a function common to methods of a class

[snippsat]

it has been my understanding that a def somewhere creates a function and that a def inside a class make that function be referenced in that class' methods table. does it work some other way?

It dos not work the way you explain here.
To explain a little that may clear it up.
If want a function inside class then need to use @staticmethod,just a def inside a class make no sense and don't work.
What's make def a method is the use of self.
The reason to use staticmethod is if you have something that could be written as a standalone function (not part of any class),
but you want to keep it within the class because it's somehow semantically related to the class.

import math

class AClass:
    def foo(self):
        '''A method because of self'''
        return 42

    @staticmethod
    def circle_area(r):
        '''
        A normal function knows nothing about the class or instance
        It's still bound to the class and can be called
        '''
        return r ** 2 * math.pi

    def bar():
        '''Make no sense and should not be here'''
        return 99

Usage:

>>> # Do not require a class instance creation
>>> AClass.circle_area(5)
78.53981633974483
>>> 
>>> obj = AClass()
>>> obj.foo()
42
>>> obj.circle_area(5)
78.53981633974483
>>> obj.bar()
Traceback (most recent call last):
  File "<interactive input>", line 1, in <module>
TypeError: bar() takes 0 positional arguments but 1 was given