Theorem
The Collatz conjecture states that for any positive integer N, the following transformational rules will if applied to N result in a set of numbers whose trajectory ends with 1.
The simplest trajectory demonstrating the rules is that of N = 1.
Rule 1. If the number is odd times by 3 and add 1
Rule 2. If the number is even divide by 2
Rule 3. Apply the rules again to the product produced.
Thus for N = 1, the trajectory is 1 -> 4 (1*3+1) -> 2 (4/2) -> 1 (2/2).
Every positive integer which has been tested eventually
reaches 1 under the Collatz map. (Equivalently, no counterexample to the
Collatz conjecture has been shown to exist.) However there is no theoretical certainty that this is so.
The following argument by contradiction, if
strong, demonstrates the Collatz conjecture to be true, and subject to peer
review, suggests extensive boundary conditions on the existence of
non-Collatz numbers in general and the ‘lowest’ non-Collatz number specifically which could be the basis for a stronger formulation if needed.
Definitions
and Setup
Let a c‑number be a positive integer
whose Collatz trajectory reaches 1. Let a z‑number be a positive integer
whose Collatz trajectory does not reach 1. Such a number if it existed
might have a looping trajectory composed entirely of z-numbers, or increase to
infinity, but the curve on which it would be the lowest point would exist
entirely of z- numbers. By definition a c-number can not give rise to a z-number, as by doing so its trajectory would cease to reach 1. The converse is also definatorally true.
Assume for contradiction that z‑numbers exist.
A lowest or least z-number must therefore
exist.
Let 
denote the least z‑number.
Lemma 1
— 
must be
odd
If were even, then its Collatz product would be 
, which is smaller than . Since is assumed to
be the least
z‑number, this would be a contradiction.
Thus is odd.
Lemma 2
— 
is the
least even z‑number
Observe that 
is even and its Collatz product would be is , a z‑number. Thus is itself a z‑number.
Suppose there were a smaller even z‑number 
. Then E's Collatz
trajectory would give a z- number smaller than , contradicting the
minimality of .
Hence is the smallest even z‑number.
Lemma 3
— 
, where 
is an even multiple >2 is the least even z‑number
having the property of producing an odd number in its Collatz trajectory after
a specific number of steps s greater than 0.
This follows from Lemma 2. is the smallest even z‑number. Observe that it also has the definable
property of being the smallest even z-number to immediately give rise to an odd
z-number. If a smaller even z-number did
this its trajectory would give rise to a smaller z-number than 
which would be a contradiction.
This chain
can be projected back thus:
is the smallest odd z‑number.
is the smallest even z‑number,
which produces an odd z-number by 1 direct transform.
I will define this as an even z-number of type
0 as the steps S between 2. Types
1,2,3….would then be definable as below:
Type 1a
is the smallest even z‑number,
which produces 1 even z-number, then an odd
Type 2
is the smallest even z‑number,
which produces 2 even z-numbers, then an odd
Type 3
is the smallest even z‑number,
which produces 3 even z-numbers, then an odd…..etc
This precusor chain can, without inherent contradiction be extended to infinity. Indeed
it is arguable that the existence of a lowest odd z-number, requires such a chain of even
z-numbers to which we can assign negative suffixes as the approach the lowest odd z-number,
The effect of this as we will see in
Lemma 4 is the creation of a set of boundary conditions governing the closeness
of even z-numbers to the lowest odd z-number .
Lemma 4
— No even number in the interval 
is a z‑number
If an even z-number in the range above exists
its Collatz trajectory includes at least one z-number < 
This would be contradictory.
Furthermore for each type of even z-number the
range above necessarily increases, so no even z-number of type 1 can exist in
the range
No even z-numbers of type 2 can exist in the
range 
Because computer checking has extended the
known set of Collatz compliant numbers to on the order of 2.36×1021
it can be seen that the likely number of even
integers in the above interval must be at the lowest on the order of 2.36x1021
/ 4.
This is important because in order as we will see to be valid Z0 ‘s trajectory will need to avoid intersection not only with that set of even integers but with every value in their Collatz trajectories, as Lemma 6 will set out.
Lemma 5
— No number in the interval Z0-1,Z0-10 is a z‑number
This follows strictly from our definition, and
is added solely because as will be shown some Collatz trajectory paths exist
such that the trajectory of an odd seed S, can be joined by that of S-1. S-10 is given as a cut off solely to reduce cases..
Lemma 6
— Any Collatz trajectory starting at must
either produce in its own trajectory an even number <2
or share
a number produced by a Collatz trajectory derived from such a number, that is
from an even number in or from an even number of a higher type as
described in(
or from the c- numbers lying in the immediate
range below 
. Such a
number must be both a z-number and a c-number and therefore contradictory.
The running together of trajectories from similar numbers is an observed property of c-numbers. Indeed all c-number trajectories must join as 1 is approached.
Trajectories can be uniquely identified by their sequence of odd-even-numbers. I will 'name' trajectories by assigning 1 to odd and 0 to even. For the first 15 steps (including the starting number) this gives 581 possible trajectories from an odd start. This gives paths from:
100000000000000 to 101010101010101
It can be shown exhaustively by analysis that for the first 15 steps from any Z0 the set of possible odd-even-etc trajectories results for all produce eithe:
1) in 551 of 581 cases
en even numbers which are < 2 x Seed value (Z0) . Such trajectories are impossible for Z0.
For example the trajectory 101010101000001 where 1 = odd, and 0 = even results in a number of the form 0.474609* S+0.412109.
If S = Z0, the trajectory at step 15 is <2Z0, thus S for that trajectory can not consistantly = Z0
2) in 30 of 581 cases
Trajectories which if followed by illustrative c-numbers lead to coalescence with trajectories in the 2x S range after 15 steps.
Table of trajectories for 15 steps showing cases which invalidate
|
Ref |
Steps 1=
odd, 0 =even |
resultant
value at step14 from SEED S |
Notes |
Path as shown for lowest
c-number |
|
1 |
100000000000000 |
0.0003662109375*S+0.0001220703125 |
Too low
at step2 for Z0 validity |
|
|
2 |
100000000000001 |
0.0003662109375*S+0.0001220703125 |
Too low
at step2 for Z0 validity |
|
|
3 |
100000000000010 |
0.002197265625*S+1.000732421875 |
Too low
at step2 for Z0 validity |
|
|
4 |
100000000000100 |
0.002197265625*S+0.500732421875 |
Too low
at step2 for Z0 validity |
|
|
5 |
100000000000101 |
0.002197265625*S+0.500732421875 |
Too low
at step2 for Z0 validity |
|
|
6 |
100000000001000 |
0.002197265625*S+0.250732421875 |
Too low
at step2 for Z0 validity |
|
|
7 |
100000000001001 |
0.002197265625*S+0.250732421875 |
Too low
at step2 for Z0 validity |
|
|
8 |
100000000001010 |
0.01318359375*S+2.50439453125 |
Too low
at step2 for Z0 validity |
|
|
9 |
100000000010000 |
0.002197265625*S+0.125732421875 |
Too low
at step2 for Z0 validity |
|
|
10 |
100000000010001 |
0.002197265625*S+0.125732421875 |
Too low
at step2 for Z0 validity |
|
|
11 |
100000000010010 |
0.01318359375*S+1.75439453125 |
Too low
at step2 for Z0 validity |
|
|
12 |
100000000010100 |
0.01318359375*S+1.25439453125 |
Too low
at step2 for Z0 validity |
|
|
13 |
100000000010101 |
0.01318359375*S+1.25439453125 |
Too low
at step2 for Z0 validity |
|
|
14 |
100000000100000 |
0.002197265625*S+0.063232421875 |
Too low
at step2 for Z0 validity |
|
|
15 |
100000000100001 |
0.002197265625*S+0.063232421875 |
Too low
at step2 for Z0 validity |
|
|
16 |
100000000100010 |
0.01318359375*S+1.37939453125 |
Too low
at step2 for Z0 validity |
|
|
17 |
100000000100100 |
0.01318359375*S+0.87939453125 |
Too low
at step2 for Z0 validity |
|
|
18 |
100000000100101 |
0.01318359375*S+0.87939453125 |
Too low
at step2 for Z0 validity |
|
|
19 |
100000000101000 |
0.01318359375*S+0.62939453125 |
Too low
at step2 for Z0 validity |
|
|
20 |
100000000101001 |
0.01318359375*S+0.62939453125 |
Too low
at step2 for Z0 validity |
|
|
21 |
100000000101010 |
0.0791015625*S+4.7763671875 |
Too low
at step2 for Z0 validity |
|
|
22 |
100000001000000 |
0.002197265625*S+0.031982421875 |
Too low
at step2 for Z0 validity |
|
|
23 |
100000001000001 |
0.002197265625*S+0.031982421875 |
Too low
at step2 for Z0 validity |
|
|
24 |
100000001000010 |
0.01318359375*S+1.19189453125 |
Too low
at step2 for Z0 validity |
|
|
25 |
100000001000100 |
0.01318359375*S+0.69189453125 |
Too low
at step2 for Z0 validity |
|
|
26 |
100000001000101 |
0.01318359375*S+0.69189453125 |
Too low
at step2 for Z0 validity |
|
|
27 |
100000001001000 |
0.01318359375*S+0.44189453125 |
Too low
at step2 for Z0 validity |
|
|
28 |
100000001001001 |
0.01318359375*S+0.44189453125 |
Too low
at step2 for Z0 validity |
|
|
29 |
100000001001010 |
0.0791015625*S+3.6513671875 |
Too low
at step2 for Z0 validity |
|
|
30 |
100000001010000 |
0.01318359375*S+0.31689453125 |
Too low
at step2 for Z0 validity |
|
|
31 |
100000001010001 |
0.01318359375*S+0.31689453125 |
Too low
at step2 for Z0 validity |
|
|
32 |
100000001010010 |
0.0791015625*S+2.9013671875 |
Too low
at step2 for Z0 validity |
|
|
33 |
100000001010100 |
0.0791015625*S+2.4013671875 |
Too low
at step2 for Z0 validity |
|
|
34 |
100000001010101 |
0.0791015625*S+2.4013671875 |
Too low
at step2 for Z0 validity |
|
|
35 |
100000010000000 |
0.002197265625*S+0.016357421875 |
Too low
at step2 for Z0 validity |
|
|
36 |
100000010000001 |
0.002197265625*S+0.016357421875 |
Too low
at step2 for Z0 validity |
|
|
37 |
100000010000010 |
0.01318359375*S+1.09814453125 |
Too low
at step2 for Z0 validity |
|
|
38 |
100000010000100 |
0.01318359375*S+0.59814453125 |
Too low
at step2 for Z0 validity |
|
|
39 |
100000010000101 |
0.01318359375*S+0.59814453125 |
Too low
at step2 for Z0 validity |
|
|
40 |
100000010001000 |
0.01318359375*S+0.34814453125 |
Too low
at step2 for Z0 validity |
|
|
41 |
100000010001010 |
0.0791015625*S+3.0888671875 |
Too low
at step2 for Z0 validity |
|
|
42 |
100000010010000 |
0.01318359375*S+0.22314453125 |
Too low
at step2 for Z0 validity |
|
|
43 |
100000010010001 |
0.01318359375*S+0.22314453125 |
Too low
at step2 for Z0 validity |
|
|
44 |
100000010010010 |
0.0791015625*S+2.3388671875 |
Too low
at step2 for Z0 validity |
|
|
45 |
100000010010100 |
0.0791015625*S+1.8388671875 |
Too low
at step2 for Z0 validity |
|
|
46 |
100000010010101 |
0.0791015625*S+1.8388671875 |
Too low
at step2 for Z0 validity |
|
|
47 |
100000010100000 |
0.01318359375*S+0.16064453125 |
Too low
at step2 for Z0 validity |
|
|
48 |
100000010100001 |
0.01318359375*S+0.16064453125 |
Too low
at step2 for Z0 validity |
|
|
49 |
100000010100010 |
0.0791015625*S+1.9638671875 |
Too low
at step2 for Z0 validity |
|
|
50 |
100000010100101 |
0.0791015625*S+1.4638671875 |
Too low
at step2 for Z0 validity |
|
|
51 |
100000010101000 |
0.0791015625*S+1.2138671875 |
Too low
at step2 for Z0 validity |
|
|
52 |
100000010101001 |
0.0791015625*S+1.2138671875 |
Too low
at step2 for Z0 validity |
|
|
53 |
100000010101010 |
0.474609375*S+8.283203125 |
Too low
at step2 for Z0 validity |
|
|
54 |
100000100000000 |
0.002197265625*S+0.008544921875 |
Too low
at step2 for Z0 validity |
|
|
55 |
100000100000001 |
0.002197265625*S+0.008544921875 |
Too low
at step2 for Z0 validity |
|
|
56 |
100000100000010 |
0.01318359375*S+1.05126953125 |
Too low
at step2 for Z0 validity |
|
|
57 |
100000100000100 |
0.01318359375*S+0.55126953125 |
Too low
at step2 for Z0 validity |
|
|
58 |
100000100000101 |
0.01318359375*S+0.55126953125 |
Too low
at step2 for Z0 validity |
|
|
59 |
100000100001000 |
0.01318359375*S+0.30126953125 |
Too low
at step2 for Z0 validity |
|
|
60 |
100000100001001 |
0.01318359375*S+0.30126953125 |
Too low
at step2 for Z0 validity |
|
|
61 |
100000100001010 |
0.0791015625*S+2.8076171875 |
Too low
at step2 for Z0 validity |
|
|
62 |
100000100010000 |
0.01318359375*S+0.17626953125 |
Too low
at step2 for Z0 validity |
|
|
63 |
100000100010001 |
0.01318359375*S+0.17626953125 |
Too low
at step2 for Z0 validity |
|
|
64 |
100000100010010 |
0.0791015625*S+2.0576171875 |
Too low
at step2 for Z0 validity |
|
|
65 |
100000100010100 |
0.0791015625*S+1.5576171875 |
Too low
at step2 for Z0 validity |
|
|
66 |
100000100010101 |
0.0791015625*S+1.5576171875 |
Too low
at step2 for Z0 validity |
|
|
67 |
100000100100000 |
0.01318359375*S+0.11376953125 |
Too low
at step2 for Z0 validity |
|
|
68 |
100000100100001 |
0.01318359375*S+0.11376953125 |
Too low
at step2 for Z0 validity |
|
|
69 |
100000100100010 |
0.0791015625*S+1.6826171875 |
Too low
at step2 for Z0 validity |
|
|
70 |
100000100100100 |
0.0791015625*S+1.1826171875 |
Too low
at step2 for Z0 validity |
|
|
71 |
100000100100101 |
0.0791015625*S+1.1826171875 |
Too low
at step2 for Z0 validity |
|
|
72 |
100000100101000 |
0.0791015625*S+0.9326171875 |
Too low
at step2 for Z0 validity |
|
|
73 |
100000100101001 |
0.0791015625*S+0.9326171875 |
Too low
at step2 for Z0 validity |
|
|
74 |
100000100101010 |
0.474609375*S+6.595703125 |
Too low
at step2 for Z0 validity |
|
|
75 |
100000101000000 |
0.01318359375*S+0.08251953125 |
Too low
at step2 for Z0 validity |
|
|
76 |
100000101000001 |
0.01318359375*S+0.08251953125 |
Too low
at step2 for Z0 validity |
|
|
77 |
100000101000010 |
0.0791015625*S+1.4951171875 |
Too low
at step2 for Z0 validity |
|
|
78 |
100000101000100 |
0.0791015625*S+0.9951171875 |
Too low
at step2 for Z0 validity |
|
|
79 |
100000101000101 |
0.0791015625*S+0.9951171875 |
Too low
at step2 for Z0 validity |
|
|
80 |
100000101001000 |
0.0791015625*S+0.7451171875 |
Too low
at step2 for Z0 validity |
|
|
81 |
100000101001001 |
0.0791015625*S+0.7451171875 |
Too low
at step2 for Z0 validity |
|
|
82 |
100000101010000 |
0.0791015625*S+0.6201171875 |
Too low
at step2 for Z0 validity |
|
|
83 |
100000101010001 |
0.0791015625*S+0.6201171875 |
Too low
at step2 for Z0 validity |
|
|
84 |
100000101010010 |
0.474609375*S+4.720703125 |
Too low
at step2 for Z0 validity |
|
|
85 |
100000101010100 |
0.474609375*S+4.220703125 |
Too low
at step2 for Z0 validity |
|
|
86 |
100000101010101 |
0.474609375*S+4.220703125 |
Too low
at step2 for Z0 validity |
|
|
87 |
100001000000001 |
0.002197265625*S+0.004638671875 |
Too low
at step2 for Z0 validity |
|
|
88 |
100001000000010 |
0.01318359375*S+1.02783203125 |
Too low
at step2 for Z0 validity |
|
|
89 |
100001000000100 |
0.01318359375*S+0.52783203125 |
Too low
at step2 for Z0 validity |
|
|
90 |
100001000000101 |
0.01318359375*S+0.52783203125 |
Too low
at step2 for Z0 validity |
|
|
91 |
100001000001000 |
0.01318359375*S+0.27783203125 |
Too low
at step2 for Z0 validity |
|
|
92 |
100001000001001 |
0.01318359375*S+0.27783203125 |
Too low
at step2 for Z0 validity |
|
|
93 |
100001000001010 |
0.0791015625*S+2.6669921875 |
Too low
at step2 for Z0 validity |
|
|
94 |
100001000010000 |
0.01318359375*S+0.15283203125 |
Too low
at step2 for Z0 validity |
|
|
95 |
100001000010001 |
0.01318359375*S+0.15283203125 |
Too low
at step2 for Z0 validity |
|
|
96 |
100001000010010 |
0.0791015625*S+1.9169921875 |
Too low
at step2 for Z0 validity |
|
|
97 |
100001000010100 |
0.0791015625*S+1.4169921875 |
Too low
at step2 for Z0 validity |
|
|
98 |
100001000010101 |
0.0791015625*S+1.4169921875 |
Too low
at step2 for Z0 validity |
|
|
99 |
100001000100000 |
0.01318359375*S+0.09033203125 |
Too low
at step2 for Z0 validity |
|
|
100 |
100001000100001 |
0.01318359375*S+0.09033203125 |
Too low
at step2 for Z0 validity |
|
|
101 |
100001000100010 |
0.0791015625*S+1.5419921875 |
Too low
at step2 for Z0 validity |
|
|
102 |
100001000100100 |
0.0791015625*S+1.0419921875 |
Too low
at step2 for Z0 validity |
|
|
103 |
100001000100101 |
0.0791015625*S+1.0419921875 |
Too low
at step2 for Z0 validity |
|
|
104 |
100001000101000 |
0.0791015625*S+0.7919921875 |
Too low
at step2 for Z0 validity |
|
|
105 |
100001000101001 |
0.0791015625*S+0.7919921875 |
Too low
at step2 for Z0 validity |
|
|
106 |
100001000101010 |
0.474609375*S+5.751953125 |
Too low
at step2 for Z0 validity |
|
|
107 |
100001001000000 |
0.01318359375*S+0.05908203125 |
Too low
at step2 for Z0 validity |
|
|
108 |
100001001000001 |
0.01318359375*S+0.05908203125 |
Too low
at step2 for Z0 validity |
|
|
109 |
100001001000010 |
0.0791015625*S+1.3544921875 |
Too low
at step2 for Z0 validity |
|
|
110 |
100001001000100 |
0.0791015625*S+0.8544921875 |
Too low
at step2 for Z0 validity |
|
|
111 |
100001001000101 |
0.0791015625*S+0.8544921875 |
Too low
at step2 for Z0 validity |
|
|
112 |
100001001001000 |
0.0791015625*S+0.6044921875 |
Too low
at step2 for Z0 validity |
|
|
113 |
100001001001001 |
0.0791015625*S+0.6044921875 |
Too low
at step2 for Z0 validity |
|
|
114 |
100001001001010 |
0.474609375*S+4.626953125 |
Too low
at step2 for Z0 validity |
|
|
115 |
100001001010000 |
0.0791015625*S+0.4794921875 |
Too low
at step2 for Z0 validity |
|
|
116 |
100001001010001 |
0.0791015625*S+0.4794921875 |
Too low
at step2 for Z0 validity |
|
|
117 |
100001001010010 |
0.474609375*S+3.876953125 |
Too low
at step2 for Z0 validity |
|
|
118 |
100001001010100 |
0.474609375*S+3.376953125 |
Too low
at step2 for Z0 validity |
|
|
119 |
100001001010101 |
0.474609375*S+3.376953125 |
Too low
at step2 for Z0 validity |
|
|
120 |
100001010000000 |
0.01318359375*S+0.04345703125 |
Too low
at step2 for Z0 validity |
|
|
121 |
100001010000001 |
0.01318359375*S+0.04345703125 |
Too low
at step2 for Z0 validity |
|
|
122 |
100001010000010 |
0.0791015625*S+1.2607421875 |
Too low
at step2 for Z0 validity |
|
|
123 |
100001010000100 |
0.0791015625*S+0.7607421875 |
Too low
at step2 for Z0 validity |
|
|
124 |
100001010000101 |
0.0791015625*S+0.7607421875 |
Too low
at step2 for Z0 validity |
|
|
125 |
100001010001000 |
0.0791015625*S+0.5107421875 |
Too low
at step2 for Z0 validity |
|
|
126 |
100001010001001 |
0.0791015625*S+0.5107421875 |
Too low
at step2 for Z0 validity |
|
|
127 |
100001010001010 |
0.474609375*S+4.064453125 |
Too low
at step2 for Z0 validity |
|
|
128 |
100001010010000 |
0.0791015625*S+0.3857421875 |
Too low
at step2 for Z0 validity |
|
|
129 |
100001010010001 |
0.0791015625*S+0.3857421875 |
Too low
at step2 for Z0 validity |
|
|
130 |
100001010010010 |
0.474609375*S+3.314453125 |
Too low
at step2 for Z0 validity |
|
|
131 |
100001010010100 |
0.474609375*S+2.814453125 |
Too low
at step2 for Z0 validity |
|
|
132 |
100001010010101 |
0.474609375*S+2.814453125 |
Too low
at step2 for Z0 validity |
|
|
133 |
100001010100000 |
0.0791015625*S+0.3232421875 |
Too low
at step2 for Z0 validity |
|
|
134 |
100001010100001 |
0.0791015625*S+0.3232421875 |
Too low
at step2 for Z0 validity |
|
|
135 |
100001010100010 |
0.474609375*S+2.939453125 |
Too low
at step2 for Z0 validity |
|
|
136 |
100001010100100 |
0.474609375*S+2.439453125 |
Too low
at step2 for Z0 validity |
|
|
137 |
100001010100101 |
0.474609375*S+2.439453125 |
Too low
at step2 for Z0 validity |
|
|
138 |
100001010101000 |
0.474609375*S+2.189453125 |
Too low
at step2 for Z0 validity |
|
|
139 |
100001010101001 |
0.474609375*S+2.189453125 |
Too low
at step2 for Z0 validity |
|
|
140 |
100001010101010 |
2.84765625*S+14.13671875 |
Too low
at step2 for Z0 validity |
|
|
141 |
100010000000000 |
0.002197265625*S+0.002685546875 |
Too low
at step2 for Z0 validity |
|
|
142 |
100010000000001 |
0.002197265625*S+0.002685546875 |
Too low
at step2 for Z0 validity |
|
|
143 |
100010000000010 |
0.01318359375*S+1.01611328125 |
Too low
at step2 for Z0 validity |
|
|
144 |
100010000000100 |
0.01318359375*S+0.51611328125 |
Too low
at step2 for Z0 validity |
|
|
145 |
100010000000101 |
0.01318359375*S+0.51611328125 |
Too low
at step2 for Z0 validity |
|
|
146 |
100010000001000 |
0.01318359375*S+0.26611328125 |
Too low
at step2 for Z0 validity |
|
|
147 |
100010000001001 |
0.01318359375*S+0.26611328125 |
Too low
at step2 for Z0 validity |
|
|
148 |
100010000001010 |
0.0791015625*S+2.5966796875 |
Too low
at step2 for Z0 validity |
|
|
149 |
100010000010000 |
0.01318359375*S+0.14111328125 |
Too low
at step2 for Z0 validity |
|
|
150 |
100010000010001 |
0.01318359375*S+0.14111328125 |
Too low
at step2 for Z0 validity |
|
|
151 |
100010000010010 |
0.0791015625*S+1.8466796875 |
Too low
at step2 for Z0 validity |
|
|
152 |
100010000010100 |
0.0791015625*S+1.3466796875 |
Too low
at step2 for Z0 validity |
|
|
153 |
100010000010101 |
0.0791015625*S+1.3466796875 |
Too low
at step2 for Z0 validity |
|
|
154 |
100010000100000 |
0.01318359375*S+0.07861328125 |
Too low
at step2 for Z0 validity |
|
|
155 |
100010000100001 |
0.01318359375*S+0.07861328125 |
Too low
at step2 for Z0 validity |
|
|
156 |
100010000100010 |
0.0791015625*S+1.4716796875 |
Too low
at step2 for Z0 validity |
|
|
157 |
100010000100100 |
0.0791015625*S+0.9716796875 |
Too low
at step2 for Z0 validity |
|
|
158 |
100010000100101 |
0.0791015625*S+0.9716796875 |
Too low
at step2 for Z0 validity |
|
|
159 |
100010000101001 |
0.0791015625*S+0.7216796875 |
Too low
at step2 for Z0 validity |
|
|
160 |
100010000101010 |
0.474609375*S+5.330078125 |
Too low
at step2 for Z0 validity |
|
|
161 |
100010001000000 |
0.01318359375*S+0.04736328125 |
Too low
at step2 for Z0 validity |
|
|
162 |
100010001000001 |
0.01318359375*S+0.04736328125 |
Too low
at step2 for Z0 validity |
|
|
163 |
100010001000010 |
0.0791015625*S+1.2841796875 |
Too low
at step2 for Z0 validity |
|
|
164 |
100010001000100 |
0.0791015625*S+0.7841796875 |
Too low
at step2 for Z0 validity |
|
|
165 |
100010001000101 |
0.0791015625*S+0.7841796875 |
Too low
at step2 for Z0 validity |
|
|
166 |
100010001001000 |
0.0791015625*S+0.5341796875 |
Too low
at step2 for Z0 validity |
|
|
167 |
100010001001001 |
0.0791015625*S+0.5341796875 |
Too low
at step2 for Z0 validity |
|
|
168 |
100010001001010 |
0.474609375*S+4.205078125 |
Too low
at step2 for Z0 validity |
|
|
169 |
100010001010000 |
0.0791015625*S+0.4091796875 |
Too low
at step2 for Z0 validity |
|
|
170 |
100010001010001 |
0.0791015625*S+0.4091796875 |
Too low
at step2 for Z0 validity |
|
|
171 |
100010001010010 |
0.474609375*S+3.455078125 |
Too low
at step2 for Z0 validity |
|
|
172 |
100010001010100 |
0.474609375*S+2.955078125 |
Too low
at step2 for Z0 validity |
|
|
173 |
100010001010101 |
0.474609375*S+2.955078125 |
Too low
at step2 for Z0 validity |
|
|
174 |
100010010000000 |
0.01318359375*S+0.03173828125 |
Too low
at step2 for Z0 validity |
|
|
175 |
100010010000001 |
0.01318359375*S+0.03173828125 |
Too low
at step2 for Z0 validity |
|
|
176 |
100010010000010 |
0.0791015625*S+1.1904296875 |
Too low
at step2 for Z0 validity |
|
|
177 |
100010010000100 |
0.0791015625*S+0.6904296875 |
Too low
at step2 for Z0 validity |
|
|
178 |
100010010000101 |
0.0791015625*S+0.6904296875 |
Too low
at step2 for Z0 validity |
|
|
179 |
100010010001000 |
0.0791015625*S+0.4404296875 |
Too low
at step2 for Z0 validity |
|
|
180 |
100010010001001 |
0.0791015625*S+0.4404296875 |
Too low
at step2 for Z0 validity |
|
|
181 |
100010010001010 |
0.474609375*S+3.642578125 |
Too low
at step2 for Z0 validity |
|
|
182 |
100010010010000 |
0.0791015625*S+0.3154296875 |
Too low
at step2 for Z0 validity |
|
|
183 |
100010010010001 |
0.0791015625*S+0.3154296875 |
Too low
at step2 for Z0 validity |
|
|
184 |
100010010010010 |
0.474609375*S+2.892578125 |
Too low
at step2 for Z0 validity |
|
|
185 |
100010010010100 |
0.474609375*S+2.392578125 |
Too low
at step2 for Z0 validity |
|
|
186 |
100010010010101 |
0.474609375*S+2.392578125 |
Too low
at step2 for Z0 validity |
|
|
187 |
100010010100000 |
0.0791015625*S+0.2529296875 |
Too low
at step2 for Z0 validity |
|
|
188 |
100010010100001 |
0.0791015625*S+0.2529296875 |
Too low
at step2 for Z0 validity |
|
|
189 |
100010010100010 |
0.474609375*S+2.517578125 |
Too low
at step2 for Z0 validity |
|
|
190 |
100010010100100 |
0.474609375*S+2.017578125 |
Too low
at step2 for Z0 validity |
|
|
191 |
100010010100101 |
0.474609375*S+2.017578125 |
Too low
at step2 for Z0 validity |
|
|
192 |
100010010101000 |
0.474609375*S+1.767578125 |
Too low
at step2 for Z0 validity |
|
|
193 |
100010010101010 |
2.84765625*S+11.60546875 |
Too low
at step2 for Z0 validity |
|
|
194 |
100010100000000 |
0.01318359375*S+0.02392578125 |
Too low
at step2 for Z0 validity |
|
|
195 |
100010100000001 |
0.01318359375*S+0.02392578125 |
Too low
at step2 for Z0 validity |
|
|
196 |
100010100000010 |
0.0791015625*S+1.1435546875 |
Too low
at step2 for Z0 validity |
|
|
197 |
100010100000100 |
0.0791015625*S+0.6435546875 |
Too low
at step2 for Z0 validity |
|
|
198 |
100010100000101 |
0.0791015625*S+0.6435546875 |
Too low
at step2 for Z0 validity |
|
|
199 |
100010100001000 |
0.0791015625*S+0.3935546875 |
Too low
at step2 for Z0 validity |
|
|
200 |
100010100001001 |
0.0791015625*S+0.3935546875 |
Too low
at step2 for Z0 validity |
|
|
201 |
100010100001010 |
0.474609375*S+3.361328125 |
Too low
at step2 for Z0 validity |
|
|
202 |
100010100010000 |
0.0791015625*S+0.2685546875 |
Too low
at step2 for Z0 validity |
|
|
203 |
100010100010001 |
0.0791015625*S+0.2685546875 |
Too low
at step2 for Z0 validity |
|
|
204 |
100010100010010 |
0.474609375*S+2.611328125 |
Too low
at step2 for Z0 validity |
|
|
205 |
100010100010100 |
0.474609375*S+2.111328125 |
Too low
at step2 for Z0 validity |
|
|
206 |
100010100010101 |
0.474609375*S+2.111328125 |
Too low
at step2 for Z0 validity |
|
|
207 |
100010100100000 |
0.0791015625*S+0.2060546875 |
Too low
at step2 for Z0 validity |
|
|
208 |
100010100100001 |
0.0791015625*S+0.2060546875 |
Too low
at step2 for Z0 validity |
|
|
209 |
100010100100010 |
0.474609375*S+2.236328125 |
Too low
at step2 for Z0 validity |
|
|
210 |
100010100100100 |
0.474609375*S+1.736328125 |
Too low
at step2 for Z0 validity |
|
|
211 |
100010100100101 |
0.474609375*S+1.736328125 |
Too low
at step2 for Z0 validity |
|
|
212 |
100010100101000 |
0.474609375*S+1.486328125 |
Too low
at step2 for Z0 validity |
|
|
213 |
100010100101001 |
0.474609375*S+1.486328125 |
Too low
at step2 for Z0 validity |
|
|
214 |
100010100101010 |
2.84765625*S+9.91796875 |
Too low
at step2 for Z0 validity |
|
|
215 |
100010101000000 |
0.0791015625*S+0.1748046875 |
Too low
at step2 for Z0 validity |
|
|
216 |
100010101000001 |
0.0791015625*S+0.1748046875 |
Too low
at step2 for Z0 validity |
|
|
217 |
100010101000010 |
0.474609375*S+2.048828125 |
Too low
at step2 for Z0 validity |
|
|
218 |
100010101000100 |
0.474609375*S+1.548828125 |
Too low
at step2 for Z0 validity |
|
|
219 |
100010101000101 |
0.474609375*S+1.548828125 |
Too low
at step2 for Z0 validity |
|
|
220 |
100010101001000 |
0.474609375*S+1.298828125 |
Too low
at step2 for Z0 validity |
|
|
221 |
100010101001001 |
0.474609375*S+1.298828125 |
Too low
at step2 for Z0 validity |
|
|
222 |
100010101001010 |
2.84765625*S+8.79296875 |
Too low
at step2 for Z0 validity |
|
|
223 |
100010101010000 |
0.474609375*S+1.173828125 |
Too low
at step2 for Z0 validity |
|
|
224 |
100010101010001 |
0.474609375*S+1.173828125 |
Too low
at step2 for Z0 validity |
|
|
225 |
100010101010010 |
2.84765625*S+8.04296875 |
Too low
at step2 for Z0 validity |
|
|
226 |
100010101010100 |
2.84765625*S+7.54296875 |
Too low
at step2 for Z0 validity |
|
|
227 |
100010101010101 |
2.84765625*S+7.54296875 |
Too low
at step2 for Z0 validity |
|
|
228 |
100100000000000 |
0.002197265625*S+0.001708984375 |
Too low
at step2 for Z0 validity |
|
|
229 |
100100000000001 |
0.002197265625*S+0.001708984375 |
Too low
at step2 for Z0 validity |
|
|
230 |
100100000000010 |
0.01318359375*S+1.01025390625 |
Too low
at step2 for Z0 validity |
|
|
231 |
100100000000100 |
0.01318359375*S+0.51025390625 |
Too low
at step2 for Z0 validity |
|
|
232 |
100100000000101 |
0.01318359375*S+0.51025390625 |
Too low
at step2 for Z0 validity |
|
|
233 |
100100000001000 |
0.01318359375*S+0.26025390625 |
Too low
at step2 for Z0 validity |
|
|
234 |
100100000001001 |
0.01318359375*S+0.26025390625 |
Too low
at step2 for Z0 validity |
|
|
235 |
100100000001010 |
0.0791015625*S+2.5615234375 |
Too low
at step2 for Z0 validity |
|
|
236 |
100100000010000 |
0.01318359375*S+0.13525390625 |
Too low
at step2 for Z0 validity |
|
|
237 |
100100000010001 |
0.01318359375*S+0.13525390625 |
Too low
at step2 for Z0 validity |
|
|
238 |
100100000010010 |
0.0791015625*S+1.8115234375 |
Too low
at step2 for Z0 validity |
|
|
239 |
100100000010100 |
0.0791015625*S+1.3115234375 |
Too low
at step2 for Z0 validity |
|
|
240 |
100100000010101 |
0.0791015625*S+1.3115234375 |
Too low
at step2 for Z0 validity |
|
|
241 |
100100000100000 |
0.01318359375*S+0.07275390625 |
Too low
at step2 for Z0 validity |
|
|
242 |
100100000100001 |
0.01318359375*S+0.07275390625 |
Too low
at step2 for Z0 validity |
|
|
243 |
100100000100010 |
0.0791015625*S+1.4365234375 |
Too low
at step2 for Z0 validity |
|
|
244 |
100100000100100 |
0.0791015625*S+0.9365234375 |
Too low
at step2 for Z0 validity |
|
|
245 |
100100000100101 |
0.0791015625*S+0.9365234375 |
Too low
at step2 for Z0 validity |
|
|
246 |
100100000101000 |
0.0791015625*S+0.6865234375 |
Too low
at step2 for Z0 validity |
|
|
247 |
100100000101001 |
0.0791015625*S+0.6865234375 |
Too low
at step2 for Z0 validity |
|
|
248 |
100100000101010 |
0.474609375*S+5.119140625 |
Too low
at step2 for Z0 validity |
|
|
249 |
100100001000000 |
0.01318359375*S+0.04150390625 |
Too low
at step2 for Z0 validity |
|
|
250 |
100100001000001 |
0.01318359375*S+0.04150390625 |
Too low
at step2 for Z0 validity |
|
|
251 |
100100001000010 |
0.0791015625*S+1.2490234375 |
Too low
at step2 for Z0 validity |
|
|
252 |
100100001000100 |
0.0791015625*S+0.7490234375 |
Too low
at step2 for Z0 validity |
|
|
253 |
100100001000101 |
0.0791015625*S+0.7490234375 |
Too low
at step2 for Z0 validity |
|
|
254 |
100100001001000 |
0.0791015625*S+0.4990234375 |
Too low
at step2 for Z0 validity |
|
|
255 |
100100001001001 |
0.0791015625*S+0.4990234375 |
Too low
at step2 for Z0 validity |
|
|
256 |
100100001001010 |
0.474609375*S+3.994140625 |
Too low
at step2 for Z0 validity |
|
|
257 |
100100001010000 |
0.0791015625*S+0.3740234375 |
Too low
at step2 for Z0 validity |
|
|
258 |
100100001010001 |
0.0791015625*S+0.3740234375 |
Too low
at step2 for Z0 validity |
|
|
259 |
100100001010100 |
0.474609375*S+2.744140625 |
Too low
at step2 for Z0 validity |
|
|
260 |
100100001010101 |
0.474609375*S+2.744140625 |
Too low
at step2 for Z0 validity |
|
|
261 |
100100010000000 |
0.01318359375*S+0.02587890625 |
Too low
at step2 for Z0 validity |
|
|
262 |
100100010000001 |
0.01318359375*S+0.02587890625 |
Too low
at step2 for Z0 validity |
|
|
263 |
100100010000010 |
0.0791015625*S+1.1552734375 |
Too low
at step2 for Z0 validity |
|
|
264 |
100100010000100 |
0.0791015625*S+0.6552734375 |
Too low
at step2 for Z0 validity |
|
|
265 |
100100010000101 |
0.0791015625*S+0.6552734375 |
Too low
at step2 for Z0 validity |
|
|
266 |
100100010001000 |
0.0791015625*S+0.4052734375 |
Too low
at step2 for Z0 validity |
|
|
267 |
100100010001001 |
0.0791015625*S+0.4052734375 |
Too low
at step2 for Z0 validity |
|
|
268 |
100100010001010 |
0.474609375*S+3.431640625 |
Too low
at step2 for Z0 validity |
|
|
269 |
100100010010000 |
0.0791015625*S+0.2802734375 |
Too low
at step2 for Z0 validity |
|
|
270 |
100100010010001 |
0.0791015625*S+0.2802734375 |
Too low
at step2 for Z0 validity |
|
|
271 |
100100010010010 |
0.474609375*S+2.681640625 |
Too low
at step2 for Z0 validity |
|
|
272 |
100100010010100 |
0.474609375*S+2.181640625 |
Too low
at step2 for Z0 validity |
|
|
273 |
100100010010101 |
0.474609375*S+2.181640625 |
Too low
at step2 for Z0 validity |
|
|
274 |
100100010100000 |
0.0791015625*S+0.2177734375 |
Too low
at step2 for Z0 validity |
|
|
275 |
100100010100001 |
0.0791015625*S+0.2177734375 |
Too low
at step2 for Z0 validity |
|
|
276 |
100100010100010 |
0.474609375*S+2.306640625 |
Too low
at step2 for Z0 validity |
|
|
277 |
100100010100100 |
0.474609375*S+1.806640625 |
Too low
at step2 for Z0 validity |
|
|
278 |
100100010100101 |
0.474609375*S+1.806640625 |
Too low
at step2 for Z0 validity |
|
|
279 |
100100010101000 |
0.474609375*S+1.556640625 |
Too low
at step2 for Z0 validity |
|
|
280 |
100100010101001 |
0.474609375*S+1.556640625 |
Too low
at step2 for Z0 validity |
|
|
281 |
100100010101010 |
2.84765625*S+10.33984375 |
Too low
at step2 for Z0 validity |
|
|
282 |
100100100000000 |
0.01318359375*S+0.01806640625 |
Too low
at step2 for Z0 validity |
|
|
283 |
100100100000001 |
0.01318359375*S+0.01806640625 |
Too low
at step2 for Z0 validity |
|
|
284 |
100100100000010 |
0.0791015625*S+1.1083984375 |
Too low
at step2 for Z0 validity |
|
|
285 |
100100100000100 |
0.0791015625*S+0.6083984375 |
Too low
at step2 for Z0 validity |
|
|
286 |
100100100000101 |
0.0791015625*S+0.6083984375 |
Too low
at step2 for Z0 validity |
|
|
287 |
100100100001000 |
0.0791015625*S+0.3583984375 |
Too low
at step2 for Z0 validity |
|
|
288 |
100100100001001 |
0.0791015625*S+0.3583984375 |
Too low
at step2 for Z0 validity |
|
|
289 |
100100100001010 |
0.474609375*S+3.150390625 |
Too low
at step2 for Z0 validity |
|
|
290 |
100100100010000 |
0.0791015625*S+0.2333984375 |
Too low
at step2 for Z0 validity |
|
|
291 |
100100100010001 |
0.0791015625*S+0.2333984375 |
Too low
at step2 for Z0 validity |
|
|
292 |
100100100010010 |
0.474609375*S+2.400390625 |
Too low
at step2 for Z0 validity |
|
|
293 |
100100100010100 |
0.474609375*S+1.900390625 |
Too low
at step2 for Z0 validity |
|
|
294 |
100100100010101 |
0.474609375*S+1.900390625 |
Too low
at step2 for Z0 validity |
|
|
295 |
100100100100000 |
0.0791015625*S+0.1708984375 |
Too low
at step2 for Z0 validity |
|
|
296 |
100100100100001 |
0.0791015625*S+0.1708984375 |
Too low
at step2 for Z0 validity |
|
|
297 |
100100100100010 |
0.474609375*S+2.025390625 |
Too low
at step2 for Z0 validity |
|
|
298 |
100100100100100 |
0.474609375*S+1.525390625 |
Too low
at step2 for Z0 validity |
|
|
299 |
100100100100101 |
0.474609375*S+1.525390625 |
Too low
at step2 for Z0 validity |
|
|
300 |
100100100101000 |
0.474609375*S+1.275390625 |
Too low
at step2 for Z0 validity |
|
|
301 |
100100100101010 |
2.84765625*S+8.65234375 |
Too low
at step2 for Z0 validity |
|
|
302 |
100100101000000 |
0.0791015625*S+0.1396484375 |
Too low
at step2 for Z0 validity |
|
|
303 |
100100101000001 |
0.0791015625*S+0.1396484375 |
Too low
at step2 for Z0 validity |
|
|
304 |
100100101000010 |
0.474609375*S+1.837890625 |
Too low
at step2 for Z0 validity |
|
|
305 |
100100101000100 |
0.474609375*S+1.337890625 |
Too low
at step2 for Z0 validity |
|
|
306 |
100100101000101 |
0.474609375*S+1.337890625 |
Too low
at step2 for Z0 validity |
|
|
307 |
100100101001000 |
0.474609375*S+1.087890625 |
Too low
at step2 for Z0 validity |
|
|
308 |
100100101001001 |
0.474609375*S+1.087890625 |
Too low
at step2 for Z0 validity |
|
|
309 |
100100101001010 |
2.84765625*S+7.52734375 |
Too low
at step2 for Z0 validity |
|
|
310 |
100100101010000 |
0.474609375*S+0.962890625 |
Too low
at step2 for Z0 validity |
|
|
311 |
100100101010001 |
0.474609375*S+0.962890625 |
Too low
at step2 for Z0 validity |
|
|
312 |
100100101010100 |
2.84765625*S+6.27734375 |
Too low
at step2 for Z0 validity |
|
|
313 |
100100101010101 |
2.84765625*S+6.27734375 |
Too low
at step2 for Z0 validity |
|
|
314 |
100101000000000 |
0.01318359375*S+0.01416015625 |
Too low
at step2 for Z0 validity |
|
|
315 |
100101000000001 |
0.01318359375*S+0.01416015625 |
Too low
at step2 for Z0 validity |
|
|
316 |
100101000000010 |
0.0791015625*S+1.0849609375 |
Too low
at step2 for Z0 validity |
|
|
317 |
100101000000100 |
0.0791015625*S+0.5849609375 |
Too low
at step2 for Z0 validity |
|
|
318 |
100101000000101 |
0.0791015625*S+0.5849609375 |
Too low
at step2 for Z0 validity |
|
|
319 |
100101000001000 |
0.0791015625*S+0.3349609375 |
Too low
at step2 for Z0 validity |
|
|
320 |
100101000001001 |
0.0791015625*S+0.3349609375 |
Too low
at step2 for Z0 validity |
|
|
321 |
100101000001010 |
0.474609375*S+3.009765625 |
Too low
at step2 for Z0 validity |
|
|
322 |
100101000010000 |
0.0791015625*S+0.2099609375 |
Too low
at step2 for Z0 validity |
|
|
323 |
100101000010001 |
0.0791015625*S+0.2099609375 |
Too low
at step2 for Z0 validity |
|
|
324 |
100101000010010 |
0.474609375*S+2.259765625 |
Too low
at step2 for Z0 validity |
|
|
325 |
100101000010100 |
0.474609375*S+1.759765625 |
Too low
at step2 for Z0 validity |
|
|
326 |
100101000010101 |
0.474609375*S+1.759765625 |
Too low
at step2 for Z0 validity |
|
|
327 |
100101000100000 |
0.0791015625*S+0.1474609375 |
Too low
at step2 for Z0 validity |
|
|
328 |
100101000100001 |
0.0791015625*S+0.1474609375 |
Too low
at step2 for Z0 validity |
|
|
329 |
100101000100010 |
0.474609375*S+1.884765625 |
Too low
at step2 for Z0 validity |
|
|
330 |
100101000100100 |
0.474609375*S+1.384765625 |
Too low
at step2 for Z0 validity |
|
|
331 |
100101000101000 |
0.474609375*S+1.134765625 |
Too low
at step2 for Z0 validity |
|
|
332 |
100101000101001 |
0.474609375*S+1.134765625 |
Too low
at step2 for Z0 validity |
|
|
333 |
100101000101010 |
2.84765625*S+7.80859375 |
Too low
at step2 for Z0 validity |
|
|
334 |
100101001000000 |
0.0791015625*S+0.1162109375 |
Too low
at step2 for Z0 validity |
|
|
335 |
100101001000001 |
0.0791015625*S+0.1162109375 |
Too low
at step2 for Z0 validity |
|
|
336 |
100101001000010 |
0.474609375*S+1.697265625 |
Too low
at step2 for Z0 validity |
|
|
337 |
100101001000100 |
0.474609375*S+1.197265625 |
Too low
at step2 for Z0 validity |
|
|
338 |
100101001000101 |
0.474609375*S+1.197265625 |
Too low
at step2 for Z0 validity |
|
|
339 |
100101001001000 |
0.474609375*S+0.947265625 |
Too low
at step2 for Z0 validity |
|
|
340 |
100101001001001 |
0.474609375*S+0.947265625 |
Too low
at step2 for Z0 validity |
|
|
341 |
100101001001010 |
2.84765625*S+6.68359375 |
Too low
at step2 for Z0 validity |
|
|
342 |
100101001010000 |
0.474609375*S+0.822265625 |
Too low
at step2 for Z0 validity |
|
|
343 |
100101001010001 |
0.474609375*S+0.822265625 |
Too low
at step2 for Z0 validity |
|
|
344 |
100101001010010 |
2.84765625*S+5.93359375 |
Too low
at step2 for Z0 validity |
|
|
345 |
100101001010100 |
2.84765625*S+5.43359375 |
Too low
at step2 for Z0 validity |
|
|
346 |
100101001010101 |
2.84765625*S+5.43359375 |
Too low
at step2 for Z0 validity |
|
|
347 |
100101010000000 |
0.0791015625*S+0.1005859375 |
Too low
at step2 for Z0 validity |
|
|
348 |
100101010000001 |
0.0791015625*S+0.1005859375 |
Too low
at step2 for Z0 validity |
|
|
349 |
100101010000010 |
0.474609375*S+1.603515625 |
Too low
at step2 for Z0 validity |
|
|
350 |
100101010000100 |
0.474609375*S+1.103515625 |
Too low
at step2 for Z0 validity |
|
|
351 |
100101010000101 |
0.474609375*S+1.103515625 |
Too low
at step2 for Z0 validity |
|
|
352 |
100101010001000 |
0.474609375*S+0.853515625 |
Too low
at step2 for Z0 validity |
|
|
353 |
100101010001001 |
0.474609375*S+0.853515625 |
Too low
at step2 for Z0 validity |
|
|
354 |
100101010001010 |
2.84765625*S+6.12109375 |
Too low
at step2 for Z0 validity |
|
|
355 |
100101010010000 |
0.474609375*S+0.728515625 |
Too low
at step2 for Z0 validity |
|
|
356 |
100101010010001 |
0.474609375*S+0.728515625 |
Too low
at step2 for Z0 validity |
|
|
357 |
100101010010010 |
2.84765625*S+5.37109375 |
Too low
at step2 for Z0 validity |
|
|
358 |
100101010010100 |
2.84765625*S+4.87109375 |
Too low
at step2 for Z0 validity |
|
|
359 |
100101010010101 |
2.84765625*S+4.87109375 |
Too low
at step2 for Z0 validity |
|
|
360 |
100101010100000 |
0.474609375*S+0.666015625 |
Too low
at step2 for Z0 validity |
|
|
361 |
100101010100001 |
0.474609375*S+0.666015625 |
Too low
at step2 for Z0 validity |
|
|
362 |
100101010100010 |
2.84765625*S+4.99609375 |
Too low
at step2 for Z0 validity |
|
|
363 |
100101010100100 |
2.84765625*S+4.49609375 |
Too low
at step2 for Z0 validity |
|
|
364 |
100101010100101 |
2.84765625*S+4.49609375 |
Too low
at step2 for Z0 validity |
|
|
365 |
100101010101000 |
2.84765625*S+4.24609375 |
Too low
at step2 for Z0 validity |
|
|
366 |
100101010101010 |
17.0859375*S+26.4765625 |
Too low
at step2 for Z0 validity |
|
|
367 |
101000000000000 |
0.002197265625*S+0.001220703125 |
Too low
at step5 for Z0 validity |
|
|
368 |
101000000000001 |
0.002197265625*S+0.001220703125 |
Too low
at step5 for Z0 validity |
|
|
369 |
101000000000010 |
0.01318359375*S+1.00732421875 |
Too low
at step5 for Z0 validity |
|
|
370 |
101000000000100 |
0.01318359375*S+0.50732421875 |
Too low
at step5 for Z0 validity |
|
|
371 |
101000000000101 |
0.01318359375*S+0.50732421875 |
Too low
at step5 for Z0 validity |
|
|
372 |
101000000001000 |
0.01318359375*S+0.25732421875 |
Too low
at step5 for Z0 validity |
|
|
373 |
101000000001001 |
0.01318359375*S+0.25732421875 |
Too low
at step5 for Z0 validity |
|
|
374 |
101000000001010 |
0.0791015625*S+2.5439453125 |
Too low
at step5 for Z0 validity |
|
|
375 |
101000000010000 |
0.01318359375*S+0.13232421875 |
Too low
at step5 for Z0 validity |
|
|
376 |
101000000010001 |
0.01318359375*S+0.13232421875 |
Too low
at step5 for Z0 validity |
|
|
377 |
101000000010010 |
0.0791015625*S+1.7939453125 |
Too low
at step5 for Z0 validity |
|
|
378 |
101000000010100 |
0.0791015625*S+1.2939453125 |
Too low
at step5 for Z0 validity |
|
|
379 |
101000000010101 |
0.0791015625*S+1.2939453125 |
Too low
at step5 for Z0 validity |
|
|
380 |
101000000100000 |
0.01318359375*S+0.06982421875 |
Too low
at step5 for Z0 validity |
|
|
381 |
101000000100001 |
0.01318359375*S+0.06982421875 |
Too low
at step5 for Z0 validity |
|
|
382 |
101000000100010 |
0.0791015625*S+1.4189453125 |
Too low
at step5 for Z0 validity |
|
|
383 |
101000000100100 |
0.0791015625*S+0.9189453125 |
Too low
at step5 for Z0 validity |
|
|
384 |
101000000100101 |
0.0791015625*S+0.9189453125 |
Too low
at step5 for Z0 validity |
|
|
385 |
101000000101000 |
0.0791015625*S+0.6689453125 |
Too low
at step5 for Z0 validity |
|
|
386 |
101000000101001 |
0.0791015625*S+0.6689453125 |
Too low
at step5 for Z0 validity |
|
|
387 |
101000000101010 |
0.474609375*S+5.013671875 |
Too low
at step5 for Z0 validity |
|
|
388 |
101000001000000 |
0.01318359375*S+0.03857421875 |
Too low
at step5 for Z0 validity |
|
|
389 |
101000001000001 |
0.01318359375*S+0.03857421875 |
Too low
at step5 for Z0 validity |
|
|
390 |
101000001000010 |
0.0791015625*S+1.2314453125 |
Too low
at step5 for Z0 validity |
|
|
391 |
101000001000100 |
0.0791015625*S+0.7314453125 |
Too low
at step5 for Z0 validity |
|
|
392 |
101000001000101 |
0.0791015625*S+0.7314453125 |
Too low
at step5 for Z0 validity |
|
|
393 |
101000001001000 |
0.0791015625*S+0.4814453125 |
Too low
at step5 for Z0 validity |
|
|
394 |
101000001001001 |
0.0791015625*S+0.4814453125 |
Too low
at step5 for Z0 validity |
|
|
395 |
101000001001010 |
0.474609375*S+3.888671875 |
Too low
at step5 for Z0 validity |
|
|
396 |
101000001010000 |
0.0791015625*S+0.3564453125 |
Too low
at step5 for Z0 validity |
|
|
397 |
101000001010001 |
0.0791015625*S+0.3564453125 |
Too low
at step5 for Z0 validity |
|
|
398 |
101000001010010 |
0.474609375*S+3.138671875 |
Too low
at step5 for Z0 validity |
|
|
399 |
101000001010100 |
0.474609375*S+2.638671875 |
Too low
at step5 for Z0 validity |
|
|
400 |
101000001010101 |
0.474609375*S+2.638671875 |
Too low
at step5 for Z0 validity |
|
|
401 |
101000010000000 |
0.01318359375*S+0.02294921875 |
Too low
at step5 for Z0 validity |
|
|
402 |
101000010000001 |
0.01318359375*S+0.02294921875 |
Too low
at step5 for Z0 validity |
|
|
403 |
101000010000010 |
0.0791015625*S+1.1376953125 |
Too low
at step5 for Z0 validity |
|
|
404 |
101000010000100 |
0.0791015625*S+0.6376953125 |
Too low
at step5 for Z0 validity |
|
|
405 |
101000010000101 |
0.0791015625*S+0.6376953125 |
Too low
at step5 for Z0 validity |
|
|
406 |
101000010001000 |
0.0791015625*S+0.3876953125 |
Too low
at step5 for Z0 validity |
|
|
407 |
101000010001001 |
0.0791015625*S+0.3876953125 |
Too low
at step5 for Z0 validity |
|
|
408 |
101000010001010 |
0.474609375*S+3.326171875 |
Too low
at step5 for Z0 validity |
|
|
409 |
101000010010000 |
0.0791015625*S+0.2626953125 |
Too low
at step5 for Z0 validity |
|
|
410 |
101000010010001 |
0.0791015625*S+0.2626953125 |
Too low
at step5 for Z0 validity |
|
|
411 |
101000010010010 |
0.474609375*S+2.576171875 |
Too low
at step5 for Z0 validity |
|
|
412 |
101000010010010 |
0.474609375*S+2.576171875 |
Too low
at step5 for Z0 validity |
|
|
413 |
101000010010100 |
0.474609375*S+2.076171875 |
Too low
at step5 for Z0 validity |
|
|
414 |
101000010010101 |
0.474609375*S+2.076171875 |
Too low
at step5 for Z0 validity |
|
|
415 |
101000010100000 |
0.0791015625*S+0.2001953125 |
Too low
at step5 for Z0 validity |
|
|
416 |
101000010100001 |
0.0791015625*S+0.2001953125 |
Too low
at step5 for Z0 validity |
|
|
417 |
101000010100010 |
0.474609375*S+2.201171875 |
Too low
at step5 for Z0 validity |
|
|
418 |
101000010100100 |
0.474609375*S+1.701171875 |
Too low
at step5 for Z0 validity |
|
|
419 |
101000010100101 |
0.474609375*S+1.701171875 |
Too low
at step5 for Z0 validity |
|
|
420 |
101000010101000 |
0.474609375*S+1.451171875 |
Too low
at step5 for Z0 validity |
|
|
421 |
101000010101010 |
2.84765625*S+9.70703125 |
Too low
at step5 for Z0 validity |
|
|
422 |
101000100000000 |
0.01318359375*S+0.01513671875 |
Too low
at step5 for Z0 validity |
|
|
423 |
101000100000001 |
0.01318359375*S+0.01513671875 |
Too low
at step5 for Z0 validity |
|
|
424 |
101000100000010 |
0.0791015625*S+1.0908203125 |
Too low
at step5 for Z0 validity |
|
|
425 |
101000100000100 |
0.0791015625*S+0.5908203125 |
Too low
at step5 for Z0 validity |
|
|
426 |
101000100000101 |
0.0791015625*S+0.5908203125 |
Too low
at step5 for Z0 validity |
|
|
427 |
101000100001000 |
0.0791015625*S+0.3408203125 |
Too low
at step5 for Z0 validity |
|
|
428 |
101000100001001 |
0.0791015625*S+0.3408203125 |
Too low
at step5 for Z0 validity |
|
|
429 |
101000100001010 |
0.474609375*S+3.044921875 |
Too low
at step5 for Z0 validity |
|
|
430 |
101000100010000 |
0.0791015625*S+0.2158203125 |
Too low
at step5 for Z0 validity |
|
|
431 |
101000100010001 |
0.0791015625*S+0.2158203125 |
Too low
at step5 for Z0 validity |
|
|
432 |
101000100010010 |
0.474609375*S+2.294921875 |
Too low
at step5 for Z0 validity |
|
|
433 |
101000100010100 |
0.474609375*S+1.794921875 |
Too low
at step5 for Z0 validity |
|
|
434 |
101000100010101 |
0.474609375*S+1.794921875 |
Too low
at step5 for Z0 validity |
|
|
435 |
101000100100000 |
0.0791015625*S+0.1533203125 |
Too low
at step5 for Z0 validity |
|
|
436 |
101000100100001 |
0.0791015625*S+0.1533203125 |
Too low
at step5 for Z0 validity |
|
|
437 |
101000100100010 |
0.474609375*S+1.919921875 |
Too low
at step5 for Z0 validity |
|
|
438 |
101000100100100 |
0.474609375*S+1.419921875 |
Too low
at step5 for Z0 validity |
|
|
439 |
101000100100101 |
0.474609375*S+1.419921875 |
Too low
at step5 for Z0 validity |
|
|
440 |
101000100101000 |
0.474609375*S+1.169921875 |
Too low
at step5 for Z0 validity |
|
|
441 |
101000100101010 |
2.84765625*S+8.01953125 |
Too low
at step5 for Z0 validity |
|
|
442 |
101001000000000 |
0.01318359375*S+0.01123046875 |
Too low
at step7 for Z0 validity |
|
|
443 |
101001000000001 |
0.01318359375*S+0.01123046875 |
Too low
at step7 for Z0 validity |
|
|
444 |
101001000000010 |
0.0791015625*S+1.0673828125 |
Too low
at step7 for Z0 validity |
|
|
445 |
101001000000100 |
0.0791015625*S+0.5673828125 |
Too low
at step7 for Z0 validity |
|
|
446 |
101001000000101 |
0.0791015625*S+0.5673828125 |
Too low
at step7 for Z0 validity |
|
|
447 |
101001000001000 |
0.0791015625*S+0.3173828125 |
Too low
at step7 for Z0 validity |
|
|
448 |
101001000001001 |
0.0791015625*S+0.3173828125 |
Too low
at step7 for Z0 validity |
|
|
449 |
101001000001010 |
0.474609375*S+2.904296875 |
Too low
at step7 for Z0 validity |
|
|
450 |
101001000010000 |
0.0791015625*S+0.1923828125 |
Too low
at step7 for Z0 validity |
|
|
451 |
101001000010001 |
0.0791015625*S+0.1923828125 |
Too low
at step7 for Z0 validity |
|
|
452 |
101001000010010 |
0.474609375*S+2.154296875 |
Too low
at step7 for Z0 validity |
|
|
453 |
101001000010100 |
0.474609375*S+1.654296875 |
Too low
at step7 for Z0 validity |
|
|
454 |
101001000010101 |
0.474609375*S+1.654296875 |
Too low
at step7 for Z0 validity |
|
|
455 |
101001000100000 |
0.0791015625*S+0.1298828125 |
Too low
at step7 for Z0 validity |
|
|
456 |
101001000100001 |
0.0791015625*S+0.1298828125 |
Too low
at step7 for Z0 validity |
|
|
457 |
101001000100010 |
0.474609375*S+1.779296875 |
Too low
at step7 for Z0 validity |
|
|
458 |
101001000100100 |
0.474609375*S+1.279296875 |
Too low
at step7 for Z0 validity |
|
|
459 |
101001000100101 |
0.474609375*S+1.279296875 |
Too low
at step7 for Z0 validity |
|
|
460 |
101001000101000 |
0.474609375*S+1.029296875 |
Too low
at step7 for Z0 validity |
|
|
461 |
101001000101001 |
0.474609375*S+1.029296875 |
Too low
at step7 for Z0 validity |
|
|
462 |
101001000101010 |
2.84765625*S+7.17578125 |
Too low
at step7 for Z0 validity |
|
|
463 |
101001001000000 |
0.0791015625*S+0.0986328125 |
Too low
at step7 for Z0 validity |
|
|
464 |
101001001000001 |
0.0791015625*S+0.0986328125 |
Too low
at step7 for Z0 validity |
|
|
465 |
101001001000010 |
0.474609375*S+1.591796875 |
Too low
at step7 for Z0 validity |
|
|
466 |
101001001000100 |
0.474609375*S+1.091796875 |
Too low
at step7 for Z0 validity |
|
|
467 |
101001001000101 |
0.474609375*S+1.091796875 |
Too low
at step7 for Z0 validity |
|
|
468 |
101001001001000 |
0.474609375*S+0.841796875 |
Too low
at step7 for Z0 validity |
|
|
469 |
101001001001001 |
0.474609375*S+0.841796875 |
Too low
at step7 for Z0 validity |
|
|
470 |
101001001001010 |
2.84765625*S+6.05078125 |
Too low
at step7 for Z0 validity |
|
|
471 |
101001001010000 |
0.474609375*S+0.716796875 |
Too low
at step7 for Z0 validity |
|
|
472 |
101001001010001 |
0.474609375*S+0.716796875 |
Too low
at step7 for Z0 validity |
|
|
473 |
101001001010010 |
2.84765625*S+5.30078125 |
Too low
at step7 for Z0 validity |
|
|
474 |
101001001010100 |
2.84765625*S+4.80078125 |
Too low
at step7 for Z0 validity |
|
|
475 |
101001001010101 |
2.84765625*S+4.80078125 |
Too low
at step7 for Z0 validity |
|
|
476 |
101001010000000 |
0.0791015625*S+0.0830078125 |
Too low
at step9 for Z0 validity |
|
|
477 |
101001010000001 |
0.0791015625*S+0.0830078125 |
Too low
at step9 for Z0 validity |
|
|
478 |
101001010000010 |
0.474609375*S+1.498046875 |
Too low
at step9 for Z0 validity |
|
|
479 |
101001010000100 |
0.474609375*S+0.998046875 |
Too low
at step9 for Z0 validity |
|
|
480 |
101001010000101 |
0.474609375*S+0.998046875 |
Too low
at step9 for Z0 validity |
|
|
481 |
101001010001000 |
0.474609375*S+0.748046875 |
Too low
at step9 for Z0 validity |
|
|
482 |
101001010001001 |
0.474609375*S+0.748046875 |
Too low
at step9 for Z0 validity |
|
|
483 |
101001010001010 |
2.84765625*S+5.48828125 |
Too low
at step9 for Z0 validity |
|
|
484 |
101001010010000 |
0.474609375*S+0.623046875 |
Too low
at step12 for Z0 validity |
|
|
485 |
101001010010001 |
0.474609375*S+0.623046875 |
Too low
at step12 for Z0 validity |
|
|
486 |
101001010010010 |
2.84765625*S+4.73828125 |
Too low
at step12 for Z0 validity |
|
|
487 |
101001010010100 |
2.84765625*S+4.23828125 |
path coalesces in <2S
range |
507 duplicated by 724 |
|
488 |
101001010010101 |
2.84765625*S+4.23828125 |
path coalesces in <2S
range |
251 duplicated by 444 |
|
489 |
101001010100000 |
0.474609375*S+0.560546875 |
Too low
at step12 for Z0 validity |
|
|
490 |
101001010100001 |
0.474609375*S+0.560546875 |
Too low
at step12 for Z0 validity |
|
|
491 |
101001010100010 |
2.84765625*S+4.36328125 |
Too low
at step12 for Z0 validity |
|
|
492 |
101001010100100 |
2.84765625*S+3.86328125 |
path coalesces in <2S
range |
347 duplicated by 462 |
|
493 |
101001010100101 |
2.84765625*S+3.86328125 |
path coalesces in <2S
range |
91 duplicated by 94 |
|
494 |
101001010101000 |
2.84765625*S+3.61328125 |
path coalesces in <2S
range |
411 duplicated by 782 |
|
495 |
101001010101001 |
2.84765625*S+3.61328125 |
path coalesces in <2S
range |
155 duplicated by 274 |
|
496 |
101001010101010 |
17.0859375*S+22.6796875 |
path coalesces in <2S
range |
27 duplicated by 46 |
|
497 |
101010000000000 |
0.01318359375*S+0.00927734375 |
Too low
at step7 for Z0 validity |
|
|
498 |
101010000000001 |
0.01318359375*S+0.00927734375 |
Too low
at step7 for Z0 validity |
|
|
499 |
101010000000010 |
0.0791015625*S+1.0556640625 |
Too low
at step7 for Z0 validity |
|
|
500 |
101010000000100 |
0.0791015625*S+0.5556640625 |
Too low
at step7 for Z0 validity |
|
|
501 |
101010000000101 |
0.0791015625*S+0.5556640625 |
Too low
at step7 for Z0 validity |
|
|
502 |
101010000001000 |
0.0791015625*S+0.3056640625 |
Too low
at step7 for Z0 validity |
|
|
503 |
101010000001001 |
0.0791015625*S+0.3056640625 |
Too low
at step7 for Z0 validity |
|
|
504 |
101010000001010 |
0.474609375*S+2.833984375 |
Too low
at step7 for Z0 validity |
|
|
505 |
101010000010000 |
0.0791015625*S+0.1806640625 |
Too low
at step7 for Z0 validity |
|
|
506 |
101010000010001 |
0.0791015625*S+0.1806640625 |
Too low
at step7 for Z0 validity |
|
|
507 |
101010000010010 |
0.474609375*S+2.083984375 |
Too low
at step7 for Z0 validity |
|
|
508 |
101010000010100 |
0.474609375*S+1.583984375 |
Too low
at step7 for Z0 validity |
|
|
509 |
101010000010101 |
0.474609375*S+1.583984375 |
Too low
at step7 for Z0 validity |
|
|
510 |
101010000100000 |
0.0791015625*S+0.1181640625 |
Too low
at step7 for Z0 validity |
|
|
511 |
101010000100001 |
0.0791015625*S+0.1181640625 |
Too low
at step7 for Z0 validity |
|
|
512 |
101010000100010 |
0.474609375*S+1.708984375 |
Too low
at step7 for Z0 validity |
|
|
513 |
101010000100100 |
0.474609375*S+1.208984375 |
Too low
at step7 for Z0 validity |
|
|
514 |
101010000100101 |
0.474609375*S+1.208984375 |
Too low
at step7 for Z0 validity |
|
|
515 |
101010000101000 |
0.474609375*S+0.958984375 |
Too low
at step7 for Z0 validity |
|
|
516 |
101010000101001 |
0.474609375*S+0.958984375 |
Too low
at step7 for Z0 validity |
|
|
517 |
101010000101010 |
2.84765625*S+6.75390625 |
Too low
at step7 for Z0 validity |
|
|
518 |
101010001000000 |
0.0791015625*S+0.0869140625 |
Too low
at step7 for Z0 validity |
|
|
519 |
101010001000001 |
0.0791015625*S+0.0869140625 |
Too low
at step7 for Z0 validity |
|
|
520 |
101010001000010 |
0.474609375*S+1.521484375 |
Too low
at step7 for Z0 validity |
|
|
521 |
101010001000100 |
0.474609375*S+1.021484375 |
Too low
at step7 for Z0 validity |
|
|
522 |
101010001000101 |
0.474609375*S+1.021484375 |
Too low
at step7 for Z0 validity |
|
|
523 |
101010001001000 |
0.474609375*S+0.771484375 |
Too low
at step7 for Z0 validity |
|
|
524 |
101010001001010 |
2.84765625*S+5.62890625 |
Too low
at step7 for Z0 validity |
|
|
525 |
101010001010000 |
0.474609375*S+0.646484375 |
Too low
at step7 for Z0 validity |
|
|
526 |
101010001010001 |
0.474609375*S+0.646484375 |
Too low
at step7 for Z0 validity |
|
|
527 |
101010001010010 |
2.84765625*S+4.87890625 |
Too low
at step7 for Z0 validity |
|
|
528 |
101010001010100 |
2.84765625*S+4.37890625 |
Too low
at step7 for Z0 validity |
|
|
529 |
101010001010101 |
2.84765625*S+4.37890625 |
Too low
at step7 for Z0 validity |
|
|
530 |
101010010000000 |
0.0791015625*S+0.0712890625 |
Too low
at step10 for Z0 validity |
|
|
531 |
101010010000001 |
0.0791015625*S+0.0712890625 |
Too low
at step10 for Z0 validity |
|
|
532 |
101010010000010 |
0.474609375*S+1.427734375 |
Too low
at step10 for Z0 validity |
|
|
533 |
101010010000100 |
0.474609375*S+0.927734375 |
Too low
at step10 for Z0 validity |
|
|
534 |
101010010001000 |
0.474609375*S+0.677734375 |
Too low
at step10 for Z0 validity |
|
|
535 |
101010010001001 |
0.474609375*S+0.677734375 |
Too low
at step10 for Z0 validity |
|
|
536 |
101010010001010 |
2.84765625*S+5.06640625 |
Too low
at step10 for Z0 validity |
|
|
537 |
101010010010000 |
0.474609375*S+0.552734375 |
Too low
at step12 for Z0 validity |
|
|
538 |
101010010010001 |
0.474609375*S+0.552734375 |
Too low
at step12 for Z0 validity |
|
|
539 |
101010010010010 |
2.84765625*S+4.31640625 |
Too low
at step12 for Z0 validity |
|
|
540 |
101010010010100 |
2.84765625*S+3.81640625 |
path coalesces in <2S
range |
71 duplicated by 124 |
|
541 |
101010010010101 |
2.84765625*S+3.81640625 |
path coalesces in <2S
range |
327 duplicated by 638 |
|
542 |
101010010100000 |
0.474609375*S+0.490234375 |
Too low
at step12 for Z0 validity |
|
|
543 |
101010010100001 |
0.474609375*S+0.490234375 |
Too low
at step12 for Z0 validity |
|
|
544 |
101010010100010 |
2.84765625*S+3.94140625 |
Too low
at step12 for Z0 validity |
|
|
545 |
101010010100100 |
2.84765625*S+3.44140625 |
path coalesces in <2S
range |
423 duplicated by 804 |
|
546 |
101010010100101 |
2.84765625*S+3.44140625 |
path coalesces in <2S
range |
167 duplicated by 330 |
|
547 |
101010010101000 |
2.84765625*S+3.19140625 |
path coalesces in <2S
range |
387 duplicated by 756 |
|
548 |
101010010101001 |
2.84765625*S+3.19140625 |
path coalesces in <2S
range |
231 duplicated by 496 |
|
549 |
101010010101010 |
17.0859375*S+20.1484375 |
path coalesces in <2S
range |
103 duplicated by 182 |
|
550 |
101010100000000 |
0.0791015625*S+0.0634765625 |
Too low
at step10 for Z0 validity |
|
|
551 |
101010100000001 |
0.0791015625*S+0.0634765625 |
Too low
at step10 for Z0 validity |
|
|
552 |
101010100000010 |
0.474609375*S+1.380859375 |
Too low
at step10 for Z0 validity |
|
|
553 |
101010100000100 |
0.474609375*S+0.880859375 |
Too low
at step10 for Z0 validity |
|
|
554 |
101010100000101 |
0.474609375*S+0.880859375 |
Too low
at step10 for Z0 validity |
|
|
555 |
101010100001000 |
0.474609375*S+0.630859375 |
Too low
at step10 for Z0 validity |
|
|
556 |
101010100001001 |
0.474609375*S+0.630859375 |
Too low
at step10 for Z0 validity |
|
|
557 |
101010100001010 |
2.84765625*S+4.78515625 |
Too low
at step10 for Z0 validity |
|
|
558 |
101010100010000 |
0.474609375*S+0.505859375 |
Too low
at step12 for Z0 validity |
|
|
559 |
101010100010001 |
0.474609375*S+0.505859375 |
Too low
at step12 for Z0 validity |
|
|
560 |
101010100010010 |
2.84765625*S+4.03515625 |
Too low
at step12 for Z0 validity |
|
|
561 |
101010100010100 |
2.84765625*S+3.53515625 |
path coalesces in <2S
range |
463 duplicated by 462,
also 924 |
|
562 |
101010100010101 |
2.84765625*S+3.53515625 |
path coalesces in <2S
range |
207 duplicated by 206,
also 412 |
|
563 |
101010100100000 |
0.474609375*S+0.443359375 |
Too low
at step12 for Z0 validity |
|
|
564 |
101010100100001 |
0.474609375*S+0.443359375 |
Too low
at step12 for Z0 validity |
|
|
565 |
101010100100010 |
2.84765625*S+3.66015625 |
Too low
at step12 for Z0 validity |
|
|
566 |
101010100100100 |
2.84765625*S+3.16015625 |
path
coalesces in <2S range |
303 duplicated by 594 |
|
567 |
101010100100101 |
2.84765625*S+3.16015625 |
path
coalesces in <2S range |
47 duplicated by 82 |
|
568 |
101010100101000 |
2.84765625*S+2.91015625 |
path
coalesces in <2S range |
367 duplicated by 698 |
|
569 |
101010100101001 |
2.84765625*S+2.91015625 |
path
coalesces in <2S range |
111 duplicated by 206 |
|
570 |
101010100101010 |
17.0859375*S+18.4609375 |
path
coalesces in <2S range |
239 duplicated by 446 |
|
571 |
101010101000000 |
0.474609375*S+0.412109375 |
Too low
at step12 for Z0 validity |
|
|
572 |
101010101000001 |
0.474609375*S+0.412109375 |
Too low
at step12 for Z0 validity |
|
|
573 |
101010101000010 |
2.84765625*S+3.47265625 |
Too low
at step12 for Z0 validity |
|
|
574 |
101010101000100 |
2.84765625*S+2.97265625 |
path
coalesces in <2S range |
479 duplicated by 478 also
934 |
|
575 |
101010101000101 |
2.84765625*S+2.97265625 |
path
coalesces in <2S range |
223 duplicated by 222 |
|
576 |
101010101001000 |
2.84765625*S+2.72265625 |
path
coalesces in <2S range |
287 duplicated by 508 |
|
577 |
101010101001001 |
2.84765625*S+2.72265625 |
path
coalesces in <2S range |
31 duplicated by 54 |
|
578 |
101010101001010 |
17.0859375*S+17.3359375 |
path
coalesces in <2S range |
159 duplicated by 310 |
|
579 |
101010101010000 |
2.84765625*S+2.59765625 |
path
coalesces in <2S range |
63 duplicated by 62 also
124 |
|
580 |
101010101010001 |
2.84765625*S+2.59765625 |
path
coalesces in <2S range |
319 duplicated is 318 |
|
581 |
101010101010100 |
17.0859375*S+16.0859375 |
path
coalesces in <2S range |
127 duplicated by 204 |
|
582 |
101010101010101 |
17.0859375*S+16.0859375 |
path
coalesces in <2S range |
255 duplicated by 254 |
Lemma — Contradiction
Let 
. It must firstly obey the boundaries shown in
Lemma 6, that is in its the first 15 steps 
it cannot follow the 551
paths which produce even values lower than 2.
It must therefore follow one of the 30 paths
shown in Lemma 6, however the paths produce the same trajectories for both
c-numbers and z-numbers as the Collatz transform effects are the same – and
where those trajectory paths are followed by illustrative c-numbers they in each case
coalesce with trajectories originating in the Seed+1 to 2Seed-2 range. Such coalescence is invalid as shown for z-numbers arising from Z0.
If only 581 15 step paths exist for and 551 result in a number < 2 – which contradicts Lemma 2, and the remain 30
paths result in 
trajectory – composed by definition only of
z-numbers to co-inciding with trajectories originating in the range defined by
Lemma 3-6 as containing only c-numbers, then the numbers at the point of
coalescence of the trajectories would be required to be both z-numbers and
c-numbers which is contradictory.
If no path is possible for 
If no least
z-number exists, no z-number exists.
If no z-number
exists, then Collatz is proven.
Conclusion
Since assuming the existence of a least z‑number leads to contradiction, no such number exists. Thus no z‑numbers exist. Therefore every positive integer is a c‑number, and the Collatz conjecture is true.
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