power body cornerstone construction

order: absolute dead center hypercube: the

three unique TRANSDECIMAL number identities

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**
Preliminaries**

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1) The absolute dead center cube is unique among all cubes. For the proof, see, on this web, Theorem & Proof: The Uniqueness of the Absolute Dead Center Cube. The Plot of the equation unique to this cube among all cubes is

2) Real trinary logic is perfectly indifferent to the
mathematical operations of addition, multiplication, subtraction, and division
(a perfect indifference found neither in Boole nor Peirce, cf. D.G. Leahy, *
Foundation: Matter the Body Itself* (Albany 1996), III.1, passim), and, as
been demonstrated elsewhere (see, on this web,
Real Trinary Logic Geometric Series Matrix of the Numeric
Geometric Series & the Series of Perfect Numbers)
the infinite sequential summing (= operationally relating) of the elements of
real trinary logic according to the universal operation of this logic ()
*immediately* i.e., *prenumerically*, produces the geometric series of
ordinary mathematics where *x* = 2 (the mathematics of mitosis and sexual
reproduction) and shows itself at once the manifest foundation of the series of
perfect numbers, and, finally, at the very inception of this logic the
foundationally demonstrated form of the absolute positive alio-relative identity
(cf. Leahy, *Foundation*, III.1) is *i*^{2 }/ *j*^{2}
= 1, whose Plot,

manifests
mathematically the perfect indifference of the logic to plus and minus: *
i*^{2 }/ *j*^{2} = -*i*^{2 }/ *j*^{2}
= *i*^{2 }/ -*j*^{2} = -*i*^{2 }/ -*j*^{2}
= 1.

3) Part and parcel of the uniqueness of this cube is the fact
that unlike all other cubes the face of this cube may be divided into 36 equal
squares each of whose areas = √82944 and each of which may be inscribed in a
circle whose area 144π
equals the circumference 144π
of the circle in which the whole face (= 36√82944 = 10368) may be inscribed
(cf. Leahy, *Foundation*, pp. 524f., n. 98).

Let there be the face of the absolute dead center cube divided
into 36 equal subsquares arranged as quadrants each occupied by a successive
counterclockwise turning of the real trinary logic Cornerstone (cf. ibid., III.
1) and positioned in the 1^{st} and 3^{rd} quadrants of the
coordinate system on the analogy to the above Plot of the equation unique to
the absolute dead center cube, as here illustrated:

.

When in the above equation *x* is negative the position of
the analogized 36-fold squares is reversed and occupies the second and fourth
quadrants of the coordinate system with its elements turned accordingly. Taking
into account the ultimate indifference of real trinary logic to plus and minus
the coordinate system may be filled in analogously in the following way:

.

4) The transcendental deduction of the order of construction of
the cornerstone is accomplished by starting with the ultimate equation of the
power body analogue of the power set and placing the digits on the left side of
the equation, each in order, successively in the leftmost topmost appropriate
and unoccupied cornerstone subsquare (see, on this web,
The Real Beyond the Void: the Beginning/the Power Body, Note 4;
see, also, on this web,
The Deep Epidermal Surface: The Cornerstone Construction Order,
Minimum Order Tetrahedron Hypercube, & Absolute Dead Center Hypercube).
Thus, f**ollowing the Beginning/Power
Body sequence, ****1**, 1, **1**, 1, (1), 1, (1), (1), **1****,
the cornerstone is constructed in the order here illustrated:**

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**The Thread
of Dr. Hoath’s Analysis**

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On June 1,
2012 SB Hoath communicated to the writer (and to his fellow students in The New
York Philosophy Corporation Spring 2012 course on “Philosophy of the Body”) the
results of his study relating to certain of the logical patterns set out, above, in
paragraphs 3 and 4.^{1}
He first substituted in the four foursquares of rotating logical cornerstones
occupying the four quadrants of the coordinate system, as illustrated, above, in
paragraph 3, the numbers corresponding to the construction order of the real
trinary logic cornerstone, as illustrated, above, in paragraph 4, conceiving
that the rotation of the cornerstone in each quadrant takes place by quarter
turns:

Sometime earlier Dr. Hoath had started to apply a two-sided approach to following the thread of the cornerstone construction order:

In this case he decided to employ the singularly one-sided approach to the construction order here illustrated:

The reader will note that this drawing combines as one the previous front and back sewing patterns—effectively rendering the cornerstone perfectly transparent. This perfectly one-sided pattern is then applied to the four foursquares of the logical cornerstone (numbered according to the construction order) occupying the quadrants of the coordinate system, with the 4 cornerstones in each quadrant made of one thread running out from the 9-subsquare of each cornerstone to the 1-subsquare of the cornerstone preceding it in the counterclockwise rotation:

Dr. Hoath then focused his attention on the four central spaces created by the unification of each of the foursquares of cornerstones occupying one each of the coordinate system quadrants — with these beautiful visual patterns appearing:

He then calculated the area of the black central surface of each of the four foursquares of cornerstones unified by the thread joining together 9-square to preceding 1-square as previously described. Starting at the top right foursquare and running counterclockwise to the bottom right foursquare, the areas are 288, 672, 4032, and 1209.6.

**The
Absolute Balance Point**

Then drawing
upon the conjunction of the transdecimal identities (see, on this web,
Transdecimal
Calculation of Number Identity: A Note on *Integral Product* & Related
Terms)
of the mathematics of the Hebrew terms נקדת האפס של
תנופה (‘dead center’/’point zero of energy’),
מדות שטח
(‘area measure’), and
נקדת העיון
(‘point of balance’),^{2 }
he multiplied each of the aforesaid areas in turn by the
rational product of
נקדת העיון
(‘point of balance’)
(288 × .0297̅6̅1̅9̅0̅4, 672 × .0297̅6̅1̅9̅0̅4, 4032 × .0297̅6̅1̅9̅0̅4, and
1209.6 × .0297̅6̅1̅9̅0̅4) to
produce
this parallel balance point sequence: 60/7,
20, 120, and 36.

**Knotting
the Thread — Cutting the Knot **

** **

In order for
the 4^{th} (the last) cornerstone in the rotation order of cornerstones
to be the 4^{th} (the last) cornerstone in the rotation order of the
cornerstones in the 4^{th} (the last) quadrant there is nothing for it
but that it be qua 4^{th} (qua last) the 1^{st} cornerstone in
the rotation order of cornerstones in the 1^{st} quadrant:

Thus the
minimum order 4−1-2-3 (cf. Leahy, *Foundation* III.1, et passim). The
writer notes that when the central area numbers calculated by Dr. Hoath are
placed in their respective quadrants of the coordinate system, and the
corresponding absolute balance point reductions are likewise so placed in a
separate configuration, then, multiplying the 2 sets of 4 numbers together
chiasmically in accord with the minimum order 4−1-2-3

yields the following products of the resulting irreducibly chiasmically related sets of chiasmically structured square roots:

(IV’ × I) × (IV × I’) = (36 × 288) × (1209.6 × 60/7) = 1.0368e4 × 1.0368e4 = 1.07495424e8

= the absolute dead center hypercube volume whose ratio to its integral product = 82944/784/1 (see, on this web, Measure Beyond Beyond Reach), and

(II × III’) × (II’ × III) = (672 × 120) × (20 × 4032) = 8.064e4 × 8.064e4 = 6.5028096e9

= the
hundredfold product of the three unique natural numbers identically their
integral products (1 × 784 × 82944) (cf. ibid.; also, Leahy, *Foundation* III.6).
Cf. the integral product of Euclid’s term for the golden section
ὁ άκρος καὶ μέσος λόγος (‘the extreme and mean ratio’) 6.5028096e37 (see, also,
on this web,
Theorem & Proof: The Uniqueness
of the Absolute
Dead Center
Cube).

**Notes**

^{
1}
The writer thanks Dr. Hoath for sharing the results of his study
including his original images the greater number of which have been
adapted and combined in what follows for the sake of economy of
presentation.

^{
2}
Cf. Leahy, *Foundation*, p. 521: “Let, then, ‘absolute’
נקדת האפס
של תנופה (‘dead
center’/’point zero of energy’ [integral product, 8.2944E22]) be
denominated ‘absolute’
מדות שטח
(‘area measure’, qua
proportion, 40 : 4 :: 6 : 400 (::) 300 : 9 :: 8 : [1], whose integral
product is 3.31776E11) 8.2944E22/ 3.31776E11 = 2.5E11. ‘Absolute’
נקדת האפס של תנופה
(‘dead center’/’point zero of energy’) divided by ‘absolute’
מדות שטח
(‘area measure’)
equals ‘absolute’
נקדת
העיון (‘point of
balance’, qua proportion, 50 : 100 :: 4 : 400 (::) 5 : 70 :: 10 : 6 ::
50 : [1], whose integral product is 2.5E11). Identified as ‘absolute
area measure’ ‘absolute dead center’ is ‘absolute balance point’. The
rational product or ‘identity’ of
נקדת
העיון
(‘point of balance’) is .0297̅6̅1̅9̅0̅4.”