docs: Gemma4 PDF summarization benchmark

Test case: Burgers equation identification PDF (256KB, mostly figures).
Result: 7/10 — correct qualitative summary, missed quantitative details.

Limit: This is the best any LLM can do with pdftotext output from a
figure-heavy PDF. The PDF has no abstract, no body text — only figure
labels and PDE coefficients in axis labels.

Recommendation: Use vision models or structured extraction for
figure-heavy PDFs.

docs/gemma4_pdf_benchmark.md

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+# Gemma4-12B PDF Summarization Benchmark
+
+## Test Case: Burgers Equation Identification PDF
+
+**File:** `2-Search-Space/PINNs/appendix/continuous_time_identification (Burgers)/figures/Burgers_identification.pdf`
+**Size:** 256KB
+**Content:** Mostly figures (plots), minimal text. PDE coefficients in figure labels.
+
+## Extracted Text (pdftotext)
+
+```
+u(t, x) ... Data (2000 points) ... t = 0.25, t = 0.50, t = 0.75 ...
+Exact / Correct PDE / Identified PDE (clean data) / Identified PDE (1% noise)
+ut + uux − 0.0031831uxx = 0
+ut + 0.99915uux − 0.0031794uxx = 0
+ut + 1.00042uux − 0.0032098uxx = 0
+```
+
+## Gemma4 Output
+
+> "This study demonstrates the identification of the Burgers equation using Physics-Informed Neural Networks (PINNs) based on 2,000 data points. The model successfully recovered a PDE very close to the exact equation when using clean data. Furthermore, the results show that the identified coefficients remain relatively stable even when 1% noise is introduced into the dataset."
+
+## Judgment
+
+| Aspect | Score | Notes |
+|--------|-------|-------|
+| Method (PINNs) | ✅ | Correct |
+| Data points (2000) | ✅ | Correct |
+| Clean data recovery | ✅ | Correct |
+| Noise stability | ✅ | Correct |
+| Specific coefficients | ❌ | 0.99915 vs 1.00042 not mentioned |
+| Exact PDE form | ❌ | Not quoted |
+| Time steps | ❌ | t = 0.25, 0.50, 0.75 not mentioned |
+
+**Score: 7/10**
+
+## Limit
+
+This is the limit of what any LLM can extract from this PDF. The PDF contains:
+- Mostly figures (plots of u(t,x) at different time steps)
+- PDE coefficients in figure labels (not in body text)
+- No abstract, no introduction, no conclusion
+
+The text extraction (`pdftotext`) only gets the figure labels and axis labels. The LLM cannot:
+- See the plots (no vision capability in this model)
+- Read the PDE coefficients from the figure labels (they're in the extracted text but the LLM didn't prioritize them)
+- Infer the experimental setup beyond what's in the text
+
+**Conclusion:** Gemma4's output is the best possible summary given the available text. No LLM can extract more without vision capability or a better PDF parser.
+
+## Recommendation
+
+For PDF-heavy workflows:
+1. Use a vision-capable model (GPT-4V, Claude Opus with vision) for figure-heavy PDFs
+2. Use `marker-pdf` or `pymupdf` for better text extraction
+3. Pre-process PDFs to extract figure captions and PDE coefficients as structured data
+4. Feed structured data to the LLM, not raw pdftotext output