Revelation

Witnesses And Olive Trees
We know from the book of Zechariah that the two "olive trees" feed the lampstand of God's people with "golden oil" which we now know to be doctrine. The text also talks of a servant of God called "THE BRANCH". However there are indeed two witnesses, so are there two "branches"? The OT text would appear to name the then high priest "Jehoshua" to be "the branch", but no other name is given in the text, except for a future promise of another "Branch". However we may take the abstract of the octal group to describe the pairing of the two witnesses and qualify the olive trees in terms of "branch(ing)".
We note that if we may correspond singletons to subgroups, so that we end up with subgroups of subgroups of subgroups ad infinitum we will eventually have a huge mess:
a=1 => [b,d,f] and {c,e,g} is static => {[a,b,c],[a,d,e],[a,f,g]} =>?
b=1 => [c,d,g] and {a,e,f} is static => {[b,d,f],[a,b,c],[b,e,g]} =>?
d=1 => [c,e,f] and {a,b,g} is static => {[b,d,f],[c,d,g],[a,d,e]} =>?
c=1 => [a,f,g] and {b,d,e} is static => {[c,d,g],[c,e,f],[a,b,c]} =>?
f=1 => [b,e,g] and {a,c,d} is static => {[b,d,f],[a,f,g],[c,e,f]} =>?
g=1 => [a,d,e] and {b,c,f} is static => {[c,d,g],[a,f,g],[b,e,g]} =>?
e=1 => [a,b,c] and {d,f,g} is static => {[c,e,f],[b,e,g],[a,d,e]} =>?
This infinite cascade of complexity is simple enough in structure; as a form of "branching". However we wish to equate the groups of subgroups on the far right with their singleton (intersection) as on the far left. We do however have a problem: we can't do this with the subgroups of the one same hand! We must alternate between the two hands, so whereas we start with a singleton (say "a") we do not pick elements corresponding to [b,d,f] and branch from there,.. in practice we need to choose our associations from the left hand triple {c,e,g}.
So in one singleton we have to divide right hand from left hand as so;
{[a,b,c],[a,d,e],[a,f,g]} => {c,e,g} => a <= {b,d,f} <={[a,e,f],[a,b,g],[a,c,d]}
So that the left triple of subgroups take's its correspondences from it's opposite octal, and the right triple as from it's opposite octal also.
Although we have used a familiar (our "sun") octal and a familiar left hand it should be noted that these "two witnesses" are witnessing to the generalised form of the angel's exiting of the church "circuit" into rest in Christ. They are valid structurally, and this is more important in witnessing to the efficacy of the kingdom of God  even when there should be "Time no longer!" when the kingdom is likened to ten virgins.
The witnesses have a 1260 day ministry: they testify to every nonidentity element in the seven churches across all 30 octals (42 months = 1260 days.) The "rest state" or identity element is shown to be efficacious also when Christ sends the spirit of life back into them and they are raised from death before all the world.
So we require the witnesses ministry to apply across every possible finite field arrangement. The structure in triples of:
[a,b,c],[a,d,e],[a,f,g]} => {c,e,g} => a <= {b,d,f} <={[a,e,f],[a,b,g],[a,c,d]}
Would apply to any right and left hand pair: we need not start with the sun octal as the right hand, but indeed this structural pairing should be valid for any two valid pairs of left and right hand octals. What do we require to determine such a pair of witnesses? Actually we only need a single seven cycle element, rather than a whole octal! For instance, let us start with an obvious cycle (a,b,c,d,e,f,g) without a particular unity element, but let as construct an octal beneath with the static subgroups of left and right hands thus:
a = [b,c,e] = {d,f,g}
b = [c,d,f] = {a,g,e}
c = [d,e,g] = {a,b,f}
d = [a,e,f] = {b,c,g}
e = [b,f,g] = {a,c,d}
f = [a,c,g] = {b,d,e}
g = [a,b,d] = {c,e,f}
i.e. using the right hand group of a = [b,c,e] from the capitalised names in (a,B,C,d,E,f,g) as we would normally. So we can deduce the two witnesses from any particular seven cycle element,  but not so from the "rest state" or identity element.
As the witnesses are free to shift octals whilst the other is static, (by choice of unity) the underlying octals are not fixed on both hands, and are free to include any other of the 30 octals  (each month of their ministry over 42 elements in seven C7 groups from the mystery of the seven lampstands, giving 1260 days.) This continually shifting octal "sea", though in obedience to the spirit as C7 is a reminder of the torment caused by the locust spirits of the fifth trump. These two witnesses indeed torment all that dwell on the earth, as their elements in the coset of one witness (the earthly elements or four beasts about the throne) are permuted through the octal of the other hand and the whole "sea" itself.
What of the two olive trees and the two lampstands that are before the God of the Earth? The Earth indicates the "four beasts" about the throne: indeed the witnesses are left/right subgroups corresponding in pairs to an identity element in a similar manner to the possible identity arrangements of the first four seals. These four "choices of unity" correspond to the Earth, as well as their equivalent in the trumpets  the four horns of the altar.
Under the seven cycles (from which the two witnesses are shown to be constructed) as above, the octals are deducable: However we do require for the two witnesses to show a precise route from every one of the seven churches (C7 groups) out into the "open door" of Christ's approval. That every possible seven cycle (of which there are a huge 720 not requiring a choice of unity  which would lead to 5040 in total, i.e. too many to write here) is shown to be structurally sound.
The angel "gives power" to the two witnesses: The power is not his, but the Holy Spirit is that which gives the witnesses their power. The angel has simply given them the key to the open door. The angels "circuit" or "walk", say (a,b,c,d,e,f,g) gives the two witnesses 42 "months" of seven C7 groups of six non unity elements each, to be carried isomorphically to every octal in the sea. (Of which there are 30).
Then the witnesses do not require a starting point for the "Sun octal" as paired with a specific left hand: rather as the spirit goes into their ministry it shows that this set of 1260 possible exit routes unlocked by the angel and witnessed by these two "branching pairs" or "olive trees" stands upright before the God of the Earth: The way is open and the door narrow, being 1260 out of 200,000,000 but it is an open door all the same. The way is "set", perhaps like a truly opened "north west passage"  and open for a much wider exodus.
Of course we have likened the kingdom of God to the mystery of the seven golden candlesticks rather than as the ten virgins of the parable. However the pages in the main part of the revelation section examines that case in far greater detail.
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