Layout reaffirming chp 9
We've seen many instances where several diverse elements participate to advance a common theme. Likewise, we have a number of chps here as shown whose various characteristics along several paths fittingly reaffirm the verse-count of chp 9. This will serve as a reminder of the intricacy involved and also as an additional evidence of the built-in proof underpinning every aspect of the text.
Across the top arrow the 74 chps from 39 to 112 and their corresponding ords (see Glossary) combine for a sum 9127. We recognize this as the V-link between 9 and 127. Furthermore, 9127 is the 1131st prime and interestingly, this just so happens to be the difference between the 39 chps and their ords from 74 to 112! (the upward pointing arrow on the right). Here, we notice the display of a crosswise symmetry between the two pairs (39, 112) and (74, 112), where, the sums and differences of chps and their ords, respectively, in each pair give rise to a prime and its ordinal position. Also, 1131 is interesting, in that, the 11th prime is 31!
Node 39 itself is of ord 19 (upward arrow on the left), where, between the two, the ords and the chps add up to 919. The two nodes 19 and 74 are accompanied through the intermediate node 82 (middle left-pointing horizontal arrows) as it V-links to 19 and provides further direct references to both 9 and 74; from 74 to 82 the 9 chps and their ords add up to 1143 = 9 × 127! Moreover, the intervening chps and their adjoin verses add up to 19 × 56, where the latter V-links back to 74 (downward arrow on the lower right), and further participates in the lower half of the diagram.
Node 56 at the lower right corner interacts diagonally with 39 where the uninit-chps and their verses give rise to the same product 19 × 56!, (dotted-curved-diagonal arrow). The occurrence of 1143 is interesting in itself since the 11th odd init-chp is 43 and their corresponding ords add up to 127! From 11 to 43, the 21 EP chps and their verses add up to 2192, where 92, 21, 112 form a V-chain. Additionally, 9221 is the 1143rd prime! Node 74 also indirectly interacts with 39 in that from 74:1 to 114 there are 741 = 19 × 39 verses.
Nodes 19 and 56 themselves are joined via an intermediate node 87, which V-links with 19, (upward arrow on the lower left) and correlates with 56 for another interesting feature relating to 9. From 56 to 87 the ords sum is 1362 and this is the number of verses up to 9:127! Remarkably, this is also the sum of the normal verses at norm 39, (dotted curved GVS arrow), from which to 9:127 there are 1273 = 19 × 67 verses spanned across! (dotted arrow in the lower half). Apart from the fact that 67 is the 19th prime, it O-links with 39 and it is the number of GC's from 19 to 112 as well. It may also be written as 38 + 29, signifying the 29 "Saad" count of chp 38.
The link between 9 and 112 is further solidified via the 1452 uninit ENV's between them. Here, we note the V-link between 14 and 52. The latter pair points back toward 9 in a symmetric way as there are 19 chps between the two whose ords are subset of the uninit chps, encompassing 1273 verses. Their corresponding number of adjoin verses is 19 × 68, serving as as an additional confirmation, since, there are 1514 init-verses from 19 to 68, and this is 1273rd composite! Comparatively, the intervening chps from 19 to 39 span out 1904 adjoin verses. This in turn is the norm at 29:69 which coincides with normal verse count 1273!
The three nodes 9, 39 and 74 engage in yet another interlocking relationship serving as an additional confirmation. The complement of the chps from 9 to 39 span 3338 verses across and from 9 to 74 the chps and their verses add up to 7053. The sum 3338 + 7053 = 10391 is the 1273rd prime!