The introduction of cobiflection (cobif), the dual of biflection (bif), led to the derivation of the dual tecot, (consisting of chps), and concluded with the pair of left and right colexors, 1 and 9, resp. The colexors, (consisting of 57 chaps, each), serve as the dual notion of lexors. They provide the mechanism to construct the (1, 9)-tecot directly from the first principles, analogous to the derivations of the other tecots, that was previously unattainable. Unlike other tecots that are bounded by pairs of tetrons, the (1, 9)-tecot is unique as it contains only one (numbered) tetron. It will be referred to as the Principal Tecot or PTC, thereafter. The subsequent splitting of PTC into the qupode-pair, lexors 1 and 9, brings into completion the analogy between chps and lexors.
The (co)bif scheme proceeds, similarly, with the mirrors acting on the disjoint subsets of verses, but now, subject to the added constraint dictated by the presence of the pair of colexors. In particular, each colexor is to be preserved under the reflections by one of the mirrors, A. This implies that each colexor remains closed under the actions of A. Specifically, the verses within the chps in colexor 1 are reflected under A to other verses within the same or different chps but still in colexor 1, and likewise in colexor 9. This is achieved via mirror A splitting into two mirrors, A1 and A9, which would, then, act independently on the two colexors 1 and 9, resp. Mirror B, on the other hand, operates exactly as before with no additional constraints. Since, it acts globally, it allows for interactions between the two colexors that would have remained closed off, otherwise.
The derivation of the PTC proceeds along the lines similar to that of the other tecots. Recall, under plain bif, the adjoin set W (the set of all verses) was acted by A, and, the set of numbered verses V, similarly acted by B. The special set T, (the tetrons), was excluded from the B actions. Since, there are no unnumbered (0-numbered) verses in PTC, (the tetrons bound all other tecots), the set W, now, consists exclusively of the numbered verses. The set V is, then, formed via the exclusion of an appropriately constructed special set. The invariance of the colexors 1 and 9 under A in the (co)bif scheme called for splitting of A into A1 and A9, acting independently on colexors 1 and 9, resp. Accordingly, the set of verses, W, splits into similarly disjoint blocks: W = W1 ∪ W9, where the two subsets W1 and W2 correspond to the disjoint sets of verses of chapters in the colexor 1 and 9, resp. The colexors are preserved under A when A1 and A2 act on their respective blocks W1 and W2.
The special set, T, to be excluded from W is accordingly defined to resemble the set of tetrons. The construction of T draws on the general structure of chps. All chps (with the exception of 1 and 9) share a common form: a title, followed by a (0-numbered) tetron, then the verses 1, 2, 3, etc. Consequently, the tetrons are the topmost verses, (vacuously true for chps 1 and 9). Since, the two chps 1 and 9 occupy a special place among all chps, (they are to chps as tetrons are to verses), their verses will, subsequently, be treated differently. A subset of the verses consisting of a pair of topmost intervals from these two chps is suitably chosen to serve as the special set: T = [1:1 - 1:u] ∪ [9:1 - 9:v], with 1 ≤ u ≤ 7 and 1 ≤ v ≤ 127, with u and v to be determined. The square brackets represent intervals, a range of consecutive verses beginning at 1 and ending at u and v in the two chps 1 and 9, resp. The complement set, V, is then, defined as before, V = W - T.
Since, a tecot is bounded by a pair of left/right tetrons, the PTC is similarly required to be bounded by two topmost verses of opposite handedness; on the left-end by 1:1 and on the right-end by 9:1. The PTC derivation begins with the action of A1 on W1 at the left-end verse 1:1 resulting in another verse in W1. It is then mapped under B to another verse which may be in one of W1 or W9, at which point either A1 or A9 is applied, accordingly, once more, (mapping it to another verse in the same set), proceeding forward alternating between one of A1 or A9 and B resulting in a verse in either W1 or W9 until it reaches the right-end verse 9:1 via A9. This procedure is in clear contrast with the plain bif derivations of the other tecots. There, the special set, T, was known in advance and the bif proceeded with the first left-end (known) tetron until it reached the second, yet known, right-end tetron. Here, it is reversed in that the two left and right end-verses of the PTC are known, (1:1 and 9:1), while, the special set, T, must be chosen accordingly to allow the PTC to begin at 1:1 and end at 9:1.
The two interval-end-verses, 1:u and 9:v, are chosen with the sole requirement that the PTC be bounded with 1:1 and 9:1. There are many such pairs, each leading to a distinct PTC. The preferred one chosen is (u, v) = (1, 9) with the corresponding intervals [1:1 - 1:1], (a singleton), and [9:1 - 9:9], an interval of length 9. The two interval-lengths, 1 and 9, reaffirm the duality between 1 and 9.
The introduction of the two colexors and their subsequent invariance under the (co)bif scheme resolved a shortcoming of the plain bif. Under the plain bif, a small subset of verses at the opposite extreme ends rendered the actions of the two mirrors identical, turning their composition, bif, into a trivial or do-nothing operation (an involution returns to its original state when repeated). As a result, each verse from the subset was mapped back to itself (a trivial operation). This is avoided in the (co)bif scheme, where the subset splits into a pair of disjoint pieces that fall under different partition blocks, W1 and W9, and are acted on by different mirrors, A1 and A9. Since, the actions of A1 and A9 are restricted to their respective blocks, W1 and W2, their compositions with B is nontrivial.