In plain bif scheme there was no PTC (principal tecot) and the two lexors 1 and 9 were constructed ad hoc from a small subset of verses that were not properly mapped. In the (co)bif scheme the PTC was derived from the first principles in line with the derivations of the other tecots. A special set, T, was formed from the two topmost intervals of chps one and nine: T = [1:1 - 1:u] ∪ [9:1 - 9:v], with 1 ≤ u ≤ 7 and 1 ≤ v ≤ 127, where the pair of end-verses (u, v) determines the lengths of the intervals. This set plays the same role as the set of tetrons in the plain bif scheme. The pair (u, v) is suitably chosen to facilitate the bounding of the PTC by the pair of topmost verses, 1:1 and 9:1, just as it is with the other tecots bounded by topmost verses, the tetrons. Of the possible (u, v) pairs, the uniquely chosen (1, 9) leads to intervals of lengths one and nine, resp.: T = [1:1 - 1:1] ∪ [9:1 - 9:9] = {1:1} ∪ {9:1-9} = {1:1, 9:1-9} with ∣T∣ = 10. It contains only one (and the only numbered) tetron.
Once, the special set T is specified, the domain of the B actions is determined as the complement set V = W - T, with W, the set of all numbered verses (no tetrons), split into disjoint blocks, W1 and W9, each separately under the actions of A1 and A9, resp. The (left, right), qupode lexor-pair (1, 9), would then follow from the splitting of the PTC.
Once, the PTC is determined, the derivations of the remaining 56 tecots under the (co)bif scheme proceeds as follows. The adjusted set, V, now contains all numbered verses except for those that appear in the PTC: V = {numbered verses - PTC verses}. The set of tecots is the same as in plain bif: T = {2:0 - 8:0, 10:0 - 114:0}. And W is the total set: W = T ∪ V, as before. The construction of the other tecots is similar to that of the PTC. The procedure begins with the action of A1 on the first tetron, 2:0 in W1, leading to another verse in W1. Under the action of B it is then mapped to a verse in one of W1 or W2 at which point it is acted upon once again by either A1 or A9, accordingly. The process then moves forward alternating between A1/A9 and B until a tetron is reached via A1 or A9 in W1 or W9, resp. resulting in a tecot. The procedure is then repeated in an analogous manner on the remaining next smallest tetron in either W1 or W9 until all the tetrons are accounted for. Under this scheme all verses are covered, in contrast with the plain bif.
The tecots thus obtained would split into symmetric pairs of lexors of opposite handedness. The left/right lexors correspond respectively to the smaller/larger tetrons. The qupode involution is defined as before, as the one-to-one mapping between a pair of verses of opposite handedness symmetrically located in the corresponding pair of lexors.