diff --git a/CLAUDE.md b/CLAUDE.md
index 993b10f193..d12fa8b9ab 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -415,3 +415,7 @@ When adding or editing PHPDoc comments in this codebase, follow these guidelines
 ### Ternary expression type narrowing in TypeSpecifier
 
 `TypeSpecifier::specifyTypesInCondition()` handles ternary expressions (`$cond ? $a : $b`) for type narrowing. In a truthy context (e.g., inside `assert()`), the ternary is semantically equivalent to `($cond && $a) || (!$cond && $b)` — meaning if the condition is true, the "if" branch must be truthy, and if false, the "else" branch must be truthy. The fix converts ternary expressions to this `BooleanOr(BooleanAnd(...), BooleanAnd(...))` form so the existing OR/AND narrowing logic handles both branches correctly. This enables `assert($cond ? $x instanceof A : $x instanceof B)` to narrow `$x` to `A|B`. The `AssertFunctionTypeSpecifyingExtension` calls `specifyTypesInCondition` with `TypeSpecifierContext::createTruthy()` context for the assert argument.
+
+### DummyMethodReflection wrapping and HasMethodType-resolved methods
+
+When `method_exists($this, 'foo')` narrows a variable's type, `HasMethodType('foo')` is added as an accessory type via intersection. The `HasMethodType::getMethod()` returns a `DummyMethodReflection` whose `getDeclaringClass()` returns `stdClass`. When this method reflection is used through `IntersectionType::getMethod()`, it gets wrapped in `ChangedTypeMethodReflection` (via `CallbackUnresolvedMethodPrototypeReflection`) and then `ResolvedMethodReflection`. Neither wrapper exposes the inner reflection, but the declaring class remains `stdClass`. Rules that check `$declaringClass->hasNativeMethod()` (like `MethodCallableRule` and `StaticMethodCallableRule`) must handle this case: when `$declaringClass->getName() === stdClass::class` and `$declaringClass->hasMethod($methodName)` is `false`, the method was resolved through `HasMethodType` and should not be treated as a non-native `@method` PHPDoc method. Note: `ClassReflection::hasMethod()` returns `bool`, not `TrinaryLogic`.
diff --git a/src/Rules/Methods/MethodCallableRule.php b/src/Rules/Methods/MethodCallableRule.php
index 395089046f..26668b2b99 100644
--- a/src/Rules/Methods/MethodCallableRule.php
+++ b/src/Rules/Methods/MethodCallableRule.php
@@ -10,6 +10,7 @@
 use PHPStan\Php\PhpVersion;
 use PHPStan\Rules\Rule;
 use PHPStan\Rules\RuleErrorBuilder;
+use stdClass;
 use function sprintf;
 
 /**
@@ -56,6 +57,10 @@ public function processNode(Node $node, Scope $scope): array
 			return $errors;
 		}
 
+		if ($declaringClass->getName() === stdClass::class && !$declaringClass->hasMethod($methodNameName)) {
+			return $errors;
+		}
+
 		$messagesMethodName = SprintfHelper::escapeFormatString($declaringClass->getDisplayName() . '::' . $methodReflection->getName() . '()');
 
 		$errors[] = RuleErrorBuilder::message(sprintf('Creating callable from a non-native method %s.', $messagesMethodName))
diff --git a/src/Rules/Methods/StaticMethodCallableRule.php b/src/Rules/Methods/StaticMethodCallableRule.php
index e1b33d1321..b31f008db4 100644
--- a/src/Rules/Methods/StaticMethodCallableRule.php
+++ b/src/Rules/Methods/StaticMethodCallableRule.php
@@ -10,6 +10,7 @@
 use PHPStan\Php\PhpVersion;
 use PHPStan\Rules\Rule;
 use PHPStan\Rules\RuleErrorBuilder;
+use stdClass;
 use function sprintf;
 
 /**
@@ -56,6 +57,10 @@ public function processNode(Node $node, Scope $scope): array
 			return $errors;
 		}
 
+		if ($declaringClass->getName() === stdClass::class && !$declaringClass->hasMethod($methodNameName)) {
+			return $errors;
+		}
+
 		$messagesMethodName = SprintfHelper::escapeFormatString($declaringClass->getDisplayName() . '::' . $methodReflection->getName() . '()');
 
 		$errors[] = RuleErrorBuilder::message(sprintf('Creating callable from a non-native static method %s.', $messagesMethodName))
diff --git a/tests/PHPStan/Rules/Methods/MethodCallableRuleTest.php b/tests/PHPStan/Rules/Methods/MethodCallableRuleTest.php
index 6dcf45e242..60511e6b15 100644
--- a/tests/PHPStan/Rules/Methods/MethodCallableRuleTest.php
+++ b/tests/PHPStan/Rules/Methods/MethodCallableRuleTest.php
@@ -39,6 +39,12 @@ public function testNotSupportedOnOlderVersions(): void
 		]);
 	}
 
+	#[RequiresPhp('>= 8.1')]
+	public function testBug13596(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-13596.php'], []);
+	}
+
 	#[RequiresPhp('>= 8.1')]
 	public function testRule(): void
 	{
diff --git a/tests/PHPStan/Rules/Methods/data/bug-13596.php b/tests/PHPStan/Rules/Methods/data/bug-13596.php
new file mode 100644
index 0000000000..f633248c0c
--- /dev/null
+++ b/tests/PHPStan/Rules/Methods/data/bug-13596.php
@@ -0,0 +1,31 @@
+<?php // lint >= 8.1
+
+namespace Bug13596;
+
+use Closure;
+
+class BaseClass
+{
+	public function getCallable(): ?Closure
+	{
+		return method_exists($this, 'myCallable') ? $this->myCallable(...) : null;
+	}
+
+	public function getCallableWithIsCallable(): ?Closure
+	{
+		return is_callable([$this, 'myCallable']) ? $this->myCallable(...) : null;
+	}
+}
+
+class ChildOne extends BaseClass
+{
+	//
+}
+
+class ChildTwo extends BaseClass
+{
+	public function myCallable(): string
+	{
+		return 'I exist on child two.';
+	}
+}