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ADDENDUM: 04-16-2020

f(x)=x⁴+16x²-256

roots in 4/√Φ thus:

±√9.88854381999...

±i√25.88854381999...

Consider:

1 = UNITY

√Φ = non-terminating, ≠1

Φ = PROGRESSION (irrational, non-terminating,

*constituency*of '1' concerning UNITY).

Φ² = DISCRETION (Φ+1) (irrational + rational and discrete '1' concerning UNITY∞NOT ).

Φ³ = GRAVITATION (√5+2) (irrational and discrete '2' +concerning DUALITY).

**{s³/t ∞ t³/s}**

Recalling π=4/√Φ, π²=9.88854381999..., thus

"empower" π=4/√Φ viz.

π²=16/Φ and "rationalize" one side

16 = Φπ² and "compare" to Einstein's General Relativity:

e=MC² and solve for UNITY

1=Φπ²/16

viz. 1 "discrete" unit of

*absolute magnitude*.

Because the four roots of f(x)=x⁴+16x²-256

are as two pairs of conjugates (±r,

*±i*)

whose both internal (±) and external (1:16)

variables are known, this axes directly relates to

the Reimann Hypothesis which states:

The axes (which conjoins the real and imaginary number systemsReimann Hypothesis:

The real part of every non-trivial zero of the Riemann zeta function is 1/2.

as needed and utilized by the concerned Reimann zeta function

is described by the two pairs (2x2) of

*conjugate roots*of f(x)=x⁴+16x²-256

wherein x=4/√Φ=π, hence x²=π²=9.88854381999... an irrational number,

**however**, recall this number represents 16/Φ=9.88854381999... a

*ratio*.

Thus it can be

*known*that the constituency of the concerned irrational

is actually composed of a

*ratio*of one rational (r) on one irrational (i) or (1r:1i),

which both implicitly and explicitly (ie. of fixed, or "scalar" nature)

*concerns*the integer '16',

as is the case with Φ and 1.618... Imaginary numbers enter the equation by taking the square

of -(1-√5)/2 as i√(2(1-√5))/2, bridging real and imaginary, rational and irrational.

It thus follows that due to the symmetry of the real/imaginary axes according to the roots of f(x)=x⁴+16x²-256,

the Reimann Hypothesis is true by Ananke (

*necessity*).

Later, I will show how this can be used to construct an expression which captures unity,

the progression Φ and gravitation Φ³ as a ± conjugate viz. Φ² ± Φ = 1, Φ³ or

"discretion to/from progression" equals "unity" and "gravity".

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Original Post (modified 04-16-2020):

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I have recovered a "rational" expression[/u] whose inverse identities are one another: 1 and Φ³.

This relates to the "progression" and gravitation of the physical universe respectively.

This expression (which is also a

*psuedo-quadratic*) relates to the Reimann Hypothesis in that

it proves that all non-trivial zeros have nowhere else to go but the 1/2 line, therefor the algorithm which determines

the distribution of primes is attainable. This identity is the real value of '1' in relation to both: Φ and π

all in a single expression whose multiplicative inverse is Φ³. Therefor, Φ³/1 and 1/Φ³

is where the real number system begins/ends (ie. as like an ∞ fabric) whose "sum" is -1/12.

https://www.youtube.com/watch?v=0Oazb7IWzbA

The reason for this strange sum relates to the numerator/denominator

progressively collapsing from bas

*e*s 180→90→45→36→18→*16→*12

whose symmetric "pattern" is a consistent 9→9→9→9→9→*7→*3

ending with 12π/144π:

11/12 → 12/12 = 1/12

13/12 → 12/12 = -1/12

11/12 →

**(+) 1/12**→ ***!1!*** ←

**1/12 (-)**← 13/12

therefor the actual "sum" of -1/12 is an

*artifact*, but this artifact is pointing to something extremely important:

because the real number system is enclosed, the identity of the

*psuedo-quadratic*"encodes" information about the primes

such that the whole number '1' in relation to Φ and π is the "blueprint" of all possible primes. This would predict that the identity

must always remain '1' regardless of how many √ operations are performed on it.

I am very sorry to hear of Bruce's health issues - I hope his health endures to find this,

I know it will make RS2 stronger, if not a new 'theory of everything' inductively rooted

in the same language the universe itself obeys.