan
 
-After brainstorming concludes, write plan to `issue-<number>-<slug>.md` in the repo root:
-
-```markdown
-# <Title from brainstorming>
-
-Issue: #<number>
-
-## Context
-<Brief problem statement>
-
-## Approach
-<Chosen approach from brainstorming>
-
-## Tasks
-1. <Specific implementation task>
-2. <Another task>
-...
-
-## Acceptance Criteria
-- <Criteria from issue/brainstorming>
-```
+After brainstorming concludes, write plan to `docs/plans/YYYY-MM-DD-<slug>.md` using `superpowers:writing-plans`:
 
 ### 5. Create PR
 
 ```bash
 # Create branch
 git checkout -b issue-<number>-<slug>
 
-# Stage only the plan file
-git add issue-<number>-<slug>.md
+# Stage the plan file
+git add docs/plans/<plan-file>.md
 
 # Commit
 git commit -m "Add plan for #<number>: <title>"
@@ -117,19 +101,19 @@ User: /issue-to-pr 42
 
 Claude: Let me fetch issue #42...
 
-[Fetches issue: "Add dark mode support"]
+[Fetches issue: "Add IndependentSet → QUBO reduction"]
 
-I'll use superpowers:brainstorming to explore this with you.
+I'll read the rules to follow in .claude/rules/adding-reductions.md and use superpowers:brainstorming to explore this with you.
 
 [Invokes brainstorming - discusses approaches, user preferences, scope]
 
-Based on our discussion, I'll create the plan...
+Based on our discussion, I'll create the plan with superpowers:writing-plans...
 
-[Writes docs/plans/issue-42-dark-mode.md]
+[Writes docs/plans/2026-02-09-independentset-to-qubo.md]
 [Creates branch, commits, pushes]
 [Creates PR with body starting with "[action]"]
 
-Created PR #45: Fix #42: Add dark mode support
+Created PR #45: Fix #42: Add IndependentSet → QUBO reduction
 The [action] trigger will automatically execute the plan.
 ```
 
@@ -139,5 +123,5 @@ The [action] trigger will automatically execute the plan.
 |---------|-----|
 | Skipping brainstorming | Always use superpowers:brainstorming (or manual discussion) first |
 | `[action]` not at start | PR body must BEGIN with `[action]` |
-| Including code in PR | Only commit the plan file |
+| Including implementation code in initial PR | First PR: plan only |
 | Generic plan | Use specifics from brainstorming |
@@ -38,11 +38,12 @@ quickcheck-tests.json
 /dist/
 /build/
 
-# Python (for pre-commit)
+# Python
 __pycache__/
 *.py[cod]
 *$py.class
 .Python
+.venv/
 venv/
 env/
 ENV/
@@ -67,3 +68,6 @@ tarpaulin-report.html
 
 # Generated documents
 *.pdf
+
+# Reference packages (downloaded for comparison)
+pkgref/
@@ -1,6 +1,6 @@
 # Makefile for problemreductions
 
-.PHONY: help build test fmt clippy doc mdbook paper clean coverage rust-export compare
+.PHONY: help build test fmt clippy doc mdbook paper clean coverage rust-export compare qubo-testdata
 
 # Default target
 help:
@@ -18,6 +18,7 @@ help:
 	@echo "  check        - Quick check (fmt + clippy + test)"
 	@echo "  rust-export  - Generate Rust mapping JSON exports"
 	@echo "  compare      - Generate and compare Rust mapping exports"
+	@echo "  qubo-testdata - Regenerate QUBO test data (requires uv)"
 
 # Build the project
 build:
@@ -65,6 +66,10 @@ clean:
 check: fmt-check clippy test
 	@echo "✅ All checks passed!"
 
+# Regenerate QUBO test data from Python (requires uv)
+qubo-testdata:
+	cd scripts && uv run python generate_qubo_tests.py
+
 # Generate Rust mapping JSON exports for all graphs and modes
 GRAPHS := diamond bull house petersen
 MODES := unweighted weighted triangular
 
@@ -72,6 +72,21 @@ make check     # Quick check before commit (fmt + clippy + test)
 ```
 
 
+## Acknowledgments
+
+This project draws inspiration from the following packages:
+
+- **[ProblemReductions.jl](https://github.com/GiggleLiu/ProblemReductions.jl)** — Julia library for computational problem reductions. Our problem trait hierarchy, reduction interface (`ReduceTo`/`ReductionResult`), and graph-based reduction registry are directly inspired by this package.
+- **[UnitDiskMapping.jl](https://github.com/QuEraComputing/UnitDiskMapping.jl)** — Julia package for mapping problems to unit disk graphs. Our unit disk graph (King's subgraph / triangular lattice) reductions and the copy-line method are based on this implementation.
+- **[qubogen](https://github.com/tamuhey/qubogen)** — Python library for generating QUBO matrices from combinatorial problems. Our QUBO reduction formulas (Vertex Cover, Graph Coloring, Set Packing, Max-2-SAT, binary ILP) reference the implementations in this package.
+
+## Related Projects
+
+- **[Karp](https://github.com/REA1/karp)** — A DSL (built on Racket) for writing and testing Karp reductions between NP-complete problems ([PLDI 2022 paper](https://dl.acm.org/doi/abs/10.1145/3519939.3523732)). Focused on education and proof verification rather than a solver pipeline.
+- **[Complexity Zoo](https://complexityzoo.net/)** — Comprehensive catalog of 550+ computational complexity classes (Scott Aaronson).
+- **[A Compendium of NP Optimization Problems](https://www.csc.kth.se/tcs/compendium/)** — Online catalog of NP optimization problems with approximability results (Crescenzi & Kann).
+- **Computers and Intractability** (Garey & Johnson, 1979) — The classic reference cataloging 300+ NP-complete problems with reductions. The most cited book in computer science.
+
 ## License
 
 MIT License - see [LICENSE](LICENSE) for details.