Zod default without making input type optional

[BrendanC23]

I'm looking for a way to have a default value while keeping the input type unchanged. I want the default value to take effect when parse is called, but not when explicitly defining an object using the type.

const schemaWithDefault = z.object({
    a: z.string(),
    b: z.string().default(""),
});

// I want { a: string; b: string; }, not { a: string; b?: string | undefined; }
type SchemaWithDefaultType = z.input<typeof schemaWithDefault>;

const data: unknown = { a: "a" };
const parsedData = schemaWithDefault.parse(data); // .default() works, b is set to "" as expected

const ExplicitlyDefinedType: SchemaWithDefaultType = {
    a: z.string(),
    // I want a TypeScript error because b is not defined
};

I've also looked at catch(), but that makes the input type unknown.

const schemaWithDefault = z.object({
    a: z.string(),
    b: z.string().catch(""),
});

// I want { a: string; b: string; }, not { a: string; b: unknown; }
type SchemaWithDefaultType = z.input<typeof schemaWithDefault>; 

Is there a way to accomplish this?