"Game state" in Magic

One easily gets the impression that the Comprehensive Rules of Magic: The Gathering read like a legal document that defines the game with mathematical precision, to the utmost detail. However, this isn't always so.

One particular example is the concept of "game state". This term is used many times in the rules but, quite surprisingly, is not defined anywhere, not even vaguely or in passing. The exact definition of the concept can become important especially when the rules talk about "the same game state" (ie. when the "game state" is the "same" before and after an event.)

Practical example: Assume that it's your turn and you have a combo that allows you to increase the power of a creature without limit, and your opponent has a combo that allows them gaining an unlimited amount of life. If you say "I increase the power of my creature by a million", your opponent may respond to it with "I gain two million life". Are you then allowed to further increase the power of your creature (thus allowing your opponent to further increase their life total and so on, potentially ad infinitum)?

The answer is no: You can't repeat this process forever. The following rule forbids it from being continued:

716.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.

This means that you cannot further increase the power of your creature (at least not without doing something else first.) Note, however, the bolded part.

Surprisingly, the concept "the same game state" is not explicitly defined anywhere in the rules.

It cannot mean "the game state is identical" because in this particular example it's not: The power of a creature has changed, as well as the life total of a player. Clearly something has changed, and thus the game state is not identical to what it was before. However, officially this rule still applies to this situation (and thus you are not allowed to repeat the combo before doing something else first.)

So what does "the same game state" mean? It's undefined by the rules, and therefore up to a judge to decide. One can come up with an intuitive definition (ie. something that the people who wrote that rule probably had in mind), but this is nevertheless up to a judge to decide.