A precise definition could be:
I think we create a minefield for ourselves as soon as we use the word 'precise."
In general, I have a strong aversion to arguments based on logic, not because logic is bad but because the destination reached by logical steps can vary enormously depending on where you start. The starting point has to be agreed before you can apply the logic sensibly. So I can easily understand why one wants to start with a 'precise' definition.
But the problem here is whether that is a pursuable goal. It is further complicated by the fact that we want here to link it with tedomari and that may also need a precise definition - and that extra goal may or may not be pursuable.
I don't know whether either goal of a precise definition is achievable, but what I do know is that we are starting from a very murky position. I know you don't like me talking about Japanese terms, but that is where 'big point' and 'last big move' come from, and so - if you stick with those terms - you have to have some feel of what raw material consists of.
(Parenthetically, I think we should start afresh with completely new Japanese-free terms based on what AI shows us, but that is probably too far away to sustain our interest at present.)
Oba is a go technical term. It is not at all a common word in ordinary Japanese. Morohashi (a 13-volume dictionary) doesn't even list it. Kojien gives some exotic uses but starts off by giving the sense as "wide place" (okii tokoro) (NB no mention of 'big'). Some Japanese (especially in go) see the adjectival sense as 'important' (NB not 'big'). Some Japanese are not even sure how to read it and say odokoro. Some Japanese go players claim there is a difference between oba and odokoro, the latter having a wider (sic) range.
So we start off with a situation where it vaguely means wide or important to a Japanese but big to English speakers, with different connotations in each case.
And that's only the first word in 'big point.' There's a major problem with 'point', too, since for many that will suggest a precise intersection. It should be area or place.
Since oba is a technical term, though, we might expect a definition. Yet even the great Kido editor Hayashi Yutaka ducked that, and instead quoted Segoe Kensaku (who wrote in the days when pros wrote their own stuff).
This is what Segoe said (I use the term 'big point' because we are stuck with it, not because I think it's accurate):
1. Big points occur in the early opening and are then often the vantage points on the four sides.
2. Big points often mean extending to the limit – that is, five spaces – along the side.
3. In cases where friendly and enemy corner positions face each other, the central points between them on the side are often big points.
4. In cases where there are friendly spheres of influence in two adjacent corners, the central points between them are often big points.
5. An extension, even if it is a narrow one, which prevents expansion by the opponent and/or creates a weak, floating group may be superior to a big point.
6. When invading the opponent’s sphere of influence, try to choose moves that allow two-space extensions to left and right, or above and below.
Note that he uses locutions such as "often" and there is a general woolliness about the whole list. Other writers add to this woolliness by claiming that an oba has to be on the 3rd or 4th lines. There are others who like to use the term yoten (key point or vantage point), which is often preferred when a precise point for both players applies. Yet others like to throw in the historical phrase Tennozan, which adds quite a few connotations for Japanese people. Furthermore, for some Japanese writers these are all terms for use in the fuseki. Other writers freely use them late in the game (e.g. in Shuei's Games the commented occurrences occur on move 30, 36, 60, 86, 60, 72, 9, 17, 25, 25, 20, 99, 46, 112, 11, 38, 7, 107, 63, 19, 8, 13 and 16).
And all that is before we even get onto tedomari, which is equally woolly and (in my opinion) rather more common in English in Japanese because of much greater interest in counting and the endgame than you see in Japanese. An extra dimension we need to assess there, therefore, is whether that extra interest is actually justified. Bill's comments seem to suggest it really is questionable, which I imagine will come as a shock to many
For those who do wish to pursue a definition of tedomari, however, I will mention that (a) it can have the meaning of simply 'the final move or moves in the endgame' and (b) one common definition, as in a Nihon Ki-in dictionary, in Japanese is "a good point [ten] or odokoro which is left over." There is no mention of oba directly (and that Nihon Ki-in dictionary is one of the sources that distinguishes odokoro as having a wider sense than oba). Again, all the associations and connotations change depending on where you start from.
Some people enjoy tinkering and will want to try to sort that mess out. I personally don't agree with that approach when the situation is as messy as it is here. Others (and I'm one) will believe the best approach is to rip out all the old rotten woodwork and start again.
As a thought experiment, let us start with a new term for oba. Let me propose 'major area'. That sounds awful but (a) it captures the main meanings and (b) as a slightly unusual phrase it is not yet bound up with existing associations - and in particular it gets rid of the 'size' connotation.
If we then look at the SL pages in that 'corrected' light, the theme of the page for the tedomari example would become something like "how to get the last major area." It still wouldn't be a good page because it still lacks the "how to" element, but then Dieter's LZ counter-example would suddenly makes sense (the 3-3 invasion is in a 'major area'). It doesn't actually help the example page itself, of course. It would just show it is plain wrong and so should be deleted (or perhaps left as an example of human pro fallibility).
But that would entrain going back into higher-level pages in SL and re-writing them (perhaps too problematical on Japanese-based pages).
A better approach, in my view, is to start afresh with brand-new English-based terms and to derive definitions based on AI examples. It may be that that is not practical yet, but I think Gomoto's technique could be promising. AS far as I can see, most people here (including me) have concentrated on looking at whole-board, whole-game positions but he seems be the only one that has reported looking at some common local shapes, and to have already found some significant human/AI differences. That may not yet lead us to a new definition to replace oba or tedomari, but it may be the way to get a handle on the way to proceed.
The bots in particular think that one class of big plays, those on the side, are not only generally worth less than other big plays, such as occupying an empty corner, they are worth less than plays that have not previously struck humans as urgent. (And the last big play is very likely to be one of the second tier big plays on the side.) There is at least one book here, and books will be written, but it will take at least a few years before we see one, I think.