diff --git a/PerfectNumbers.Core/ULongExtensions.Gpu.cs b/PerfectNumbers.Core/ULongExtensions.Gpu.cs
index 67eb9ef..7a01d10 100644
--- a/PerfectNumbers.Core/ULongExtensions.Gpu.cs
+++ b/PerfectNumbers.Core/ULongExtensions.Gpu.cs
@@ -81,7 +81,7 @@ public static partial class ULongExtensions
 		while (index >= 0)
 		{
 			ulong currentBit = (exponent >> index) & 1UL;
-			ulong squared = result.MulMod64(result, modulus);
+			ulong squared = result.GpuCompatibleMulModSimplifiedExtension(result, modulus);
 			result = currentBit == 0UL ? squared : result;
 			index = currentBit == 0UL ? index - 1 : index;
 			if (currentBit == 0UL)
@@ -101,14 +101,14 @@ public static partial class ULongExtensions
 			int windowLength = index - windowStart + 1;
 			for (int square = 0; square < windowLength; square++)
 			{
-				result = result.MulMod64(result, modulus);
+				result = result.GpuCompatibleMulModSimplifiedExtension(result, modulus);
 			}
 
 			ulong mask = (1UL << windowLength) - 1UL;
 			ulong windowValue = (exponent >> windowStart) & mask;
 			int tableIndex = (int)((windowValue - 1UL) >> 1);
 			ulong multiplier = oddPowers[tableIndex];
-			result = result.MulMod64(multiplier, modulus);
+			result = result.GpuCompatibleMulModSimplifiedExtension(multiplier, modulus);
 
 			index = windowStart - 1;
 		}
@@ -311,11 +311,11 @@ public static partial class ULongExtensions
 			return;
 		}
 
-		ulong square = baseValue.MulMod64(baseValue, modulus);
+		ulong square = baseValue.GpuCompatibleMulModSimplifiedExtension(baseValue, modulus);
 		for (int i = 1; i < oddPowers.Length; i++)
 		{
 			ulong previous = oddPowers[i - 1];
-			oddPowers[i] = previous.MulMod64(square, modulus);
+			oddPowers[i] = previous.GpuCompatibleMulModSimplifiedExtension(square, modulus);
 		}
 	}
 
diff --git a/docs/gpu-bydivisor-mulmod-audit.md b/docs/gpu-bydivisor-mulmod-audit.md
index cdbf42f..8eda027 100644
--- a/docs/gpu-bydivisor-mulmod-audit.md
+++ b/docs/gpu-bydivisor-mulmod-audit.md
@@ -8,8 +8,8 @@ This note tracks every `MulMod` call site in the GPU-only `--mersenne=bydivisor`
 | --- | --- |
 | `ULongExtensions.GpuCompatibleMulModSimplifiedExtension` | Wraps `GpuUInt128.MulModSimplified` so host code mirrors the benchmark winner without reimplementing GPU logic.【F:PerfectNumbers.Core/ULongExtensions.Gpu.cs†L23-L31】 |
 | `ULongExtensions.MulMod64Gpu` | Marked obsolete; migrate to `ULongExtensions.GpuCompatibleMulModSimplifiedExtension` for GPU-compatible host code or `GpuUInt128.MulMod` when running inside kernels.【F:PerfectNumbers.Core/ULongExtensions.Gpu.cs†L17-L24】 |
-| `ULongExtensions.Pow2ModWindowedGpu` | Migrated to call `MulMod64` for every square and multiply, eliminating the 6–18× slowdown that the shim introduced while executing on the host.【F:PerfectNumbers.Core/ULongExtensions.Gpu.cs†L39-L109】 |
-| `ULongExtensions.InitializeStandardOddPowers` | Populates the odd-power table through `MulMod64`, so the host setup costs now match the CPU benchmark baseline.【F:PerfectNumbers.Core/ULongExtensions.Gpu.cs†L286-L309】 |
+| `ULongExtensions.Pow2ModWindowedGpu` | Migrated to call `GpuCompatibleMulModSimplifiedExtension` for every square and multiply, eliminating the 6–18× slowdown that the shim introduced while executing on the host and aligning host math with the new production helper.【F:PerfectNumbers.Core/ULongExtensions.Gpu.cs†L39-L109】 |
+| `ULongExtensions.InitializeStandardOddPowers` | Populates the odd-power table through `GpuCompatibleMulModSimplifiedExtension`, so the host setup costs now match the GPU-compatible benchmark winner.【F:PerfectNumbers.Core/ULongExtensions.Gpu.cs†L286-L309】 |
 
 All host-executed `MulMod` operations in the GPU pipeline now target the optimized CPU helper.