Collatz Conjecture Unique Solution
Murgu Table2To3
but here we are to introduce one of its new Mathematics tool
Marker USA Murgu Arrow Array

obtained using :
Murgu Infinity Table2To3Functions

((2^(2k+2)[1+6i]) - 1) = 3 Q_i
((2^(2l+1)[5+6j]) - 1) = 3 Q_j

and Murgu Collatz Conjecture Grids LET's Formulas

Grouped 2 by 2 for k=l = 0 to ∞ like Arrows heading Unity
those solved Collatz Conjecture by covering
All Positive Integers Domain.

LET₁_i = (1 + 6i)
LDN_i = (3 + 6i)
LET₂_i = (5 + 6i)

Will Keep also any old material about
Collatz Conjecture Unique Solution
Murgu Table2To3
and remind - if not understood yet - I am here to explain.
First Marker USA Murgu Arrow Array
which generate Collatz Conjecture Murgu Pocket Map.

All Collatz Conjecture Murgu Formulas authority over Collatz Conjecture are demonstrated.
Murgu Collatz Conjecture Inverse Method and Formulas revealed Logical Dead Nodes Propieties
1. Logical Dead Nodes do not have Up Collatz Connection.
2. For Every Logical Dead Node a Collatz Pattern started will not pass via Collatz Procedures another Logical Dead Node.
3. For every Logical Dead Node first Down Connection will be only and only an LET.
4. Do not have 2 or more Logical Dead Node for which first LET Connection to be the same.
You will see lots of Collatz Conjecture Formulas which pretend to solve Collatz Conjecture

but neither one are coming with all Math rigor demonstrations ,
but as proofs - we can't proof Infinity margin -
Murgu Table2To3 and Infinity Murgu Table2To3 , instead , including Collatz Conjecture Murgu Formulas are Demonstrated.
also Collatz Conjecture Murgu Grids is first Conditional which make
Murgu Table2To3 - Collatz Conjecture Unique Solution

Marker USA Murgu Arrow Array or Collatz Conjecture One-Dimensional Array

came as a result revelation
and for sure became All Science Good.

Above Equations for k=l will define "Marker USA Murgu Arrow"
((2^(2k+2)[1+6i]) - 1) = 3 Q_i
((2^(2k+1)[5+6j]) - 1) = 3 Q_j

and for k=l = 0 to ∞ - Collatz Conjecture Nodes Murgu Formulas
Infinity Marker USA Murgu Arrows
will reveal all
Collatz Conjectures Nodes
as Evens as Conjecture Nodes are defined as
(2^t)Q_i and
(2^t)Q_j
Above Equations as,
Collatz Conjecture Nodes Murgu Formulas
COVER all Positive Integers if add
(2^∞)Q_i and
(2^∞)Q_j

Marker USA Murgu Arrow Array

At this time Marker USA Murgu Arrow Array cover 2000 Grids and to be extended need an Strong Computer for.
Marker USA Murgu Arrow Array needed 2 JavaScript programs , one to generate The Array and second to generate Collatz Patterns .

At this time javascript program can generate Collatz Patterns for Positive Integers smallest then 5400 but a part of them will be partial - as a part of patern is out of our database .
Repeat via a strong Server our array- database can be extinded to 200000 Grids or more-
and hope soon Google , or APPLE , or Intel , Or Cisco, or Microsoft will offer access to ONE.
here now you can see and generate Collatz Patterns from what we have and soon if computers powers admit I will extend it to 1500 Grids.

To make an image or idea about - One-Dimension - Marker USA Murgu Arrow Array - Can see first 512 elements from 12000 if make a click down on BUTTON .
not any confusions- here Collatz Murgu Formulas value are exposed in Collatz Terms then apparent loss Collatz Unicity.

anyway can see all array into Javascript
Collatz Conjecture Enclosed into One-Dimensional Array is an H-Intel Success and to hope
Not The Last One as Science yet need H-Intel.

Marker USA Murgu Arrow ARRAY
One-Dimension Arry
now have 12000 elements "only" , but can be extended and for an strong server can go to 4 000 000 elements or even more.
Is a result of 2 Javascript progams

Under Open Sources MIT License

And hope MIT ,or Apple , or Google , or Intel, Or CISCO, or Microsoft will offer a online server wich to use those Javascript hich to push array to maxim elements.

Here our program will have any limits as any Collatz patterns will fal out of this array.
Soon will try to extend the array , but will became heavy on generating Collatz Patterns.

We let Collatz Patterns to be revealed into an alert , as you to can check if are correct.
This was tested with Opera.

For Mathematics
Collatz Table2To3 or Murgu Table2To3
Solved Collatz Conjecture
But For Public Infinity Table2To3 or Infinity Murgu Table2To3
CERTIFY via demonstrations Collatz Conjecture Solved by Murgu Table2To3

BUT MORE THEN THAT Brought and Reveal a New Science Tool

Collatz Conjecture One-Dimensional Array
Marker USA Murgu Arrow One-Dimensional Array

Here wearing Collatz Conjecture - but - can be applied in ALL SCIENCE in approprited Issues .
Down you can test this , via generating instant Collatz Paterns.

We chose "prompt" and after "Ok" "alert" for output , as output patterns to can be copied, and or , as to can be checked without Copy.
Also any patterns will be partial as are be evolving out of our
Collatz Conjecture One-Dimensional Array
AND need extension.
Also please chose every time an Odd Positive Integer as to make the answer instant.

Chose an Positive Odd as to easy server of suplimenatry work, please!
Chose an Positive Odd smaller then 23999 :

Collatz Table2To3 - Murgu Table2To3 .

Under Humanity Natural Law Of Copyright

& USA ISBN-978-1-63972-042-2

Collatz Conjecture Solved and Brought any Beauty Logicals