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
BetterV4qwen2.5-coder-3b-instruct
BetterV5cerebras/qwen-3-235b-a22b-instruct-2507
BetterV7qwen2.5-coder-7b-instruct
BetterV8openai/gpt-4.1
BetterV9anthropic/claude-opus-4-7
BetterV12openai/gpt-4o
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