Round #999

19 May 2026, 09:53· math· Meta-Llama-3.3-70B-Instruct· r13-clean-hints
Complexity
band 0
ZP / UO / OBS
3 / 0 / 0
Journey weight
220
Lightshift ΔL

Prompt

A right-angled triangle has legs of length 5 and 12. Find the length of the hypotenuse.

Zero-point index (what the engine surfaced)

ZPI-ZPI-0003 | 2026-05-19T09:53:00Z A right-angled triangle has legs of length 5 and 12. Find the length of the hypotenuse. ZERO POINT — 3 entries (structural invariants) ● hsl(304.59, 100%, 15%) a² + b² = c² [contract] ● hsl(3.75, 100%, 50%) right-angle hypothesis [contract] ● hsl(58.68, 100%, 15%) Euclidean metric on right triangle [contract] UNOBSERVED — 0 entries (implied truths) OBSERVED — 0 entries (explicit in request) COMPLEXITY │ 3 entries │ spread: 0° │ band: LOW

Baseline response (no ZPI)

```csharp using System; class Program { static void Main() { // Given lengths of the legs double a = 5; double b = 12; // Calculate the length of the hypotenuse using the Pythagorean theorem double c = Math.Sqrt(a * a + b * b); Console.WriteLine("The length of the hypotenuse is: " + c); } } ```

Enhanced response (with ZPI)

```csharp using System; public class RightTriangle { public static double CalculateHypotenuse(double a, double b) { if (a < 0 || b < 0) { throw new ArgumentException("Leg lengths cannot be negative."); } return Math.Sqrt(a * a + b * b); } public static void Main(string[] args) { double a = 5; double b = 12; double c = CalculateHypotenuse(a, b); Console.WriteLine($"The length of the hypotenuse is {c}."); } } ``` This C# code calculates the length of the hypotenuse of a right-angled triangle using the Pythagorean theorem, which states that a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse. The `CalculateHypotenuse` method takes the lengths of the legs as input and returns the length of the hypotenuse. The `Main` method demonstrates how to use this method with the given leg lengths of 5 and 12. The length of the hypotenuse is then printed to the console.

Grader chain

Each grader reads the same baseline + enhanced pair and casts an independent verdict. Disagreement is the framework's own signal — not noise to be averaged away.

V1samba/Meta-Llama-3.3-70B-Instruct
Better
V4qwen2.5-coder-3b-instruct
Better
V5cerebras/qwen-3-235b-a22b-instruct-2507
Better
V7qwen2.5-coder-7b-instruct
Better
V8openai/gpt-4.1
Better
V9anthropic/claude-opus-4-7
Better
V12openai/gpt-4o
Better

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