“… as far as I know it can be checked by the numbers of the mold, painting and artist …”

There is no general number database which would allow you to simply enter a code and see who made an item, what pattern name was used, or what the mold was called.

Next to the fact that each company/producer had their own numbering scheme, the displayed information was also not unified, meaning that numbers included could be mold codes, series codes; color codes, painter IDs, batch numbers, or foreman control codes just to name a few. So one would definitely have to know which producer one is looking at in the first place before trying to deduce any other info from the numeric codes applied on the item.