docs(autoresearch): add example research project and README

Add LoRA rank convergence study example demonstrating:
- Bootstrap phase with literature search
- Hypothesis formation and testing
- Inner/outer loop workflow
- Progress tracking and findings synthesis

skills/research/autoresearch/examples/README.md

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+# Autoresearch Examples
+
+This directory contains example research projects using the autoresearch methodology.
+
+## Available Examples
+
+### `lora-rank-study.md`
+
+**Question:** Does LoRA rank affect convergence speed on small datasets?
+
+**Type:** Benchmark optimization, hyperparameter study
+
+**Skills Used:**
+- `arxiv` — Literature search
+- `mlops` — Model training
+- `tensorboard` — Experiment tracking
+
+**Key Takeaway:** Higher rank improves convergence speed up to a point (r=16), then diminishing returns.
+
+---
+
+## Creating Your Own Research
+
+1. Start with `/autoresearch "your question"`
+2. Follow the two-loop architecture
+3. Commit protocols before running
+4. Generate progress reports with `/research-report`
+
+## Tips from Examples
+
+- **Start small:** First experiment should complete in <30 minutes
+- **Define metrics upfront:** Know what you're measuring before you start
+- **Document surprises:** Negative results are progress too
+- **Show your work:** Progress reports help humans follow along

skills/research/autoresearch/examples/lora-rank-study.md

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+# LoRA Rank Convergence Study
+
+**Research Question:** Does LoRA rank affect convergence speed on small datasets?
+
+## Bootstrap
+
+### Literature
+
+Key papers:
+- Hu et al. (2021) — LoRA: Low-Rank Adaptation of Large Language Models
+- Valipour et al. (2023) — DyLoRA: Parameter-Efficient Tuning with Dynamic Search
+
+Gap: Most papers focus on final performance, not convergence dynamics.
+
+### Hypotheses
+
+- **H1:** Higher rank (r=16) converges faster but may overfit on small data
+- **H2:** Lower rank (r=4) converges slower but generalizes better
+- **H3:** There's an optimal rank (r=8) that balances speed and generalization
+
+## Experiments
+
+### H001 — Baseline (r=8)
+
+```bash
+# Protocol: Train with rank 8, measure convergence steps to 90% of max accuracy
+# Prediction: Baseline behavior, ~50 steps to converge
+```
+
+**Results:**
+- Convergence steps: 47
+- Final accuracy: 0.892
+- Wall time: 12 min
+
+### H002 — Low Rank (r=4)
+
+**Results:**
+- Convergence steps: 68 (+44% vs baseline)
+- Final accuracy: 0.887 (-0.6%)
+
+### H003 — High Rank (r=16)
+
+**Results:**
+- Convergence steps: 41 (-13% vs baseline)
+- Final accuracy: 0.894 (+0.2%)
+
+## Outer Loop #1
+
+**Pattern:** Higher rank → faster convergence, minimal overfit on this dataset
+
+**Decision:** DEEPEN — Test r=32 and r=64 to find saturation point
+
+### H004 — Very High Rank (r=32)
+
+**Results:**
+- Convergence steps: 38 (-6% vs r=16)
+- Final accuracy: 0.891 (-0.3%)
+- **Diminishing returns observed**
+
+### H005 — Optimal Search (r=6, r=10, r=12)
+
+[Running...]
+
+## Current Findings
+
+1. Convergence speed improves with rank up to r=16, then plateaus
+2. Final accuracy relatively stable across ranks (±0.5%)
+3. For small datasets, r=8-12 appears optimal (speed vs compute tradeoff)
+
+## Next Steps
+
+- Complete H005-H007
+- Test on different dataset sizes (generalization)
+- Write up findings