On the transmission of Arabian horse strains and the notion of authenticity

In Arabian horses, strains are traditionally transmitted by the dam. This is how Bedouins did it for about half a millennium, for reasons I discussed elsewhere. Strains, and their transmissions are intimately connected to the concepts of asil/atiq (roughly, authentic) in an Arabian horse. In other words, the daughter of an asil/atiq Hamdaniyah Simriyah and an English Thoroughbred is not a Hamdaniyah Simriyah. She is a hajin, a part-bred, not an Arabian horse. I think there is a universal consensus on that. Now let us assume that this half-Arabian part-bred daughter of the asil/atiq Hamdaniyah Simriyah is bred to an asil/atiq Arabian for one more generation. You still don’t have a Hamdaniyah Simiriyah. You’d still have a hajin, a partbred with 25% Engligh Thoroughbred blood and 75% Arabian blood. One more generation of breeding of this line to an asil/atiq Arabian horse will not get you your Hamdani Simri label back. You’d still have a hajin on your hands, this time with 12.5% Engligh Thoroughbred blood and 87.5% Arabian blood. The consensus on this horse not being an Arabian horse still holds, pretty much across the spectrum of the Arabian horse world. Where the consensus falls apart is on how…