# Quality Evaluation

**Timestamp**: 2026-03-09T15:08:26
**Reference**: /Users/davidvandijcke/University of Michigan Dropbox/David Van Dijcke/coarse/data/refine_examples/coset_codes/reference_review.md
**Model**: gemini/gemini-3.1-pro-preview
**Mode**: single

## Overall Score: 5.38/6.0

## Dimensions

| Dimension | Score | Reasoning |
|-----------|-------|-----------|
| coverage | 5.5/6 | The generated review covers a wide range of issues, identifying several legitimate mathematical and typographical errors in the paper that the reference review missed (e.g., the formula for fundamental coding gain, the G^4 typo in Table I, the duplicate H16 row). While it includes a few incorrect critiques, its overall coverage of the paper's technical details is outstanding. |
| specificity | 5.5/6 | The review is highly specific, quoting exact equations, table entries, and mathematical claims. It pinpoints exact locations of typos (like \phi^u instead of \phi^\mu) and provides concrete numerical examples to test the paper's formulas. |
| depth | 5.5/6 | The analysis engages deeply with the paper's lattice theory and coding gain derivations. It successfully catches subtle errors in the paper's equations (such as the incorrect use of 'e' instead of '\rho' for the coding gain formula). A few of its own mathematical checks are flawed (e.g., the Gaussian primes at norm 5, and the volume of RD_4), but the depth of engagement exceeds the reference. |
| format | 5.0/6 | The generated review perfectly adheres to the requested format, including the Overall Feedback section and Detailed Comments with numbered entries containing Quote and Feedback sections. |

## Strengths

- Identifies multiple subtle mathematical and typographical errors in the paper's equations and tables that the reference review missed.
- Engages deeply with the paper's lattice definitions, coding gain formulas, and complexity normalizations.
- Follows the required structural format flawlessly.

## Weaknesses

- Contains a few mathematical errors of its own (e.g., misunderstanding that 1+2i is a unit multiple of 2-i, and miscalculating the volume of RD_4).
- Confuses the D4/2D4 partition in the main table with the D4/RD4 partition mentioned in the proof note.
