ALM's and ALR's
Among all the chps, the initialed ones form an interesting subset. And within the init-chps, there are those that have strong correlations with each other. In particular, we see the six ALM chps have various links to the five ALR chps as their sums of the corresponding letters are illustrated in the Fig. via the top and the bottom sums. The counts of ALM's and ALR's in those chps add up to 19874 and 9462 respectively. The first sum simply signifies the inter-relationships that exist between 8, 19, and 74: The 8th prime is 19, which itself is mentioned only in chp 74. The ALR sum 9462 relates to both groups via its components 94 and 62. The five ALR chps 10, 11, 12, 14, and 15 add up to 62. Their verses add up to 494 = 19 × 26. And in chp 26 there are 94 init-letters "S". Moreover, 94 links with the digit sums of the individual counts as we see in more details below.
The correspondence between these two sets of chps becomes more apparent if we look at the components of the individual letter-counts. In the first sum we have the counts 8945, 6493, and 4436. From the second set we have 5073, 3294, and 1095. We may break these into their components 89, 45, 64, 93, 44, 36, 50, 73, 32, 94, 10, and 95. We also notice the two partial sums 6493 + 4436 = 10929 from the top sum in the Fig. (the L + M sum), and the 3294 + 1095 = 4389 = 19 × 231, (231 is the gematric value of ALR), from the bottom sum (the L + R sum). Here, we immediately recognize several important ties between the components and the partial sums: Chp 10 has 109 verses which itself is the 29th prime and chp 43 has 89 verses. The 10th ord (see Glossary) is 19, the 19th ord is 36, the 36th ord is 64, and the 64th ord is 93 as shown with the solid and dotted arrows on the top sum. The 44th ord is 73, chp 50 has 45 verses, and the 45th ord is 74 as illustrated by various upward/downward pointing arrows and the top long solid arrow. We also notice 95 is linked to 8 via its verses. Furthermore, the 32nd ord is 60 and the 60th ord is 89. And 60 itself has 13 verses which ties it up with 43 again. More on the relationships between 874 and 4389 can be found here.
The counts of the letters A, L, M, and R show additional ties when we take into account the sums of their digits as illustrated via the two smaller sums (pointed to by the DS dotted arrows). The ALM digit-sum (DS) on the left is 65, and on the right is 29, with their sum 94. The corresponding DS for the ALR has the left and right sums 48 and 21 which add up to 69. Again, here, we observe several interesting relationships. We notice that 21st ord is 48, which itself has 29 verses and 29 has 69 verses along with 94 being the 65th ord.
The six ALM chps form several smaller subsets with mutually inter-related letter counts. The digits of the A, L, and M counts in chps 2 and 3 add up to 35 and 46 respectively. Here, we recognize the hint of chp 46 and its 35 verses. The occurrence of this pair is not totally unexpected, since, they both indirectly point back to 74: chp 35 has 45 verses and as we saw earlier 45 pointing to 74. And 46 × 19 = 874. The sum 46 + 35 = 81 also has tie-in with the L-count 1892 in chp 3. The mirror opposite of this is 2981 which reveals that link between 81 and its 29 verses. The verses from 29 to 81 equals the ALR count in chps 10 and 11, 2489. More on this is covered here.
The remaining four chps 29, 30, 31, and 32 have their ALM counts add up to 4313 = 19 × 227, which hints at 13 and its 43 verses. The reference to 13 may actually point to the ALM counts of 2 and 3. From 1 to 13 there are 819 free verses. And 19 × 819 is the sum of the ALM's of chps 2 and 3. We also encountered 26 above in reference to its 94 "S"'s. Here, it's indirectly pointed to via its 227 verses. It is also the number of init-letters "Saad" in chp 19. These four chps may further be divided into two pairs (29, 31), and (30, 32) where, within each pair, the members share a common property. The digit-sum of the ALM counts for chps 29 and 31 is 43 each. Similarly, the sum for each chp in the second pair is 39, which happens to be of ord 19.
The links between the two initialed sets are not restricted just to their respective counts of the init-letters or their DS. There's a strong correlation between these two groups on one hand, and the normal/free verses on the other. We saw the mutual connections between 8, 19, and 74. Now, we can pin down additional paths between them: The set :8 of all verses numbered 8, we notice 74 of them are FV's. Similarly, :74 has 19 FV's, and :19 has 56 FV's. And of course, 56 is the verses of chp 74!
The individual counts of the two sums in the Fig. also interact with each other bearing additional and deeper links with some other components. Consider the A's and the L's counts 8945 and 6493. Their difference is 2452 affirming 52 as the 24th ord. We already notice that 24 itself is the 13th ord and that 24th ord is 43 and 89 is the 24th prime. As a side note, from 13 to 52 there are 40 chps and 2346 FV's! We recognize this number, since, it's the number of verses from 1 to 19! And the 40th ord is 69, which itself has 52 verses. Furthermore, 2413 = 19 × 127 is the sum of the GV's in chp 10.
Earlier we saw 10929 in relation to the partial sum 6493 with 4436 from the top sum. We note, 109 is the verses of chp 10 and itself is of ord 80. Furthermore, 80109 is the total gematric of the ALR's in chp 10!!! Additionally, from 10 to 80 there are 4436 verses! The six ALM chps add up to 127 which happens to be the verses of chp 9. Chp 52 has 49 verses which is also the number of GV's in chp 10. And it so happens that 2452 is also the number of FV's from 9 to 49! Additionally, the R-count 1095 from the bottom sum is also the sum of the GV's in chp 29! The L-count 6493 from the ALM sum further interacts with the ALR sum 9462 to bring forth yet another tie to chp 29 and its verses 69; 9462 − 6493 = 2969. Since, both 64 and 69 appear in these counts and partial sums, it may serve as a hint that further link may exists between them. We recall that 64 is the number of verses of chp 24 and with that in mind we may put down the following relationship: 9462 − 2464 = 6998, where 98 is of ord 69 and also is the verses of chp 19.
The individual elements in the two ALM and ALR sums have broader significance in relation to each other than merely providing divisible sums. We've seen so far how their partial sums and differences provided links to diverse and disparate results. For instance, the A-count 5073 = 19 × 267 points indirectly to 1709, the gematirc sum of the 14 init-sets, which happens to be the 267th prime. We also note 8945 − 4389 = 4556, where we see 56, the verses of 74, itself of ord 45. And to top it off, from 1 to 56 there are 5073 verses!!! The 18 ALM counts further divide themselves into smaller subsets which are separately divisible. For instance, the 8 even counts and the 10 odd counts are themselves divisible. From the odd set, there are 6 prime ones which add up to 4864 = 19 × 256. It's noteworthy that the digit 6 does not appear anywhere in the 18 ALM counts! The prime counts interact with the ALR's of chp 10, 11, and 12 in that 2489 + 2375 = 4864. Similarly, 4864 + 798 = 5662, relating init-counts of chp 19 to that of chp 3.