The Tenth Part

Now, the great city, (formed of nothing but tares now) is as the structure of S5, so a tenth part of the city would be 12 elements.

However we note that the "dead witness" octal;

(a,b,c), (a,d,e), (a,f,g), with {(b,e,f), (b,d,g), (c,d,f), (c,e,g)} with unity (a = 1)

Has the coset (comprising of the rightmost four groups) formed by swapping elements with the transpositions (b,c), (d,e) or (f,g). Any one of these three acting on the "sun octal" subgroups will provide the four groups on the right. Likewise the pairing of disjoint transpositions "(b,c)(d,e)" etc will also produce those four groups preserving the other three (but are not constructible). So there are essentially three elements of the group S6 already that are absorbed in the stride of the seven cycle.

We actually have two octals present underneath this K4 system held in cartesian product: One forms the elements of the first three columns and the second the rows we constructed as from the serpents in opposition: We used the original seven cycle to permute in columns downward - forming our "earthquake".

So we see from the two octals in view "in that same hour" (a single seven cycle) of the quake, that when filling in the coset of [[a,b,c], [a,d,e], [a,f,g]] (with a = 1) we have two octals we can construct using these sets of order two elements (transpositions) (b,c), (d,e) or (f,g).

Since there are only two octals underneath the K4 ultrafilter;

a = [a,b,c]
b = [a,d,e]
c = [a,f,g]

i.e. {[a,b,c],[a,d,e],[a,f,g],[b,d,f],[b,e,g],[c,e,f],[c,d,g]} and {[a,b,c],[a,d,e],[a,f,g],[b,e,f],[b,d,g],[c,e,g],[c,d,f]}

Then if [a,b,c] = [[a,b,c],[a,d,e],[a,f,g]]
then {d,e,f,g} = {[b,d,f],[b,e,g],[c,e,f],[c,d,g]} or {d,e,f,g} = {[b,e,f],[b,d,g],[c,e,g],[c,d,f]} by process of elimination.

In the hour that the two witnesses stand on their feet as before their enemies (stood as upon the static subgroup before three "antichrists" forming one "bow") we see the answer from God to the formation of the cartesian pair or "key to opening the bottomless pit." We see the reality of a cartesian product of octals as acted on by the self same dialectic devices that satan has use of.

Then if (x,y) is (subgroup from row x, subgroup from column y) and we may write "x - y" or "x + Ty" where T is our possible "transposition" on the set of the "sun octal" to the "dead witness octal".

Properly then we have two octals [a,b,c,d,e,f,g] and [a,b,c,D,E,F,G], where the elements {d,e,f,g} and {D,E,F,G} are actually different elements. In our products we actually see the witnesses ascend to heaven as the sun octal under the Holy Spirit's action separate from the earthy elements. We must examine what happens to the two sets of octals given that they contain the same K4 ultrafilter [a,b,c] with a=1.

if H is the additive group of [a,b,c],[a,d,e],[a,f,g] then we have under a seven cycle C every element in the witnesses as some C(x,Ty) where x and T(y) are in H. Then the remaining elements (if Ty is in the octal but not in H) are described by C(x,Ty) also.

Now C has six non-identity elements that can be formed, and T also many possible values. However we have two witnesses sharing "the self same hour" giving us a second pair of octals underneath a different K4 ultrafilter. For instance;

a = [a,e,f]
f = [a,c,d]
e = [a,b,g]

Now we can form pairs in C(w,Sz) also for the second witness. However we know that S and T form at least 6 transpositions together, and these two sets so far are different (disjoint);

{"(bc)", "(de)", "(fg)"}, and {"(ef)", "(cd)", "(bg)""}

Moreover we must note that the four "earthy" elements {d,e,f,g} are permuted with the K4 ultrafilter under frobenius by one witness (with the transposition (b,c)) from the ordering [d,e,f,g] to [f,g,d,e]. (As if our Lord were crucified in that same "city".) So all three of those elements are permutations of the earthy elements forming a subset of S4. The remaining three permutations from the second witness' octal correspond to the element (e,f) acting as would frobenius on the K4 ultrafilter of the left hand.

We now see the reason why we do not consider the maps of products (d,e)(f,g) etc. -They may not be formed as frobenius upon GF(4) with a floating unity.

We are also in using frobenius on the left hand, inducing frobenius on the right, (we use the same seven cycle!) So these six elements are equal in three pairs. We must also observe that cycling the K4 ultrafilter in GF(8) to apply a different pair as would say (d,e) (acting like frobenius in GF(4)) and cycling back provides the same effect as frobenius on GF(4) had the ultrafilter not been cycled in the octal using frobnenius in GF(8) .

So truthfully applying frobenius as (b,c) on a = 1 = [a,b,c] has the same effect as using frobenius in the octal to map to "a = 1 = [a,d,e]", applying frobenius as in GF(4) and then cycling back in the octal to a= 1 = [a,b,c]. There is no effective difference. However the serpent opposition is truthfully equivalent to mapping the octal elements (d,e) in a transposition. But the structure of the original field GF(8) does not permute elements in this manner, even when reduced to the K4 ultrafilter under frobenius.

For another look, see the page "A Bag Full Of Holes" in the "Insanity of satan" section of the metamath area of the site.

We must also note that the correspondence of "hail and fire mingled with blood" must be preserved. We may write out again; (as under the seven cycle (a,b,d,c,f,g,e))

[a,b,c] = 1 = a = [a,e,f]
[b,d,f] = b = [a,b,g]
[c,d,g] = d = [b,d,e]
[c,e,f] = c = [a,c,d]
[a,f,g] = f = [b,c,f]
[b,e,g] = g = [d,f,g]
[a,d,e] = e = [c,g,e] which is completely valid.

However the following is invalid.

[a,b,c] = 1 = a = [a,c,d]
[b,d,f] = b = [b,c,f]
[c,d,g] = d = [d,f,g]
[c,e,f] = c = [c,g,e]
[a,f,g] = f = [a,e,f]
[b,e,g] = g = [a,b,g]
[a,d,e] = e = [b,d,e]

There is no octal equivalence here with a=1 (The correspondence from the left hand would imply c=1 also!)

Therefore the only valid association for the K4 ultrafilter is say, for the transposition (e,f) from the left hand, thus where the left and right hands are in a valid "octal reversal" still. However we are concerned with the K4 ultrafilters.

a = [a,e,f]
e = [a,c,d]
f = [a,b,g]

and with the right hand

a = [a,b,c]
b = [a,d,e]
c = [a,f,g]

The action of the K4 ultrafilter under frobenius supplies the remaining permutations of the elements. The elements are aligned on the basis of which elements are "earthy" and which subgroup "static".

The seven cycle C acting both upon the sun octal as upon the euphrates octal (as C upon C(x,Ty)) has frobenius automorphisms in the sun octal that induce C3 in the K4 ultrafilter (a = 1 = [a,b,c], b= [a,d,e], c = [a,f,g]) and also movement (as C3) on the different euphrates octals formed about the valid K4 ultrafilter's elements.

frobenius on the euphrates octal using the sun octal's seven cycle sends

a = [a,b,c]
b = [a,d,e]
c = [a,f,g] to

a = [a,b,c]
b = [a,e,f]
c = [a,d,g] and to

a = [a,b,c]
b = [a,d,f]
c = [a,e,g] and back

i.e as from the first, second and fourth rows of

(a,b,c), (a,d,e) , (a,f,g), with (b,e,f), (b,d,g), (c,d,f), (c,e,g) with unity (a = 1)
(b,d,f), (a,b,c) , (b,e,g), with (a,d,g), (c,d,e), (c,f,g), (a,e,f) with unity (b = 1)
(c,d,g), (b,d,f) , (a,d,e), with (b,c,e), (a,c,f), (e,f,g), (a,b,g) with unity (d = 1)
(c,e,f), (c,d,g) , (a,b,c), with (a,d,f), (b,f,g), (a,e,g), (b,d,e) with unity (c = 1)
(a,f,g), (c,e,f) , (b,d,f), with (b,c,g), (d,e,g), (a,b,e), (a,c,d) with unity (f = 1)
(b,e,g), (a,f,g) , (c,d,g), with (d,e,f), (a,c,e), (a,b,d), (b,c,f) with unity (g = 1)
(a,d,e), (b,e,g) , (c,e,f), with (a,c,g), (a,b,f), (b,c,d), (d,f,g) with unity (e = 1) On the right hand

Likewise in sets of three permuations (as (b,c), (d,e), (f,g) previously) the seven cycle downward permits the earthy elements {d.e.f.g} to be permuted in twelve ways from the octal about the induced and valid K4 ultrafilter the result of a = 1 with [a,b,c] static.

{[d,e,f,g] [e,d,f,g],[d,e,g,f],[f,g,d,e]}, {[e,f,d,g],[d,g,e,f],[d,f,e,g],[e,g,f,d]} and lastly {[d,f,e,g],[e,g,d,f],[e,f,g,d],[d,g,e,f]}

With frobenius automorphisms upon the sun octal's seven cycle C on C(x,Ty) (that correspond in rows above to [a,b,c]) we see these twelve permutations on S4 in {d,e,f,g} are in fact not generated or induced by the K4 ultrafilter in the Sun octal even as under the map T with action of C. In this sense the serpent spirits have claimed "ownership" of these 12 permutations, whereas the valid K4 ultrafilter permits no such permutations in the sun octal.

Then in applying those original three transpositions (our 'T') to find an orbit of length two in the octal we have found that there are no "pseudo-octals" containing the GF(4) ultrafilter that may under any T provide an orbit of the octal of length two. The GF(4) ultrafilter has a three cycle in the octal, but no cycle of length two. (despite GF(4) having the Galois group C2 in its own setting).

Therefore the serpent spirits only have access to those twelve permutation elements of S4 induced by the ultrafilter, and the locusts find no multiplicative subgroup or orbit of C2 upon them, (they as elements {d,e,f,g} being separate from the star with the key to the pit adjoined to form S5) - i.e. they must rely solely upon the ultrafilters elements, since every octal filter must allow the GF(4) ultrafilter alongside it as in the last three seals. There is only one valid or "sun" octal with the angel's specific circuit: These permutations do not permit an orbit of length two.

Moreover these twelve elements of S4 generated (as by these invalid K4 filters) form one tenth of S5.

One may ask the question, "Why only these twelve?". Or, "Why not switch more octals and find the rest of S4?". The text merely states that the one octal is used with a single seven cycle, i.e. "In the same hour there was a great earthquake..." In effect the completion of the angel's cycle as carried over every octal is in view here. If the angel's cicuit holds then the devices of satan fail. Therefore only the one octal is the target of the device (as then upon everyone, upon the least of the kingdom of God), and the only elements of S4 are these twelve.

In summary thus far, the structure of the euphrates octal permits only the twelve possible permutations of the elements {d,e,f,g} as described. (we do not consider their products. - There are no "four" or "three cycles" of these elements {d,e,f,g} in the serpents) Accurately put, the only twelve elements able to be constructed with the key to the bottomless pit are those already constructed in the "earthy" elements using one element fixed (unity) and elements of three cycles of the remainder. This is a "woe" that shows that the way to hell is a broad path rather than as the narrow or "strait" gate.

In standing in the sabbath rest of Christ, the revelation states that final victory is already won in Christ with the resurrection of the believer. Those twelve permutations upon the octal (that permute the K4 ultrafilter's proper action) do not interrupt the angel's seven cycle (as across every possible labelling) and shows that God has "sole ownership" of these twelve elements of S4. Likewise there are twelve elements of S4 that He does not permit or may not be constructed!

Which of these two sets fall in the quake? Both are part of the city, yet those other twelve (the non-constructible) are not connected to the ultrafilters in the same manner. Neither set form A4 (since (d,e)(f,g) is missing in the constructable twelve.) Yet if twelve are not constructible, adjoining a fifth element with the slogan "anything goes" would not change the matter concerning the inner workings of S4 upon the four earthy elements. The last missing twelve would remain non-constructible. They are a "fallen part" of the city forming one tenth of the total of S5.

In effect with the completion of the ministry of the witnesses, the K4 ultrafilters apply to make manifest the victory of the testimony of Jesus Christ as the resurrection upon (or across) the whole "sea of glass". I.e. In the fashion that the twelve permutations on the earthly elements are completely "powerless" across all octals, so that "the kingdoms of this world are become that of our God and of His Christ".

So we see how these 12 elements of S5 (1/10 of 120) that fail under the strength of the K4 ultrafilter and the octal are inconstructible and may not subvert/corrupt the octal by the constructs of the fifth and sixth trumpets. (The Father is not letting His house be "spoiled" by the devil, a weak entity, along with this fallen star with the key to the pit). This accounts for the tenth part of the city falling in the earthquake.

The two sets forming S and T are the very same "serpent spirits", and we see the two witnesses defeating both serpents and scorpions (locusts) in this passage. In the "great city" or "whole world" of the five refining churches we see gifts exchanged: these are transpositions over these five "elements" to generate S5. We may assume Philadelphia does not take part. (And also counting Laodicea as an abstraction or unity).

In the sense of the two witnesses there is no "sun octal" - both left and right pairs are equally valid, and as their ministry is finished they are at "unity" or in their "rest state" or "sabbath", which is present in both hands. Both "hands" or the "witnesses" are as valid for the use of the seven cycle as each other - being the two octals to which the one seven cycle will preserve subgroups whilst keeping the static subgroup of their opposite intact.

Therefore in forming the locusts to hurt men for "five months" of a seven cycle, we see actually the twisting of a seven cycle into S5, and not as truly from the octal underneath. Likewise the army of the horsemen is some 200,000,000 strong but the rest state of the witnesses is a continuation of a generalised form of the angel's circuit: In witnessing to the method by which the church's false doctrine is overcome, (in walking the angel's seven cycle across every church and seven cycle (Holy Spirit) element) the witnesses continue in a form of rest in every church lampstand. In carrying this into every octal (there are 30) it is shown through isomorphism to be a correct method or "example"; (the witnesses really only carry and witness to a rest state "everywhere".)

We can now draw a line beneath the battered serpent and scorpion spirits and move on: The second woe is interpreted.

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