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** Proof of uniqueness of encoding**

Let us satisfy ourselves that a different (but still sequential) ordering of polygons would not
also give rise to an encoding of either CTOL or N overlapping Trees, where N is larger than 91. The table lists the
yod populations of the polygons in the inner Tree of Life and their running totals when the second set of seven
polygons is reversed, so that they end with the dodecagon instead of the triangle. As before, the first seven
polygons and the root edge have the same number of yods as the **49**-tree has SLs. The first 12
polygons up the octagon now correspond to **76** overlapping Trees. This is uninteresting (hence
the cross against this number) because **76** is smaller than 91, so it has no meaning in the
wider context of CTOL. The first 13 polygons correspond to the 86-tree. This is permissable, being less than 91,
but uninteresting because it is not 86 *overlapping* Trees.There is, therefore, no combination of
polygons that is the counterpart of N overlapping Trees, where N>91. It is straightforward to confirm (see p.
394 in the author's new book) that neither of the two remaining possible orderings of polygons:

dodecagon-triangle-triangle-dodecagon

dodecagon-triangle-dodecagon-triangle

are satisfactory, the first case because it generates the same results as before, the second
case because, whilst it leads to 91 overlapping Trees, a subset of sequential polygons is also equivalent to
**36** overlapping Trees, which makes no sense in the context of CTOL with 91 overlapping Trees.
Only *one* ordering of polygons leads to a meaningful set of 91 overlapping Trees. We conclude that the
encoding of CTOL in the inner Tree of Life is unique, as one would expect.

Those visitors to this website who are Theosophists need to realise that this proof of the
encoding of CTOL in a unique subset of the set of 14 regular polygons is *tantamount to a
mathematical proof of the Theosophical doctrine of the seven planes of consciousness, each divided into seven
subplanes*. The fact proven above that the seven polygons making up one half of the inner Tree of Life
encode the **49** subplanes of the cosmic physical plane is remarkable evidence supporting this
proof and refutes the suggestion that the encoding could arise by chance. The two halves of the inner Tree of Life
express the distinction between the words "physical" and "superphysical" — not in their normal sense, in which the
former refers to the physical universe and the latter denotes non-material realms of existence, but in a much more
profound sense that will be familiar only to students of mystical traditions. The proof confirms the elaboration of
the teaching by Alice Bailey and others that the seven planes of consciousness discussed in the early
Theosophical literature constitute but the lowest plane of seven cosmic planes. The five largest polygons in the
other half of the inner Tree of Life encode the Tree of Life/tetractys map of the six superphysical cosmic
planes. Their nature can be understood only in a faint, intuitive sense by means of the hermetic principle of
correspondence: "As above, so below," although Bailey's writings may help to provide insight.

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