FILLING THE GAPS
While
filling the gaps in the sequence of (nx108)^{3} symmetric structures in the Periodic
Table, we find that there may be two or more compounds with the exact TRUE
volume to fill the gaps, increasing in number as n
increases. We also discover that,
after n
= 9, there are symmetric compounds equal in TRUE volume to some elements. H_{2}O,
for example, has a TRUE volume of (10x108)^{3}, the same TRUE volume as
the inert gas Neon. The TRUEunit analyses for the compounds in the Table
immediately above are displayed below.
Helium Hydride, Valence =  2 + 3 = +1
Compound

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

He + H_{}

3e

3

315

318

32,157,432

3P^{+}

51

21

72

373,248


3N^{0}

66

48

114

1,481,544


Totals

120

384

504

34,012,224=(324)^{3}
= (3x108)^{3}

Lithium Hydride, Valence =  2 + 4 = +2
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

Li + H2

4e

4

420

424

76,225,024

4P^{+}

68

28

96

884,736


4N^{0}

88

64

152

3,511,808


Totals

160

512

672

80,621,568=(432)^{3}
= (4x108)^{3}

(He)_{2}H, Valence =  2 + 5 = +3
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

(He)_{2}H

5e

5

525

530

148,877,000

5P^{+}

85

35

120

1,728,000


5N^{0}

110

80

190

6,859,000


Totals

186

640

826

157,464,000=(540)^{3}
= (5x108)^{3}

HeH_{3}, Valence =  2 + 5 = +3
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

(He)_{2}H

5e

5

525

530

148,877,000

5P^{+}

85

35

120

1,728,000


5N^{0}

110

80

190

6,859,000


Totals

186

640

826

157,464,000=(540)^{3}
= (5x108)^{3}

HO, Hydroxide Ion, Valence =  2 + 9 = +7
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

2H + O^{}

9e

9

945

954

868,250,664

9P^{+}

153

63

216

10,077,696


1Cג+8N^{0}

176

166

342

40,001,688


Totals

338

1,174

1,512

918,330,048=(972)^{3}
=
(9x108)^{3}

H_{2}N, Valence =  2 + 9 = +7
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

2H_{ }+
N^{}

9e

9

945

954

868,250,664

9P^{+}

153

63

216

10,077,696


9N^{0}

176

166

342

40,001,688


Totals

338

1,174

1,512

918,330,048=(972)^{3}
=
(9x108)^{3}

CH_{3}, Valence =  2 + 9 = +7
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

C + 3H^{}

9e

9

945

954

868,250,664

9P^{+}

153

63

216

10,077,696


9N^{0}

176

166

342

40,001,688


Totals

338

1,174

1,512

918,330,048=(972)^{3}
=
(9x108)^{3}

H_{2}O, Water, Valence = 2 8 + 10 = 0
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

2(H2)+O^{*}

10e

10

1050

1060

1,191,016,000

10P^{+}

170

70

240

13,824,000


8N^{0}+2C_{ג}

176

204

380

54,872,000


Totals

356

1,324

1,680

1,259,712,000=(1,080)^{3}
=(10x108)^{3}

H_{4}N, Valence = 11 2 – 8 = +1
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

4H1+ N^{}

11e

11

1,155

1,166

1,585,242,296

11P^{+}

187

77

264

18,399,744


4Cג+7N^{0}

154

264

418

73,034,632


Totals

352

1,496

1,848

1,676,676,672=(1,188)^{3}
=(11x108)^{3}

C_{2}H, Valence = 13 2 – 8 = +3
Atoms

Particles

Mass/Energy

ג

Total TRUE
Units

Volume

2C + H^{}

13e

13

1,365

1,378

2,616,662,152

13P^{+}

221

91

312

30,371,328


Cג+12N^{0}

264

230

494

120,553,784


Totals

498

1,686

2,184

2,767,587,264=(1,404)^{3}
=(13x108)^{3}

SUMMARY AND CONCLUSION
Applying the process of rotation and
unitary projection from dimension to dimension in Euclidean space, we find that
the mathematical structure of basic number theory requires the existence of
nine finite orthogonal dimensions embedded successively in an infinitely
continuous substrate. Applying the logic of the Calculus of Dimensional Distinctions,
an application and extension of George Spencer Brown’s Laws of Form, to LHC
particlecollider mass/energy data for electrons, protons and neutrons,
considered as spinning distinctions of content occupying unitary distinctions
of extent in the 3S1t dimensional domain of physical observations, we find
that the lightspeed limitation of Einstein’s special relativity and Planck’s
quantization of mass and energy define a minimal unitary distinction. This
minimal mass/energy, spacetime distinction is the smallest possible finite
building block of the 3S1t universe.. As such, it replaces the infinitesimal
of the differential calculus of Newton and Leibniz in the mathematical analysis
of physical reality. The Calculus of Dimensional Distinctions provides us with
the tool needed to extend the work of Minkowski, Einstein, Kaluza, Klein,
Pauli, and others who have attempted to use multidimensional analysis to
integrate and explain the laws of physics.
The process of rotation and unitary
orthogonal projection from the planes of one dimension to the next in Euclidean
space utilizes the Pythagorean Theorem. Generalization of the Pythagorean
Theorem equation to three dimensions and application to the minimal quantized
distinctions of extent and content produces a set of Diophantine expressions
that perfectly describe the combination of elementary particles. Integer
solutions of these equations represent stable, symmetric combinations of
elementary particles; but when there are no integer solutions, the expressions
are inequalities representing unstable combinations that decay quickly.
Fermat’s Last Theorem applied to the equation describing the combination of two
elementary particles tells us that there are no integer solutions, and thus no
stable combinations. The equation for the combination of three particles, on
the other hand, does have integer solutions. This explains why three quarks,
not two, combine to form protons and neutrons.
Application of the equation
describing the combination of three particles to particlecollider mass/energy
data expressed as multiples of the minimal unit, reveals that, in order for
stable combinations to form, in addition to the volumetrically equivalent forms
of mass and energy, there has to be a third equivalent form that does not
register in physical measurements as mass or energy. Representing the third
equivalent form with the symbol ג in the equations describing the combination of three particles as integer
multiples of the minimal unit, we are able to calculate the unique number of
mass/energy units and ג units needed to produce the stable protons and neutrons of
the atoms that make up the physical universe, i.e., the elements of the
Periodic Table.
Analyzing the new information
provided by the third form of the “stuff” of the physical universe, we find
interesting patterns in the structure of the Elements. For example, Carbon,
Nitrogen, Oxygen, and Sulfur have the exact same percentage of ג units. This
exact ratio in elements that play a major role in lifesupporting organisms is
not accidental. Without the presence of ג units, no stable structures
could form and there would be no physical universe. This means that ג TRUE units had to be present from the formation of the
first elementary particle, guiding the formation of the physical universe to
produce structures capable of supporting life. This supports the hypothesis
that logical structure, meaning, purpose and life are not emergent epiphenomena,
but intrinsic features of reality.
TDVP provides a “mechanism”
explaining why there is something rather than nothing. In TDVP, the form and
structure of reality is determined by the intrinsic logic of ninedimensional
reality, without requiring any transfer of mass or energy.
These results strongly suggest
that, in a ninedimensional spin reality, stable structures are purposefully
formed for use as vehicles through which the consciousness of the Csubstrate
may experience spacetime reality.
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