Update Automated MNLP evaluation report (2026-05-20)

EVAL_REPORT.md

@@ -2,7 +2,7 @@
 
 - **Model repo:** [`cs-552-2026-mnlplus/general_knowledge_model`](https://huggingface.co/cs-552-2026-mnlplus/general_knowledge_model)
 - **Owner(s):** group **mnlplus**
-- **Generated at:** 2026-05-19T03:22:52+00:00 (UTC)
+- **Generated at:** 2026-05-20T05:49:46+00:00 (UTC)
 - **Pipeline:** [mnlp-project-ci](https://github.com/eric11eca/mnlp-project-ci)
 
 _This PR is opened automatically by the course CI. It is **non-blocking** — you do not need to merge it. The next nightly run will refresh this file._
@@ -12,7 +12,7 @@ _This PR is opened automatically by the course CI. It is **non-blocking** — yo
 | Benchmark | Accuracy | Status |
 |---|---:|---|
 | Math | — | not run |
-| Knowledge | 0.0200 | ok |
+| Knowledge | 0.2600 | ok |
 | Multilingual | — | not run |
 | Safety | — | not run |
 
@@ -31,97 +31,67 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
     ```text
     <think>
-    The question asks to select the function subprogram that evaluates PD(A, I, J) = [A(I-1,J) + A(I+1,J) + A(I,J-1) + A(I,J+1)] / 4, and then applies it to compute B_ij = (1-\alpha)B_ij + \alpha[(B_i-1,j + B_i+1,j + B_i,j-1 + B_i,j+1) / 4].
-    Looking at the choices, we can see that the correct answer is G.
-    The answer is \boxed{G}
     </think>
     
-    To determine the correct function subprogram that evalu
-    
-    ... [truncated 774 chars] ...
-    
-    Incorrect. It uses a different weighting scheme and includes an extra term, which does not match the function definition.
-    - **Choice B:** Incorrect. The weighting is $ \frac{1}{5} $, and the indices do not match the function definition.
-    - **Choice C:** Incorrect. The weighting is $ \frac{1}{5} $, and the indices do not match the function definition.
-    - **Choice D:** Incorrect. The weighting is $ \frac{1}{6} $, and the indices do not match the function definition.
-    - **Choice E:** Incorrect. The indices do not match the function definition.
-    - **Choice F:** Incorrect. The indices do not match the function definition.
-    - **Choice G:** **Correct.** The function computes the weighted average with weight $ \frac{1}{4} $, and the indices match the function definition.
-    - **Choice H:** Incorrect. The weighting is $ \frac{1}{2} $, and the indices do not match the function definition.
-    - **Choice I:** Incorrect. The indices do not match the function definition.
-    
-    ---
-    
-    **Conclusion:**
-    
-    The only function subprogram that matches the requirements — namely, computing a weighted average of four neighboring values with weight $ \frac{1}{4} $, and applying this to a target variable — is:
-    
-    $$
     \boxed{G}
-    $$
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `D`
+- **reference**: `B`
 - **overall** (0/1 completions correct)
-- **extracted** (✗): `C. \ 2.81 \times 10^{-7} \text{ M}`
+- **extracted** (✗): `C`
 - **completion**:
 
     ```text
     <think>
-    The question asks to determine the concentration of orthophosphate ions (HPO4^2-) in a 200.00 cm3 solution at T = 25 °C that contains 1.00 g KH2PO4 (Mw = 136.09 g/mol) and 1.00 g Na2HPO4●2H2O (Mw = 177.99 g/mol). The given Ka values are Ka1 = 7.5x10^-3, Ka2 = 6.2x10^-8, and Ka3 = 1.8x10^-12.
-    </think>
+    The user is asking about the volume integral of the divergence of a vector field over the interior of a sphere. The vector field is directed purely along the radial direction, and its magnitude decreases as 1/r². The answer choices are given, and the task is to choose the most appropriate value for the integral.
     
-    To determine the concentration of orthophosphate ions (HPO4^2-) in the solution, we must
+    First, I need to recall the divergence theorem, which relates the volume inte
     
     ... [truncated 823 chars] ...
     
-    Step 4: Calculate the Molar Concentration of HPO₄²⁻**
+    ield $\vec{f}(r)$ is directed purely along the radial direction, meaning it points outward from the origin, and its magnitude decreases as $f(r) = \frac{1}{r^2}$. In spherical coordinates, this corresponds to a radial vector field.
     
-    We know the total volume of the solution is 200.00 cm³ = 0.200 L.
+    ---
     
-    Total moles of species present = 0.00735 mol + 0.00562 mol = 0.01297 mol
+    ### Step 2: Use the Divergence Theorem
     
-    Using the Henderson-Hasselbalch equation:
+    The divergence theorem relates the volume integral of the divergence of a vector field to the flux of the field through the surface of the region. It states:
     
     $$
-    \text{pH} = \text{p}K_a + \log\left( \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^{-}]} \right)
+    \iiint_V (\nabla \cdot \vec{f}) \, dV = \iint_S \vec{f} \cdot d\vec{S}
     $$
     
-    $$
-    \text{pH} = -\log(1.8 \times 10^{-12}) + \log\left( \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^{-}]} \right)
-    $$
+    where $V$ is the region enclosed by the surface $S$.
     
-    $$
-    \text{pH} = 11.74 + \log\left( \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^{-}]} \right)
-    $$
+    ---
     
-    Assume that the pH of the solution is approximately neutral (7), so:
+    ### Step 3: Compute the Divergence
     
-    $$
-    7 = 11.74 + \log\left( \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^{-}]} \right)
-    $$
+    For a radial vector field in spherical coordinates, the divergence is:
     
     $$
-    \log\left( \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^{-}]} \right) = -4.74
+    \nabla \cdot \vec{f} = \frac{1}{r^2} \frac{d}{dr}(r^2 f(r)) = \frac{1}{r^2} \frac{d}{dr}(r^2 \cdot \frac{1}{r^2}) = \frac{1}{r^2} \frac{d}{dr}(1) = 0
     $$
     
-    $$
-    \frac{[\text{HPO}_4^{2-}]}{[\text{H}_2\text{PO}_4^{-}]} = 10^{-4.74} \approx 1.8 \times 10^{-5}
-    $$
+    Thus, the divergence of the vector field is **zero** everywhere except at the origin, where the field is undefined.
+    
+    ---
+    
+    ### Step 4: Evaluate the Volume Integral
     
-    Now, the total moles of species present = 0.01297 mol
+    Since the divergence is zero everywhere, the volume integral of the divergence over any region is also zero:
     
     $$
-    [\text{HPO}_4^{2-}] = \frac{0.01297 \times 1.8 \times 10^{-5}}{1 + 1.8 \times 10^{-5}} \approx \boxed{2.81 \times 10^{-7}} \text{ M}
+    \iiint_V (\nabla \cdot \vec{f}) \, dV = 0
     $$
     
     ---
     
-    ### **Final Answer:**
+    ### Final Answer
     
     $$
-    \boxed{C. \ 2.81 \times 10^{-7} \text{ M}}
+    \boxed{C}
     $$
     ```