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RE: How to Know if it's Pure
If you're looking at "All my parents were ..." or "All my parents and grandparents were ..." or "For 259 generations, every ancestor was ..." (which are the sort of statements the OP was after) then you are quite correct, it is not possible to be 100% certain. No matter how many ancestors, for any number of generations, there will always remain a probability that something else lurked and still does.
However, you CAN with 100% certainty, determine the hidden/recessive trait value for some cats based upon their genetic heritage.
If, for example, that determination shows the hidden/recessive for BOTH parents was the shown trait for their box, you are 100% certain that box is "pure". Note: neither parent showed the box's trait .. this is exactly opposite of the OP's Pedigree statements, does NOT require the parents only hide the current true recessive, and does NOT require the box be birthed.
A Simple Example:
Mom1: Genesis Coco III
Mom2: Foxie Salt & Pepper Mask
Dad1: Genesis Diamond III
Dad2: Snowshoe Cream
Box1 (Mom1 x Dad2): Russian White (hiding Snowshoe Cream or better). Therefor Mom1 hides Russian White, exactly, 100% certain.
Box2 (Mom2 x Dad1): Russian White (hiding Foxie Salt & Pepper Mask or better). Therefore Dad1 hides Russian White, exactly, 100% certain.
Box3 (Mom1 x Dad1): Russian White (hiding Russian White). Box3 is proven "pure" with 100% certainty. Russian White is NOT the current True Recessive. All ancestors are Starters. NONE of the ancestors show Russian White.
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