Tomato size
 

Each year I have been lured by the size of tomato fruit. This year I thought all was well until I cut into those large fruit and discovered green streaks running through the fruit. In most cases the entire fruit was wasted.
The one exception has been Berkeley Tie Die. There is no streaking in this fruit.
Next year there will be more of them in the garden.

None of my giants have any green in them,not exactly sure what your issue is.

NAR , Dinner Plate, Giant italian,Anna Russian, not all but many of these above 2 pounds have tuff green seams. They ripened about 2 weeks late but were watered during dry periods. I use 6-24-24 fertilizer twice , upon planting and again mid season.

In my experience, core issues are similar to catfacing, hard shoulders, even blossom end rot are at least partly environmental.

This has been an exceptionally hot, dry summer. I notice all of these problems, as well as heat-related blossom failure. I have tried to maintain even moisture, but the crop this year will be "meh".

A number of years ago we invested in a spremy tomato mill and can a fair amount of juice/pulp. Even the weirdoes make juice/sauce/ etc.

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Probably nutrition related mostly (environmental is also nutrition related at the end of the day, since those factors affect the nutrition). There are definitely some varieties that have a bigger woody core than others, but it's still just the core, not the whole tomato.
Apply fertilizer more often once the fruit starts growing, and with less P. 15-5-30 is a popular 'finisher'. 6-24-24 seems like a strange ratio, especially at the beginning of the season, unless you supplement that to something organic.

Blotch ripening, It is caused by lack of K. You will also see greywall and yellow shoulder with a lack of K

Such core issues have been extremely rare, here. But when I do get them, it's usually a heart of 2 lbs + (which have also been extremely rare). I wonder if the tomato "knows" to produce a larger core, in order for it to remain attached to the stem, to maturity.

You have hit it. Thanks