Interesting. At least among many Brits, I've got is often a paraphrase for the stative I have in my possession (etc, as in I've got a bike / a new boat / ten minutes to spare / measles ...). When used in the I have obtained (etc, as in I've got this splinter out of my finger at last, where many in the US would prefer 'gotten') sense, it feels like more of a true present perfect. 'I have V-d' in the present perfect usually corresponds loosely to 'I did V'. // I have got to is almost certainly best seen as an idiom (irregular syntax), and best left intact. 'I must.'
– Edwin AshworthOct 22 '20 at 10:31
@EdwinAshworth Don't you think that the "I've got this splinter out of my finger" usage is more like "I have achieved my aim of" rather than "I have obtained"? I think that "I have got (obtained) my ticket for the train up Snowdon" and "I have got (achieved my aim of reaching) [to] the top of Snowdon" are two different usages for the same word. The splinter sentence is more like "I have got (achieved my aim of extracting) the splinter [out of]¦[from] my finger". I don't think that "I have obtained the splinter out of my finger" works at all.
– BoldBenOct 22 '20 at 11:25
@BoldBen Hence the etc; I didn't have space (or time) for three say examples. Space is limited in 'comments', but this question is too basic / overscoped if only asking for 'have got ...' examples, and I haven't got a reference to back my 'consider have got to a lexeme' opinion (though I seem to remember John Lawler addressing this before). hence no 'answer'.
– Edwin AshworthOct 22 '20 at 15:17