According to the Rambam that the tekhelet strand if only half-dyed, where exactly should the halfway-mark (or, in the strings I've seen, the transition portion) fall? Should it be up against the hole in the garment through which it is threaded (as is apparent in the diagrams put out by the Tekhelet Institute)? Should the tekhelet portion only begin in the first knot? Or should it only begin with the first tekhelet chulyah (as is perhaps implied by those who say the core should always be lavan according to the Rambam)?
How are the tzitzit made? One begins from the corner of a garment - i.e., the end of its woven portion. One ascends upward no more than three fingerbreadths from the edge, but no less than the distance from the knuckle of the thumb to its end.
[A hole is made] and four strands inserted, [causing them] to be folded in half. Thus, there will be eight strands hanging down from the corner. These eight strands must be at least four fingerbreadths long. If they are longer - even if they are a cubit or two long - it is acceptable. The term "fingerbreadth" refers to a thumbbreadth.
One of the eight strands should be techelet; the other seven should be white.
Hil. Ssissith 1:6
The tekheleth strand is one of the threads hanging off the corner of the garment. It is the hole that divides the strand into two strands "hanging down from the corner." Therefore, the tekheleth goes right up to the hole.