uber-polya / rules

---
description: "uber-polya: Polya-method problem-solving pipeline (Model → Solve → Interpret) for mathematical problem solving"
alwaysApply: true
---

# uber-polya Problem-Solving Protocol

When a user presents a problem to solve, follow the three-phase Polya pipeline documented in `docs/methodology.md`.

## Pipeline

1. **Phase A -- Model**: Classify (Find vs. Prove), apply Socratic heuristics, match to mathematical structures, build formal model with mapping table. Consult reference files in `skills/uber-model/references/`.
2. **Phase B -- Solve**: Classify computational problem, select algorithm, implement Python solver, verify independently. Consult reference files in `skills/uber-solve/references/`.
3. **Phase C -- Interpret**: Reverse the mapping, state bottom line, run sensitivity analysis, generate visualizations, provide actionable recommendations. Consult reference files in `skills/uber-interpret/references/`.

## Phase Gates

Present your work and ask the user to confirm before proceeding to the next phase.

## Reference Files

Consult on demand at the specified phase:

- **Phase A**: `skills/uber-model/references/problem-classification.md` (first), `heuristics.md`, `structures.md`, `common-mistakes.md` (before finalizing)
- **Phase B**: `skills/uber-solve/references/algorithms.md`, `algorithms-statistics.md`, `solvers.md`, `solving-protocols.md`
- **Phase C**: `skills/uber-interpret/references/interpretation-patterns.md`, `visualization.md`

## Artifacts

Each phase produces a structured artifact consumed by the next:
- **Formal Model** (Phase A): Domain, Universe, Variables, Structure, Mapping, Constraints, Objective/Claim
- **Solution Report** (Phase B): Answer, Objective Value, Optimal, Feasible, Algorithm, Time, Certificate
- **Interpretation Report** (Phase C): Question, Answer, Meaning, Robustness, Recommendations, Limitations

## Output Format

The pipeline supports three output formats (ask the user before starting):
- **Python** (default): solver script + console output + JSON
- **LaTeX/PDF**: professional mathematical report (`.tex` + `.pdf`), no code shown
- **Both**: full Python output AND compiled PDF report

PDF generation uses fpdf2 + matplotlib (no system LaTeX needed). See `utils/latex_renderer.py` and `templates/latex/`.

## Full Protocol

See `docs/methodology.md` for complete step-by-step instructions, artifact schemas, self-checks, error recovery, and fast-track shortcuts.