Self adjoin symmetry
It is readily apparent that the QCD (see Glossary) is not solely based on divisibility alone. We have seen numerous cases so far that demonstrate the existence of an intricate and sophisticated design that governs all the elements and components throughout the book.
One of the special and interesting aspects of the QCD is the case involving the opening verses. Their key distinguishing factor relative to other verses is that they're present in all chps except 1 and 9. In chp 1, it comes as verse 1, rather than as the commonly occurring opening verse. It's entirely absent in chp 9. In chp 27 it appears twice, once as the opening verse, and additionally, inside verse 30, thus, compensating for its absence in chp 9. In all other cases, the tetron's appear as the opening verses and are always unnumbered and thus affect the verse-counts accordingly. The symmetric interplay between the adjoin and the base verses is illustrated above, where we look at the two pairs of chps (21, 49) and (48, 78) in a tight and mutual correspondence that complement each other in an intriguing way.
The chps in each pair are linked to each other through the long horizontal arrows via the spanned intervening verses. The top V-arrow shows the 2147 verses in the 29 chps from 21 to 49, and similarly, the bottom W-arrow links the 1160 adjoin verses of the 31 intermediate chps from 48 to 78. We immediately recognize the mutual symmetry displayed between the two pairs. As indicated by the top arrow, 2147 = 113 × 19, which is the product of the adjoin verses of 21 and 49 (curly W-arrows) respectively! Similarly, 1160 = 29 × 40, which is the product of the verses of 48 and 78 (curly V-arrows) respectively! We notice the reciprocal interplay between the two pairs. The top pair relates the verses spanning between the two chps to the individual adjoin verses of each chp. In contrast, the bottom pair relates the adjoin verses spanned between the two chps to the individual base verse of each chp! Furthermore, chps 48 and 78 are of ords 21 and 49 (vertical U-arrows) respectively.
The interlocking relationship between the two pairs runs deeper as we take a closer look. As mentioned earlier, 29 and 31 chps account for the intervening verses for the two pairs. 29 from the top pair can be cross-linked to the bottom pair readily, since, it's the verses of chp 48. Similar link for 31 can also be established when we consider the components of 2147, (21 and 47), and write down the following: 2147 ± 21 × 47 = 3134, 1160! This reproduces 1160, plus the neat reference to 31 and its 34 verses! Moreover, 3134 is the 2688th composite - a reference to chp 88 and its 26 verses. Additionally, 88 is of ord 59, itself of ord 31. Furthermore, the 26th ord is 45, which itself is the verses of 35. This is also the number of isotupes corresponding to base verses ranging from 26 to 88, which consist of 49 chps and 2516 total number of verses. The latter happens to be the 2147th composite! On a similar note, 2147 itself is the 1822nd composite, providing further links to 49 and 78: chp 49 is of ord 22 and has 18 verses, and 22 has 78 verses! From 21 to 78 we may also establish a link via the latter's 40 verses, which itself is of ord 21.
The count of 31 chps from 48 to 78 is indirectly linked to both 48 and 78. Let's consider these two chps and their verses 29 and 40 respectively (bottom curly arrows) and note the following: 7840 − 4829 = 3011. The 3011th composite is 3501 and that's the number of verses from chp 1 to 31. Chp 31 is of ord 17, which itself has a nice tie-in with the base verses, covered below.
There are 2176 intervening AV's between the two chps in the first pair, and this is the 1849th composite! Similarly, there are 1129 verses between the chps in the second pair. This is also the sum of the 21 chps in the 16 isotupes corresponding to BV's ranging from 34 to 54. Here, we notice the references to 21 and 34. Chp 34 is of ord 16 and also has 54 verses. Chp 54 is of ord 26 and 34 + 54 = 88!
The two pairs (21, 49) and (48, 78) can be derived from the auxiliary pairs (35, 14) and (63, 15), respectively as follows: 35 ± 14 = 49, 21, and 63 ± 15 = 78, 48. We note several points: 35th ord is 63, and 63rd ord is 92, which itself has 21 verses. Additionally, the norm 2192 occurs at verse 40:29!, pointing back to the second pair. Interestingly, 2192 is also the 1864th composite!, where, we see the reference to 64 and its 18 verses. Chp 48 has 29 verses, which itself has 69 verses, and from 48 to 69 the un-init chps and verses also add up to 1864. Furthermore, 19 × 63 is the init-count of chp 14 and likewise, 19 × 48 is the init-count of chp 15! As an interesting side note, 35 is of ord 17, and there are 15 isotupes corresponding to BV's ranging from 17 to 35, whose chps add up to 1763!!!