```python
from typing import List

def fork_paths(pattern: str) -> List[str]:
    if not isinstance(pattern, str):
        raise ValueError("Pattern must be a non-empty string")
    
    def is_valid_segment(segment):
        return segment and all(c in "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_-" for c in segment)
    
    def is_valid_option(option):
        return option and all(c in "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_-" for c in option)
    
    def is_valid_fork(fork):
        return fork and all(c in "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_-" for c in fork)
    
    def is_valid_pattern(pattern):
        if not pattern:
            return False
        
        segments = pattern.split("/")
        
        if len(segments) == 0:
            return False
        
        for segment in segments:
            if not is_valid_segment(segment):
                return False
            
            if segment.startswith("{") and segment.endswith("}"):
                options = segment[1:-1].split(",")
                if not all(is_valid_option(option) for option in options):
                    return False
            elif not is_valid_option(segment):
                return False
        
        return True
    
    if not is_valid_pattern(pattern):
        raise ValueError("Pattern must be a non-empty string, an empty segment, an empty option, and a curly brace or comma sitting inside a literal segment or an option")
    
    def expand_fork(fork, path):
        options = fork[1:-1].split(",")
        for option in options:
            new_path = f"{path}/{option}"
            yield new_path
    
    paths = []
    for segment in pattern.split("/"):
        if segment.startswith("{") and segment.endswith("}"):
            for new_path in expand_fork(segment, ""):
                paths.append(new_path)
        else:
            paths.append(segment)
    
    return paths
```