Well ... latte makkiato ist immer gut! 
I think that the two real h's (of the t's) corresponding to the same b = sqrt(2), this time only with the + sign (sorry, Bo, ... it's the age), i.e. h = 2 and h = 4 must be different indeed. Any ... serious serial development should indeed show this situation. We cannot think that we may start from b = sqrt(2) and than, ... bingo! ... we suddely have two different values. The "strange object" that we may call h or t is the result of the application of a "two-valued function". But, two-valued "functions" are not politically correct animals.
But, perhaps, I don't understand what you precisely said. I didn't sleep well, last night. I shall improve! Tomorrow is another day.
GFR
I think that the two real h's (of the t's) corresponding to the same b = sqrt(2), this time only with the + sign (sorry, Bo, ... it's the age), i.e. h = 2 and h = 4 must be different indeed. Any ... serious serial development should indeed show this situation. We cannot think that we may start from b = sqrt(2) and than, ... bingo! ... we suddely have two different values. The "strange object" that we may call h or t is the result of the application of a "two-valued function". But, two-valued "functions" are not politically correct animals.
But, perhaps, I don't understand what you precisely said. I didn't sleep well, last night. I shall improve! Tomorrow is another day.
GFR