Update Automated MNLP evaluation report (2026-06-11)

EVAL_REPORT.md

@@ -2,16 +2,16 @@
 
 - **Model repo:** [`cs-552-2026-the-transformers/math_model`](https://huggingface.co/cs-552-2026-the-transformers/math_model)
 - **Owner(s):** group **the-transformers**
-- **Generated at:** 2026-06-11T04:19:46+00:00 (UTC)
+- **Generated at:** 2026-06-11T06:23:10+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._
 
 ## Evaluated checkpoint
 
-- **Commit:** [`e414833`](https://huggingface.co/cs-552-2026-the-transformers/math_model/commit/e4148337b3b2a712f907564447849020a345f369)
+- **Commit:** [`f9658b7`](https://huggingface.co/cs-552-2026-the-transformers/math_model/commit/f9658b7782b5e50dd8aa2a81f67c1d03d3476f92)
 - **Message:** Update model
-- **Committed:** 2026-06-08T13:05:54+00:00
+- **Committed:** 2026-06-10T17:25:31+00:00
 
 ## Summary
 
@@ -30,130 +30,115 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `720`
-- **overall** (4/8 completions correct)
-- **extracted** (✓): `720`
+- **reference**: `40_9`
+- **overall** (7/8 completions correct)
+- **extracted** (✓): `40_9`
 - **completion**:
 
     ```text
     <think>
-    Okay, so I need to figure out how many distinct seating arrangements there are for 8 people around a circular table, with the condition that Pierre, Rosa, and Thomas must sit in three consecutive seats. And rotations are considered the same arrangement. Hmm, let me start by recalling some combinatorics principles here.
-    
-    First, in circular permutations, when arranging n people around a circ
+    Okay, let's see. I need to subtract two numbers in base 9: 58₉ minus 18₉. Hmm, base 9... I remember that subtracting in different bases can be similar to decimal, but you have to remember that each digit goes from 0 to 8 instead of 0 to 9. So maybe I should convert both numbers to base 10, subtract them, and then convert the result back to base 9? That might be easier for me, since I'm mor
     
     ... [truncated 823 chars] ...
     
-    ar, rotations of the same arrangement are considered identical. Thus, the number of circular arrangements is:
-    
-    $$
-    (8 - 1)! = 7!
-    $$
-    
-    This is because fixing one person eliminates rotational symmetry.
-    
-    ---
-    
-    ### **Step 2: Treat Pierre, Rosa, and Thomas as a Single Block**
-    
-    We now treat Pierre, Rosa, and Thomas (PRT) as a single block to simplify the problem. This means we are arranging:
-    
-    - 1 block (PRT)
-    - 5 other individuals
-    
-    So, we have **6 units** to arrange around the table: the block and the 5 individuals.
-    
-    In a circular arrangement of \( n \) units, the number of ways to arrange them is:
-    
-    $$
-    (n - 1)!
-    $$
-    
-    So, the number of ways to arrange the 6 units is:
-    
-    $$
-    (6 - 1)! = 5!
-    $$
-    
-    ---
-    
-    ### **Step 3: Internal Arrangement of the Block**
-    
-    Within the block, Pierre, Rosa, and Thomas can be arranged in any order. The number of ways to arrange 3 people in a block is:
-    
-    $$
-    3!
-    $$
-    
-    ---
-    
-    ### **Step 4: Combine the Results**
-    
-    Now, we multiply the number of ways to arrange the 6 units around the table (5!) by the number of internal arrangements of the block (3!). The total number of distinct seating arrangements is:
-    
-    $$
-    5! \times 3! = 120 \times 6 = 720
-    $$
-    
-    ---
-    
-    ### **Final Answer**
-    
-    $$
-    \boxed{720}
-    $$
+    I think the answer is correct.
+    </think>
+    
+    To solve the problem of evaluating \(58_9 - 18_9\) and writing the result in base 9, we can follow these steps:
+    
+    1. **Convert both numbers to base 10:**
+       - Convert \(58_9\) to base 10:
+         \[
+         58_9 = 5 \times 9^1 + 8 \times 9^0 = 5 \times 9 + 8 = 45 + 8 = 53_{10}
+         \]
+       - Convert \(18_9\) to base 10:
+         \[
+         18_9 = 1 \times 9^1 + 8 \times 9^0 = 1 \times 9 + 8 = 9 + 8 = 17_{10}
+         \]
+    
+    2. **Subtract the two base 10 numbers:**
+       \[
+       53_{10} - 17_{10} = 36_{10}
+       \]
+    
+    3. **Convert the result back to base 9:**
+       - Divide 36 by 9 to find the quotient and remainder:
+         \[
+         36 \div 9 = 4 \text{ remainder } 0
+         \]
+       - Therefore, \(36_{10}\) in base 9 is \(40_9\).
+    
+    4. **Verify the result:**
+       - Convert \(40_9\) back to base 10:
+         \[
+         40_9 = 4 \times 9^1 + 0 \times 9^0 = 4 \times 9 + 0 = 36_{10}
+         \]
+       - Convert \(58_9\) and \(18_9\) back to base 10:
+         \[
+         58_9 = 53_{10}, \quad 18_9 = 17_{10}
+         \]
+       - Subtract the base 10 numbers:
+         \[
+         53_{10} - 17_{10} = 36_{10}
+         \]
+       - Convert \(36_{10}\) back to base 9:
+         \[
+         36_{10} = 40_9
+         \]
+    
+    Thus, the final answer is \(\boxed{40_9}\).
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `$1,3,5$`
+- **reference**: `$f(x,y)= g(x+y, xy(x-y)^{2})$ for some polynomial $g$`
 - **overall** (0/8 completions correct)
-- **extracted** (✗): `3`
+- **extracted** (✗): `c`
 - **completion**:
 
     ```text
     <think>
-    Okay, so I need to solve this problem where for each positive integer n, m is the exponent of 2 in its prime factors, and f(n) = n / 2^m. Then, we have to find all positive integers v such that there exists some u where the expression [f(u + v + k) - f(u + k)] is divisible by 4 for every integer k between 0 and v-1 inclusive.
+    Okay, let's try to figure out this problem. So, we need to find all polynomials f(x, y) in complex numbers such that for any complex numbers a and b, the equation f(a², b²) equals f((a - b)² / 2, (a + b)² / 2). Hmm, interesting. Let me start by understanding what this condition means.
     
-    Hmm, let me break this down. The function f(n) essentially remo
+    First, maybe I should consider specific values for a and b to see if I can spot a pattern or figure out t
     
-    ... [truncated 823 chars] ...
+    ... [truncated 822 chars] ...
+    
+    + q}{2}\right)a^2 + \left(\frac{p + q}{2}\right)b^2 - pqab + r.
+    \]
+    Equating the coefficients with the left-hand side:
+    \[
+    p a^2 + q b^2 + r = \left(\frac{p + q}{2}\right)a^2 + \left(\frac{p + q}{2}\right)b^2 - pqab + r.
+    \]
+    For this to hold for all $ a $ and $ b $, the coefficients must match:
+    \[
+    p = \frac{p + q}{2} \implies 2p = p + q \implies q = p,
+    \]
+    \[
+    q = \frac{p + q}{2} \implies 2q = p + q \implies p = q,
+    \]
+    \[
+    -pq = 0 \implies pq = 0 \implies p = 0 \text{ (since } p \neq 0).
+    \]
+    Thus, the only solution for linear polynomials is $ f(x, y) = 0 $, which is a constant.
     
-    *
-         We need \( f(u+3) - f(u+0) \equiv 0 \pmod{4} \) and \( f(u+3+1) - f(u+1) \equiv 0 \pmod{4} \).
-         - For \( u = 1 \):
-           \[
-           f(1+3) - f(1) = f(4) - f(1) = 1 - 1 = 0 \pmod{4}
-           \]
-           \[
-           f(1+3+1) - f(1+1) = f(5) - f(2) = 5 - 1 = 4 \equiv 0 \pmod{4}
-           \]
-           Both conditions are satisfied.
-         - Therefore, \( v = 3 \) is valid.
-    
-       - **Case \( v = 4 \):**
-         We need \( f(u+4) - f(u) \equiv 0 \pmod{4} \), \( f(u+4+1) - f(u+1) \equiv 0 \pmod{4} \), and \( f(u+4+2) - f(u+2) \equiv 0 \pmod{4} \).
-         - For \( u = 3 \):
-           \[
-           f(3+4) - f(3) = f(7) - f(3) = 7 - 3 = 4 \equiv 0 \pmod{4}
-           \]
-           \[
-           f(3+4+1) - f(3+1) = f(8) - f(4) = 1 - 1 = 0 \pmod{4}
-           \]
-           \[
-           f(3+4+2) - f(3+2) = f(9) - f(5) = 9 - 5 = 4 \equiv 0 \pmod{4}
-           \]
-           All conditions are satisfied.
-         - However, for \( k = 3 \):
-           \[
-           f(3+4+3) - f(3+3) = f(10) - f(6) = 5 - 3 = 2 \not\equiv 0 \pmod{4}
-           \]
-           This fails.
-         - Therefore, \( v = 4 \) is not valid.
-    
-    4. **Conclusion:**
-       After checking all cases, the only valid values of \( v \) are \( 1 \) and \( 3 \).
+    #### Quadratic Polynomials
     
+    Assume $ f(x, y) = Ax^2 + By^2 + Cxy + Dx + Ey + F $. Substitute into the equation and equate coefficients. This leads to:
     \[
-    \boxed{1} \quad \text{and} \quad \boxed{3}
+    A = B = C = D = E = F = 0.
     \]
+    Thus, the only solution is $ f(x, y) = c $.
+    
+    ### Step 4: Higher-Degree Polynomials
+    
+    Higher-degree polynomials will similarly force all coefficients to zero, confirming that only constant polynomials satisfy the condition.
+    
+    ### Conclusion
+    
+    After testing various forms and deriving constraints, the only polynomials $ f(x, y) \in \mathbb{C}[x, y] \) that satisfy the given functional equation are the constant polynomials.
+    
+    $$
+    \boxed{c}
+    $$
     ```