Update Automated MNLP evaluation report (2026-06-10)

EVAL_REPORT.md

@@ -2,22 +2,22 @@
 
 - **Model repo:** [`cs-552-2026-momy/math_model`](https://huggingface.co/cs-552-2026-momy/math_model)
 - **Owner(s):** group **momy**
-- **Generated at:** 2026-06-09T11:04:23+00:00 (UTC)
+- **Generated at:** 2026-06-10T21:20:55+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:** [`5f3f77e`](https://huggingface.co/cs-552-2026-momy/math_model/commit/5f3f77e315d6a775251d07fc1f393b25155a745d)
+- **Commit:** [`c2f0884`](https://huggingface.co/cs-552-2026-momy/math_model/commit/c2f088438104be4b9b57a49e32f652bc36f365be)
 - **Message:** Upload folder using huggingface_hub
-- **Committed:** 2026-06-08T16:38:52+00:00
+- **Committed:** 2026-06-09T21:50:51+00:00
 
 ## Summary
 
 | Benchmark | Accuracy | Status |
 |---|---:|---|
-| Math | 0.4400 | ok |
+| Math | 0.4100 | ok |
 | Knowledge | — | not run |
 | Multilingual | — | not run |
 | Safety | — | not run |
@@ -30,67 +30,86 @@ _Prompts are intentionally omitted to avoid revealing benchmark contents. For mu
 
 **Correct** (1 shown)
 
-- **reference**: `3`
-- **overall** (8/8 completions correct)
-- **extracted** (✓): `3`
+- **reference**: `(3,2,5)`
+- **overall** (6/8 completions correct)
+- **extracted** (✓): `(3, 2, 5)`
 - **completion**:
 
     ```text
-    Okay, let's see. I need to find the degree of the polynomial g, given that (x - 1) times g(x) equals this quartic polynomial: 3x⁴ + x³ - 25x² + 38x - 17. Hmm, right. So, the problem is about polynomial division or maybe using the factor theorem? Let me think.
+    Okay, let me try to figure out this problem. So, we need to find all ordered triples (p, m, n) where p is a prime greater than 2, and m and n are positive integers with m ≤ n. The conditions are that both m^{p-1} + n and n^{p-1} + m are powers of p. Hmm, interesting.
     
-    First, since (x - 1) is a factor of the polynomial on the right-hand side, that means when we divide the quartic by (x - 1), there's no rem
+    First, let me recall some properties of primes and exponents. Since p is prime and greater than 2, p is an odd prime. Let me note t
     
-    ... [truncated 822 chars] ...
-    
-    t that (x - 1) is a factor of the quartic polynomial with multiplicity 2, then the quotient would be a quadratic, but in this case, we saw that when x = 1, the polynomial is 0, so multiplicity is 1. Therefore, the quotient is cubic, so degree 3. Therefore, the answer is 3. So, I think that's solid.
-    
-    **Final Answer**
-    The degree of \(g\) is \boxed{3}.
-    </think>To determine the degree of the polynomial \(g(x)\), we start by analyzing the given equation:
-    
-    \[
-    (x - 1)g(x) = 3x^4 + x^3 - 25x^2 + 38x - 17.
-    \]
-    
-    First, we check if \(x = 1\) is a root of the polynomial on the right-hand side. Substituting \(x = 1\) into the polynomial, we get:
-    
-    \[
-    3(1)^4 + (1)^3 - 25(1)^2 + 38(1) - 17 = 3 + 1 - 25 + 38 - 17 = 0.
-    \]
-    
-    Since the polynomial evaluates to 0 at \(x = 1\), it follows that \(x - 1\) is a factor of the polynomial on the right-hand side. Therefore, we can perform polynomial long division to divide the quartic polynomial by \(x - 1\).
-    
-    The degree of the polynomial on the right-hand side is 4, and the degree of \(x - 1\) is 1. When we divide a polynomial of degree 4 by a polynomial of degree 1, the degree of the quotient is \(4 - 1 = 3\).
+    ... [truncated 823 chars] ...
     
-    Thus, the degree of \(g(x)\) is:
+    m = 2\):**
+       - For \(m = 2\), we have:
+         \[
+         2^2 + n = 3^k \implies 4 + n = 3^k \implies n = 3^k - 4
+         \]
+       - We need \(n\) to be a positive integer. Let's test \(k = 3\):
+         \[
+         n = 3^3 - 4 = 27 - 4 = 23
+         \]
+       - Check the second equation:
+         \[
+         n^2 + m = 23^2 + 2 = 529 + 2 = 531
+         \]
+         531 is not a power of 3.
+    
+    4. **Testing \(m = 1\):**
+       - For \(m = 1\), we have:
+         \[
+         1 + n = 3^k \implies n = 3^k - 1
+         \]
+       - We need \(n\) to be a positive integer. Let's test \(k = 2\):
+         \[
+         n = 3^2 - 1 = 8
+         \]
+       - Check the second equation:
+         \[
+         n^2 + m = 8^2 + 1 = 64 + 1 = 65
+         \]
+         65 is not a power of 3.
+    
+    5. **Testing \(m = 2\) and \(n = 5\):**
+       - For \(m = 2\) and \(n = 5\), we have:
+         \[
+         2^2 + 5 = 4 + 5 = 9 = 3^2
+         \]
+         \[
+         5^2 + 2 = 25 + 2 = 27 = 3^3
+         \]
+       - Both are powers of 3, and \(m = 2 \le n = 5\).
+    
+    6. **Verification for Other Primes:**
+       - For other primes such as \(p = 5\), \(p = 7\), etc., similar checks show that no other pairs \((m, n)\) satisfy the conditions.
+    
+    ### Conclusion:
+    The only ordered triple \((p, m, n)\) that satisfies the given conditions is:
     
     \[
-    \boxed{3}.
+    \boxed{(3, 2, 5)}
     \]
     ```
 
 **Incorrect** (1 shown)
 
-- **reference**: `$g(x)=c, g(x)=\lceil x \rceil, g(x)=\lfloor x \rfloor$`
+- **reference**: `756`
 - **overall** (0/8 completions correct)
-- **extracted** (✗): `h(x) = c`
+- **extracted** (✗): `<no answer>`
 - **completion**:
 
     ```text
-    Okay, so I need to find all functions h from Q to Z such that for every rational number x, every integer a, and every positive integer b, the function h(x) is equal to h((h(bx - a) + a)/b). Hmm, that seems a bit complex, but let me try to break it down step by step.
+    Okay, so I need to solve this geometry problem involving three spherical balloons with radii 11, 13, and 19. Each pair is externally tangent, and a plane cuts them into three congruent circular cross-sections. The centers of the balloons lie on one side of the plane, and we're given that XY² = 560. We need to find XZ².
     
-    First, let me restate the problem to make sure I understand it. The equation is h(x) = h((h(bx - a) + a)/b) for all x ∈ Q, a ∈ Z, an
+    First, let me visualize the problem. Three spheres with radii r1, r2, r3 are e
     
-    ... [truncated 823 chars] ...
-    
-    ue for all \( x, a, b \). Therefore, constant functions are solutions.
+    ... [truncated 822 chars] ...
     
-    2. **Non-Constant Functions**: Suppose \( h \) is not constant. For any non-constant function, there exist \( x_1 \) and \( x_2 \) such that \( h(x_1) \neq h(x_2) \). However, the equation must hold for all \( x, a, b \), which would require that \( h(x) \) equals the value of the right-hand side expression for all \( x \). This is impossible unless \( h \) is constant, as the equation would force different values for \( h(x) \) which contradicts the requirement that \( h \) is a function from \( \mathbb{Q} \) to \( \mathbb{Z} \).
+    gruent. Therefore, the problem is to find XZ² given that XY² = 560. But how does that relate to the triangle ABC?
     
-    3. **Functional Equation Analysis**: By examining the functional equation, we note that if \( h \) were not constant, the equation would require \( h(x) \) to equal the value of the right-hand side expression for all \( x \), which is only possible if \( h \) is constant. This is because the right-hand side expression involves \( h \) evaluated at some other rational number, which must also be constant for the equation to hold.
+    Alternatively, maybe the problem is using different notation. Let me check again: "Three spherical balloons have radii 11, 13, and 19, and each pair is externally tangent. A plane cuts the balloons in three congruent circular cross-sections whose centers are X, Y, and Z, respectively; the centers of the balloons all lie on one side of the plane. If XY² = 560, determine XZ²."
     
-    Thus, the only solutions to the equation are constant functions. Therefore, the final answer is:
-    \[
-    \boxed{h(x) = c} \quad \text{where } c \in \mathbb{Z}.
-    \]
+    Wait, perhaps the problem is not about the triangle ABC but about the triangle formed by the centers projected onto the plane. Wait, but if the plane is the perpendicular bisector, then the projections of the centers onto the plane form the triangle ABC. Therefore, the cross-sections are circles in the plane, and their radii are equal because the plane is equidistant from all three centers. Therefore, the problem is to find XZ² given that XY² = 560. But if the plane is the perpendicular bisector, then all three centers are equidistant from the plane, so the distances from each center to the plane are equal. Therefore, the radii of the cross-sections are equal. Therefore, the problem is to find XZ²
     ```