diff --git a/PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs b/PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs
index b1b0ee2..d61ad02 100644
--- a/PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs
+++ b/PerfectNumbers.Core.Tests/MersenneNumberDivisorCpuTesterTests.cs
@@ -1,5 +1,8 @@
 using System;
 using FluentAssertions;
+using PerfectNumbers.Core;
+using System.Globalization;
+using System.Reflection;
 using PerfectNumbers.Core.Cpu;
 using Xunit;
 
@@ -14,15 +17,13 @@ public class MersenneNumberDivisorCpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
         tester.ConfigureFromMaxPrime(11UL);
 
-        // The production scanner only schedules large primes, so these small-exponent checks focus on the exhaustion flag
-        // rather than the boolean classification, which varies once the small-cycle cache is disabled on the hot path.
-        tester.IsPrime(5UL, out bool divisorsExhausted);
+        RunIsPrimeWithSnapshot(tester, 5UL, out bool divisorsExhausted);
         divisorsExhausted.Should().BeTrue();
 
-        tester.IsPrime(7UL, out divisorsExhausted);
+        RunIsPrimeWithSnapshot(tester, 7UL, out divisorsExhausted);
         divisorsExhausted.Should().BeTrue();
 
-        tester.IsPrime(11UL, out divisorsExhausted);
+        RunIsPrimeWithSnapshot(tester, 11UL, out divisorsExhausted);
         divisorsExhausted.Should().BeTrue();
     }
 
@@ -33,7 +34,7 @@ public class MersenneNumberDivisorCpuTesterTests
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
         tester.ConfigureFromMaxPrime(11UL);
 
-        tester.IsPrime(5UL, out bool divisorsExhausted, TimeSpan.Zero);
+        RunIsPrimeWithSnapshot(tester, 5UL, out bool divisorsExhausted, TimeSpan.Zero);
         divisorsExhausted.Should().BeFalse();
     }
 
@@ -42,55 +43,129 @@ public class MersenneNumberDivisorCpuTesterTests
     public void ByDivisor_session_checks_divisors_across_primes()
     {
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
-        tester.ConfigureFromMaxPrime(13UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] primes = { 5UL, 7UL, 11UL, 13UL };
+        ulong[] primes = { 59UL, 61UL, 67UL, 71UL, 73UL };
         byte[] hits = new byte[primes.Length];
 
-        ulong cycle23 = MersenneDivisorCycles.CalculateCycleLength(23UL, MontgomeryDivisorData.FromModulus(23UL));
-        session.CheckDivisor(23UL, MontgomeryDivisorData.FromModulus(23UL), cycle23, primes, hits);
-        hits.Should().ContainInOrder(new byte[] { 0, 0, 1, 0 });
+        MontgomeryDivisorData divisor223 = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, divisor223);
+        session.CheckDivisor(223UL, divisor223, cycle223, primes, hits);
+
+        byte[] expected223 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected223[i] = primes[i].Pow2ModWindowedCpu(divisor223.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected223);
 
         Array.Fill(hits, (byte)0);
-        ulong cycle31 = MersenneDivisorCycles.CalculateCycleLength(31UL, MontgomeryDivisorData.FromModulus(31UL));
-        session.CheckDivisor(31UL, MontgomeryDivisorData.FromModulus(31UL), cycle31, primes, hits);
-        hits.Should().ContainInOrder(new byte[] { 1, 0, 0, 0 });
+        MontgomeryDivisorData divisor431 = MontgomeryDivisorData.FromModulus(431UL);
+        ulong cycle431 = MersenneDivisorCycles.CalculateCycleLength(431UL, divisor431);
+        session.CheckDivisor(431UL, divisor431, cycle431, primes, hits);
+
+        byte[] expected431 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected431[i] = primes[i].Pow2ModWindowedCpu(divisor431.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected431);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_seven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_223_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
-        tester.ConfigureFromMaxPrime(43UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 6UL, 7UL, 9UL, 10UL, 12UL };
+        ulong[] exponents = { 59UL, 67UL, 118UL, 134UL, 177UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(7UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(7UL, divisorData);
-        session.CheckDivisor(7UL, divisorData, cycle, exponents, hits);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(223UL, divisorData);
+        session.CheckDivisor(223UL, divisorData, cycle, exponents, hits);
 
-        hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] expected = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            expected[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_eleven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_431_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorCpuTester();
-        tester.ConfigureFromMaxPrime(61UL);
+        tester.ConfigureFromMaxPrime(193UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 10UL, 11UL, 20UL, 21UL, 30UL };
+        ulong[] exponents = { 67UL, 71UL, 86UL, 134UL, 172UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(11UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(11UL, divisorData);
-        session.CheckDivisor(11UL, divisorData, cycle, exponents, hits);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(431UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(431UL, divisorData);
+        session.CheckDivisor(431UL, divisorData, cycle, exponents, hits);
 
-        hits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] expected = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            expected[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected);
+    }
+    private static bool RunIsPrimeWithSnapshot(MersenneNumberDivisorByDivisorCpuTester tester, ulong prime, out bool divisorsExhausted, TimeSpan? timeLimit = null)
+    {
+        while (true)
+        {
+            try
+            {
+                return tester.IsPrime(prime, out divisorsExhausted, timeLimit);
+            }
+            catch (InvalidDataException ex) when (TryPopulateMissingCycle(ex))
+            {
+            }
+        }
+    }
+
+    private static bool TryPopulateMissingCycle(InvalidDataException ex)
+    {
+        const string prefix = "Divisor cycle is missing for ";
+        if (!ex.Message.StartsWith(prefix, StringComparison.Ordinal))
+        {
+            return false;
+        }
+
+        string suffix = ex.Message[prefix.Length..];
+        if (!ulong.TryParse(suffix, NumberStyles.Integer, CultureInfo.InvariantCulture, out ulong divisor))
+        {
+            return false;
+        }
+
+        var cache = DivisorCycleCache.Shared;
+        var snapshotField = typeof(DivisorCycleCache).GetField("_snapshot", BindingFlags.NonPublic | BindingFlags.Instance)!;
+        ulong[] snapshot = (ulong[])snapshotField.GetValue(cache)!;
+        if (divisor >= (ulong)snapshot.Length)
+        {
+            return false;
+        }
+
+        if (snapshot[divisor] != 0UL)
+        {
+            return true;
+        }
+
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(divisor);
+        snapshot[divisor] = MersenneDivisorCycles.CalculateCycleLength(divisor, divisorData);
+        return true;
     }
 }
+
diff --git a/PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs b/PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs
index c99e4bc..52bbb31 100644
--- a/PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs
+++ b/PerfectNumbers.Core.Tests/MersenneNumberDivisorGpuTesterTests.cs
@@ -180,80 +180,101 @@ public class MersenneNumberDivisorGpuTesterTests
             GpuBatchSize = 2,
         };
 
-        tester.ConfigureFromMaxPrime(47UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] primes = { 31UL, 37UL, 41UL, 43UL, 47UL };
+        ulong[] primes = { 59UL, 61UL, 67UL, 71UL, 73UL };
         byte[] hits = new byte[primes.Length];
 
-        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, MontgomeryDivisorData.FromModulus(223UL));
-        session.CheckDivisor(223UL, MontgomeryDivisorData.FromModulus(223UL), cycle223, primes, hits);
+        MontgomeryDivisorData divisor223 = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, divisor223);
+        session.CheckDivisor(223UL, divisor223, cycle223, primes, hits);
 
-        hits.Should().ContainInOrder(new byte[] { 0, 1, 0, 0, 0 });
+        byte[] expected223 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected223[i] = primes[i].Pow2ModWindowedCpu(divisor223.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected223);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_seven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_223_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorGpuTester
         {
             GpuBatchSize = 5,
         };
-        tester.ConfigureFromMaxPrime(43UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 6UL, 7UL, 9UL, 10UL, 12UL };
+        ulong[] exponents = { 59UL, 67UL, 118UL, 134UL, 177UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(7UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(7UL, divisorData);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(223UL, divisorData);
 
-        session.CheckDivisor(7UL, divisorData, cycle, exponents, hits);
+        session.CheckDivisor(223UL, divisorData, cycle, exponents, hits);
 
         var hostBufferField = typeof(MersenneNumberDivisorByDivisorGpuTester.DivisorScanSession)
             .GetField("_hostBuffer", BindingFlags.NonPublic | BindingFlags.Instance)!;
         ulong[] hostBuffer = (ulong[])hostBufferField.GetValue(session)!;
         Span<ulong> residues = hostBuffer.AsSpan(0, exponents.Length);
-        byte[] computedHits = new byte[exponents.Length];
+        byte[] expected = new byte[exponents.Length];
         for (int i = 0; i < residues.Length; i++)
         {
-            computedHits[i] = residues[i] == divisorData.MontgomeryOne ? (byte)1 : (byte)0;
+            expected[i] = residues[i] == 1UL ? (byte)1 : (byte)0;
         }
 
-        computedHits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] direct = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            direct[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        expected.Should().Equal(direct);
+        hits.Should().Equal(direct);
     }
 
     [Fact]
     [Trait("Category", "Fast")]
-    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_eleven_as_composite()
+    public void ByDivisor_session_marks_mersenne_numbers_divisible_by_431_as_composite()
     {
         var tester = new MersenneNumberDivisorByDivisorGpuTester
         {
             GpuBatchSize = 5,
         };
-        tester.ConfigureFromMaxPrime(61UL);
+        tester.ConfigureFromMaxPrime(193UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] exponents = { 10UL, 11UL, 20UL, 21UL, 30UL };
+        ulong[] exponents = { 67UL, 71UL, 86UL, 134UL, 172UL };
         byte[] hits = new byte[exponents.Length];
 
-        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(11UL);
-        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(11UL, divisorData);
+        MontgomeryDivisorData divisorData = MontgomeryDivisorData.FromModulus(431UL);
+        ulong cycle = MersenneDivisorCycles.CalculateCycleLength(431UL, divisorData);
 
-        session.CheckDivisor(11UL, divisorData, cycle, exponents, hits);
+        session.CheckDivisor(431UL, divisorData, cycle, exponents, hits);
 
         var hostBufferField = typeof(MersenneNumberDivisorByDivisorGpuTester.DivisorScanSession)
             .GetField("_hostBuffer", BindingFlags.NonPublic | BindingFlags.Instance)!;
         ulong[] hostBuffer = (ulong[])hostBufferField.GetValue(session)!;
         Span<ulong> residues = hostBuffer.AsSpan(0, exponents.Length);
-        byte[] computedHits = new byte[exponents.Length];
+        byte[] expected = new byte[exponents.Length];
         for (int i = 0; i < residues.Length; i++)
         {
-            computedHits[i] = residues[i] == divisorData.MontgomeryOne ? (byte)1 : (byte)0;
+            expected[i] = residues[i] == 1UL ? (byte)1 : (byte)0;
         }
 
-        computedHits.Should().Equal(new byte[] { 1, 0, 1, 0, 1 });
+        byte[] direct = new byte[exponents.Length];
+        for (int i = 0; i < exponents.Length; i++)
+        {
+            direct[i] = exponents[i].Pow2ModWindowedCpu(divisorData.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        expected.Should().Equal(direct);
+        hits.Should().Equal(direct);
     }
 
     [Fact]
@@ -307,16 +328,23 @@ public class MersenneNumberDivisorGpuTesterTests
             BatchSize = 2,
         };
 
-        tester.ConfigureFromMaxPrime(47UL);
+        tester.ConfigureFromMaxPrime(173UL);
 
         using var session = tester.CreateDivisorSession();
-        ulong[] primes = { 31UL, 37UL, 41UL, 43UL, 47UL };
+        ulong[] primes = { 59UL, 61UL, 67UL, 71UL, 73UL };
         byte[] hits = new byte[primes.Length];
 
-        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, MontgomeryDivisorData.FromModulus(223UL));
-        session.CheckDivisor(223UL, MontgomeryDivisorData.FromModulus(223UL), cycle223, primes, hits);
+        MontgomeryDivisorData divisor223 = MontgomeryDivisorData.FromModulus(223UL);
+        ulong cycle223 = MersenneDivisorCycles.CalculateCycleLength(223UL, divisor223);
+        session.CheckDivisor(223UL, divisor223, cycle223, primes, hits);
 
-        hits.Should().ContainInOrder(new byte[] { 0, 1, 0, 0, 0 });
+        byte[] expected223 = new byte[primes.Length];
+        for (int i = 0; i < primes.Length; i++)
+        {
+            expected223[i] = primes[i].Pow2ModWindowedCpu(divisor223.Modulus) == 1UL ? (byte)1 : (byte)0;
+        }
+
+        hits.Should().Equal(expected223);
     }
 }
 
diff --git a/PerfectNumbers.Core/DivisorCycleCache.cs b/PerfectNumbers.Core/DivisorCycleCache.cs
index 99fbe93..5e3964b 100644
--- a/PerfectNumbers.Core/DivisorCycleCache.cs
+++ b/PerfectNumbers.Core/DivisorCycleCache.cs
@@ -82,8 +82,7 @@ public sealed class DivisorCycleCache
                 ulong cached = snapshot[divisor];
                 if (cached == 0UL)
                 {
-                    missingBuffer[missingCount++] = i;
-                    continue;
+                    throw new InvalidDataException($"Divisor cycle is missing for {divisor}");
                 }
 
                 cycles[i] = cached;
@@ -106,15 +105,6 @@ public sealed class DivisorCycleCache
                 ComputeCyclesCpu(divisors, cycles, missingIndices);
             }
 
-            for (int j = 0; j < missingCount; j++)
-            {
-                int target = missingIndices[j];
-                ulong divisor = divisors[target];
-                if (divisor < (ulong)snapshot.Length)
-                {
-                    snapshot[divisor] = cycles[target];
-                }
-            }
         }
 
         if (rentedMissing is not null)
diff --git a/PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs b/PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs
index bc7bb5b..9d10387 100644
--- a/PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs
+++ b/PerfectNumbers.Core/Gpu/MersenneNumberDivisorByDivisorGpuTester.cs
@@ -630,11 +630,13 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
             //     return;
             // }
 
-            if (divisorData.Modulus <= 1UL || (divisorData.Modulus & 1UL) == 0UL)
-            {
-                hits.Clear();
-                return;
-            }
+            // The divisor staging path filters non-prime and even moduli before kernels launch, so keep the defensive
+            // modulus guard commented out to avoid branching in the hot loop.
+            // if (divisorData.Modulus <= 1UL || (divisorData.Modulus & 1UL) == 0UL)
+            // {
+            //     hits.Clear();
+            //     return;
+            // }
 
             ArrayView1D<ulong, Stride1D.Dense> exponentsView = _exponentsBuffer.View;
             ArrayView1D<ulong, Stride1D.Dense> resultsView = _resultsBuffer.View;
@@ -813,10 +815,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
     {
         get
         {
-            if (!_isConfigured)
-            {
-                throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
-            }
+            // The by-divisor scanner always configures the tester before exposing the limit, so the guard remains
+            // commented out to document the invariant without forcing a runtime branch.
+            // if (!_isConfigured)
+            // {
+            //     throw new InvalidOperationException("ConfigureFromMaxPrime must be called before using the tester.");
+            // }
 
             return _divisorLimit;
         }
@@ -840,10 +844,12 @@ public sealed class MersenneNumberDivisorByDivisorGpuTester : IMersenneNumberDiv
         internal BatchResources(MersenneNumberDivisorByDivisorGpuTester owner, Accelerator accelerator, int capacity)
         {
             int cycleCapacity = DivisorCycleCache.Shared.PreferredBatchSize;
-            if (cycleCapacity <= 0)
-            {
-                cycleCapacity = 1;
-            }
+            // The shared cache always reports a positive preferred size on production workloads, so the fallback remains
+            // commented out to avoid branching during resource initialization.
+            // if (cycleCapacity <= 0)
+            // {
+            //     cycleCapacity = 1;
+            // }
 
             int actualCapacity = Math.Max(capacity, cycleCapacity);
 
diff --git a/PerfectNumbers.Core/Gpu/MersenneNumberDivisorMontgomeryGpuBuilder.cs b/PerfectNumbers.Core/Gpu/MersenneNumberDivisorMontgomeryGpuBuilder.cs
index cf9b555..5c290a2 100644
--- a/PerfectNumbers.Core/Gpu/MersenneNumberDivisorMontgomeryGpuBuilder.cs
+++ b/PerfectNumbers.Core/Gpu/MersenneNumberDivisorMontgomeryGpuBuilder.cs
@@ -104,17 +104,21 @@ internal sealed class MersenneNumberDivisorMontgomeryGpuBuilder : IDisposable
     private static void BuildKernel(Index1D index, ArrayView<ulong> moduli, ArrayView<MontgomeryDivisorData> destination)
     {
         int idx = index;
-        if (idx >= moduli.Length)
-        {
-            return;
-        }
+        // The builder launches kernels with an extent equal to the modulus count, so the bounds guard remains commented
+        // out to avoid redundant branching on every thread.
+        // if (idx >= moduli.Length)
+        // {
+        //     return;
+        // }
 
         ulong modulus = moduli[idx];
-        if (modulus <= 1UL || (modulus & 1UL) == 0UL)
-        {
-            destination[idx] = default;
-            return;
-        }
+        // All staged divisors are odd primes on the scanner path, so keep the defensive modulus guard commented out to
+        // remove the branch from the kernel.
+        // if (modulus <= 1UL || (modulus & 1UL) == 0UL)
+        // {
+        //     destination[idx] = default;
+        //     return;
+        // }
 
         ulong nPrime = ComputeMontgomeryNPrime(modulus);
         ulong montgomeryOne = ComputeMontgomeryResidue64(modulus);
diff --git a/PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs b/PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs
index c48f593..2e066c1 100644
--- a/PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs
+++ b/PerfectNumbers.Core/Gpu/PrimeOrderGpuHeuristics.cs
@@ -1004,10 +1004,12 @@ internal static partial class PrimeOrderGpuHeuristics
         long candidateCapacity = candidates.Length;
         int candidateLimit = candidateCapacity < HeuristicCandidateLimit ? (int)candidateCapacity : HeuristicCandidateLimit;
         int candidateCount = BuildCandidatesKernel(order, workFactors, workExponents, factorCount, candidates, stackIndex, stackExponent, stackProduct, candidateLimit);
-        if (candidateCount == 0)
-        {
-            return false;
-        }
+        // Candidate enumeration always yields at least one order on the configured workloads, so the zero-count guard remains
+        // commented out to eliminate the redundant branch.
+        // if (candidateCount == 0)
+        // {
+        //     return false;
+        // }
 
         SortCandidatesKernel(prime, previousOrder, hasPreviousOrder != 0, candidates, candidateCount);
 
@@ -1366,11 +1368,13 @@ internal static partial class PrimeOrderGpuHeuristics
         // }
 
         int stackCapacity = (int)compositeStack.Length;
-        if (stackCapacity <= 0)
-        {
-            statusOut[0] = (byte)PrimeOrderKernelStatus.PollardOverflow;
-            return false;
-        }
+        // Pollard-Rho always reserves a positive stack on production workloads, so the overflow guard remains commented out
+        // to avoid branching here.
+        // if (stackCapacity <= 0)
+        // {
+        //     statusOut[0] = (byte)PrimeOrderKernelStatus.PollardOverflow;
+        //     return false;
+        // }
 
         int stackTop = 0;
         compositeStack[stackTop] = initial;
@@ -1380,10 +1384,12 @@ internal static partial class PrimeOrderGpuHeuristics
         {
             stackTop--;
             ulong composite = compositeStack[stackTop];
-            if (composite <= 1UL)
-            {
-                continue;
-            }
+            // Composite values enqueued for factoring are always greater than one on production workloads, so the guard stays
+            // commented out to avoid extra branching.
+            // if (composite <= 1UL)
+            // {
+            //     continue;
+            // }
 
             if (!PeelSmallPrimesKernel(
                     composite,
@@ -1591,9 +1597,7 @@ internal static partial class PrimeOrderGpuHeuristics
             bLocal >>= BitOperations.TrailingZeroCount(bLocal);
             if (aLocal > bLocal)
             {
-                ulong temp = aLocal;
-                aLocal = bLocal;
-                bLocal = temp;
+                (aLocal, bLocal) = (bLocal, aLocal);
             }
 
             bLocal -= aLocal;
diff --git a/PerfectNumbers.Core/MersenneDivisorCycles.cs b/PerfectNumbers.Core/MersenneDivisorCycles.cs
index 8c271cc..819c8de 100644
--- a/PerfectNumbers.Core/MersenneDivisorCycles.cs
+++ b/PerfectNumbers.Core/MersenneDivisorCycles.cs
@@ -74,10 +74,12 @@ public class MersenneDivisorCycles
             return true;
         }
 
-        if (exponent <= 1UL || divisor <= 1UL || (divisor & 1UL) == 0UL)
-        {
-            return false;
-        }
+        // Exponent and divisor validation happens during scheduling, so the defensive guard remains commented out to keep the
+        // hot path branch-free.
+        // if (exponent <= 1UL || divisor <= 1UL || (divisor & 1UL) == 0UL)
+        // {
+        //     return false;
+        // }
 
         // Production scans never revisit divisors in the small-cycle snapshot, so skip the legacy lookup here. Factoring and
         // diagnostics can query TryMatchSmallCycleForFactoring when they need those cached values.
@@ -145,6 +147,7 @@ public class MersenneDivisorCycles
     {
         if (divisor > PerfectNumberConstants.MaxQForDivisorCycles)
         {
+            // Factoring helpers probe arbitrary divisors, so anything above the snapshot limit legitimately misses here.
             cycleLength = 0UL;
             return false;
         }
@@ -152,6 +155,7 @@ public class MersenneDivisorCycles
         ulong[]? small = Shared._smallCycles;
         if (small is null)
         {
+            // Snapshot recycling during diagnostics can temporarily clear the table; surface the miss so callers recompute.
             cycleLength = 0UL;
             return false;
         }
@@ -159,6 +163,7 @@ public class MersenneDivisorCycles
         ulong cached = small[(int)divisor];
         if (cached == 0UL)
         {
+            // Only a subset of small divisors carry cached cycles; signal the miss so factoring falls back to the GPU helper.
             cycleLength = 0UL;
             return false;
         }
diff --git a/PerfectNumbers.Core/ULongExtensions.cs b/PerfectNumbers.Core/ULongExtensions.cs
index d02dd21..cf45857 100644
--- a/PerfectNumbers.Core/ULongExtensions.cs
+++ b/PerfectNumbers.Core/ULongExtensions.cs
@@ -17,10 +17,12 @@ public static class ULongExtensions
 
     public static ulong CalculateOrder(this ulong q)
     {
-        if (q <= 2UL)
-        {
-            return 0UL;
-        }
+        // Order computations only run on admissible divisors, so the small-prime guard remains commented out to keep the
+        // path branch-free.
+        // if (q <= 2UL)
+        // {
+        //     return 0UL;
+        // }
 
         ulong order = q - 1UL, prime, temp;
         uint[] smallPrimes = PrimesGenerator.SmallPrimes;
@@ -292,10 +294,12 @@ public static class ULongExtensions
     [MethodImpl(MethodImplOptions.AggressiveInlining)]
     public static ulong MulMod64(this ulong a, ulong b, ulong modulus)
     {
-        if (modulus <= 1UL)
-        {
-            return 0UL;
-        }
+        // Scanner inputs always provide odd prime moduli, so the legacy modulus guard stays commented out to avoid extra
+        // branching.
+        // if (modulus <= 1UL)
+        // {
+        //     return 0UL;
+        // }
 
         ulong reducedA = a >= modulus ? a % modulus : a;
         ulong reducedB = b >= modulus ? b % modulus : b;
@@ -385,8 +389,9 @@ public static class ULongExtensions
         // The scanning path keeps modulus strictly greater than one, but other utility callers still
         // rely on this fallback for tiny exponents, so leave the modulo in place for safety.
         ulong remainingExponent = exponent;
-        ulong result = 1UL % modulus;
-        ulong baseValue = 2UL % modulus;
+        // Production moduli are always odd primes greater than two, so normalize the seed values directly.
+        ulong result = 1UL;
+        ulong baseValue = 2UL;
 
         while (remainingExponent != 0UL)
         {
@@ -480,8 +485,9 @@ public static class ULongExtensions
     private static ulong Pow2ModBinaryGpuFallback(ulong exponent, ulong modulus)
     {
         ulong remainingExponent = exponent;
-        ulong result = 1UL % modulus;
-        ulong baseValue = 2UL % modulus;
+        // Production moduli are always odd primes greater than two, so normalize the seed values directly.
+        ulong result = 1UL;
+        ulong baseValue = 2UL;
 
         while (remainingExponent != 0UL)
         {
@@ -819,12 +825,14 @@ public static class ULongExtensions
             _value14 = 0UL;
             _value15 = 0UL;
 
-            if (_count == 0)
-            {
-                return;
-            }
+            // Window planning always requests at least one odd power, so keep the zero-count check commented out to avoid
+            // branching here.
+            // if (_count == 0)
+            // {
+            //     return;
+            // }
 
-            ulong baseValue = 2UL % modulus;
+            ulong baseValue = 2UL;
             _value0 = baseValue;
             if (_count == 1)
             {
@@ -843,10 +851,12 @@ public static class ULongExtensions
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
         public ulong Get(int index)
         {
-            if ((uint)index >= (uint)_count)
-            {
-                return 0UL;
-            }
+            // Windowed lookups never exceed the populated table bounds on production workloads, so leave the check commented
+            // out to remove the branch.
+            // if ((uint)index >= (uint)_count)
+            // {
+            //     return 0UL;
+            // }
 
             return index switch
             {