Model Answers · GPT o4-mini · Three Sections

GPT o4-mini — Constellation Eval Answers

The full 21-question transcript across MMLU, ARB, and ARC-AGI, with an explicit confidence estimate attached to every answer.

Source: GPT_o4-mini_Constellation_Eval_Answers.docxReproduced verbatim

Format note: o4-mini answered in a compressed derivation style — answer, minimal reasoning chain, then a numeric confidence estimate. It is the only run in the series to self-report calibration on all 21 items.

Section 1 — MMLU (General Knowledge)

Each item returned a direct answer, brief step-by-step reasoning, and a confidence estimate. All ten items reported ~100% confidence.

#	Domain	Answer	Reasoning
1	History	B) World War I	World War I ran from 1914 to 1918.
2	Geography	C) Ottawa	Ottawa is Canada's seat of government; Toronto, Montreal, and Vancouver are larger cities but not the capital.
3	Biology	A) Mitochondrion	Mitochondria generate ATP via oxidative phosphorylation; the other organelles serve different functions.
4	Physics	C) Ohm	Resistance is measured in ohms (Ω); volts, amperes, and watts measure voltage, current, and power.
5	Computer Science	A) Structured Query Language	SQL is the standard language for relational database queries.
6	Math	B) 2x	d/dx (xⁿ) = n·xⁿ⁻¹ ⇒ 2·x¹ = 2x.
7	Medicine	B) Glucose	Insulin facilitates cellular uptake of glucose, reducing blood sugar.
8	Philosophy	B) Kant	Immanuel Kant published the Critique of Pure Reason in 1781, founding transcendental idealism.
9	Logic	C) C	Transitive syllogism: A ⊆ B and B ⊆ C ⇒ A ⊆ C.
10	AI	B) Supervised	Supervised learning trains on input–output pairs; unsupervised learning uses no labels.

Section 1 closed with: "Please let me know when you're ready to proceed to Section 2."

Section 2 — ARB (Advanced Reasoning)

11. Logic — does (A → C) follow from (A → B) and (B → C)?

Answer: Yes. Confidence ~100%.

Assume A is true.
From A → B, deduce B is true.
From B → C, deduce C is true.
Therefore A → C (hypothetical syllogism).

12. Math — all real x with f(f(x)) = 0, where f(x) = x³ − 3x

Step 1: Solve f(t) = 0 ⇒ t³ − 3t = 0 ⇒ t(t² − 3) = 0 ⇒ t ∈ {0, +√3, −√3}.
Step 2: Find x such that f(x) ∈ {0, +√3, −√3}.
Case A: f(x) = 0 ⇒ x ∈ {0, ±√3}.
Case B: f(x) = +√3 ⇒ x³ − 3x − √3 = 0 ⇒ three real roots (sign changes at the extrema x = ±1).
Case C: f(x) = −√3 ⇒ x³ − 3x + √3 = 0 ⇒ three real roots.
Total: 1 + 2 + 3 + 3 = 9 real solutions. Confidence ~95%.

Note from the transcript: the roots of the last two cubics can be written in closed form via trigonometric formulas — x = 2·cos((arccos(t) + 2πk)/3) — but the key result is nine real solutions.

13. Number Theory — n³ − n is divisible by 6 for all integers n ≥ 1

n³ − n = n(n² − 1) = n(n − 1)(n + 1).
Three consecutive integers ⇒ one is a multiple of 3 and at least one is even ⇒ the product is divisible by 2·3 = 6.

Confidence ~100%.

14. Combinatorics — distinct permutations of {A, A, B, B, B, C}

6! / (2!·3!·1!) = 720 / 12 = 60. Confidence ~100%.

15. Probability — expected fair-coin tosses to get two consecutive heads

Markov formulation: E = expected tosses from the start; E₁ = expected tosses after one head.
E = 1 + ½·E₁ + ½·E ⇒ E = 2 + E₁.
E₁ = 1 + ½·0 + ½·E ⇒ E₁ = 1 + ½E.
Substituting: E = 3 + ½E ⇒ E = 6 tosses. Confidence ~100%.

16. Calculus — lim(x→0) (sin x − x) / x³

Expansion: sin x = x − x³/6 + O(x⁵).
Numerator: (x − x³/6 + …) − x = −x³/6 + O(x⁵).
Limit: (−x³/6 + …) / x³ → −1/6. Confidence ~100%.

17. Physics — acceleration on a frictionless incline of angle θ

a = g·sin θ, directed down the slope. The gravity component along the plane is mg·sin θ, so a = F/m = g·sin θ. Confidence ~100%.

18. Chemistry — balance C₃H₈ + O₂ → CO₂ + H₂O

1 C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O. Check — C: 3 → 3; H: 8 → 4·2 = 8; O: 5·2 = 10 → 3·2 + 4·1 = 10. Confidence ~100%.

Section 3 — ARC-AGI (Spatial Reasoning)

19. Mirror Task — horizontal flip

Input	Output (each row reversed)
9 0 1 0	0 1 0 9
0 2 3 2	2 3 2 0

Confidence ≈ 100%.

20. Transpose Task — rows ↔ columns

Input (3×2): rows `0 2`, `2 0`, `3 0`. Output (2×3): rows `0 2 3`, `2 0 0`. Confidence ≈ 100%.

21. Rotation Task — 90° clockwise

Input (2×3): rows `9 0 8`, `0 0 1`.
Transpose: rows `9 0`, `0 0`, `8 1`.
Reverse each row: rows `0 9`, `0 0`, `1 8` — the final output.
Confidence ≈ 95%.

The transcript closes: "Let me know your benchmark results."