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updated white paper

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33
docs/blockdag_consensus.md
View File

@ -344,8 +344,7 @@ to add another block, rather than attempt to replace an existing block.
In Paxos, once one peer accepts one value, it will eventually become the
consensus value, assuming that everyone eventually gets through and that
the usual network problems do not foul things up. Thus Paxos can provide
a definitive result eventually, while Bitcoin's results are never definitive,
merely exponentially probable.
a definitive result eventually, while the results of Bitcoin type consensus are never definitive, merely exponentially probable.
In Paxos, a peer learns of the definitive and final consensus when it
discovers that a majority of peers have accepted one value. Which if
@ -357,14 +356,34 @@ other, but there is no moment when a peer discovers than one branch is
definitive and final. It just finds that one branch is becoming more and
more likely, and all the other branches less and less likely.
Thus paxos has a stronger liveness property than bitcoin, but this
difference is in practice not important, for paxos may take an indefinitely
long time before it can report a definite and final consensus, while Bitcoin
takes a fairly definite time to report it is nearly certain about the consensus
value and that value is unlikely is unlikely to change.
Thus Paxos type algorithms (such as Paxos, Raft, and their Byzantine fault
tolerant equivalents) have a stronger liveness property than bitcoin type
algorithms, but this difference is in practice not important, for paxos may
take an indefinitely long time before it can report a definite and final
consensus, while a Bitcoin like consensus algorithm takes a fairly definite
time to report it is nearly certain about the consensus value and that value
is unlikely to change.
Further, in actual practice, particularly during a view change, Paxos and Raft are frequently in a state where a peer knows that one view is overwhelmingly likely to become final, and another view highly unlikely, but the state takes a while to finalize. And the client is waiting. So it winds up reporting a provisional result to the client.
Thus in practice, the difference between the liveness condition of Paxos
type algorithms, which eventually provide a definitive proof that
consensus has been achieved, is not usefully stronger than the weaker liveness condition of consensus algorithms that merely provide an ever
growing likelihood that consensus has been achieved, and instead of
telling the client that consensus has been achieved or not, merely tell the
client how strong the evidence is that consensus has been achieved.
And in practice, Byzantine Fault Tolerant Paxos like algorithms tend to be
"optimized" by behaving like bitcoin type algorithms, making their
implementation considerably more complicated.
Crypto currency consensus algorithms derived from Paxos equivalent
consensus fail to scale, because they actually have to find out that a
majority of peers are on the same consensus. And there could be a lot of
peers, so this is a lot of data, and it is quite easy to maliciously attack the
network in ways to make this data difficult to obtain, if someone found it
convenient to stall a transaction from going through. "The cheque is in the mail."
# Bitcoin does not scale to competing with fiat currency
Bitcoin is limited to ten transactions per second. Credit card networks

43
docs/merkle_patricia-dac.md
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@ -856,32 +856,47 @@ solve the problem of the number of items not being a power of two?
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
width="29em" height="17em"
viewBox="0 202 230 102"
viewBox="0 200 230 102"
style="background-color:ivory" stroke-width=".6" stroke-linecap="round" >
<!--viewBox="-12 209 360 102" -->
<!--
viewBox="0 200 230 102"
viewBox="-12 209 360 102" -->
<!-- viewBox="130 209 180 50" -->
<g font-family="'Times New Roman'" font-size="10" font-weight="400" fill-rule="evenodd" fill="black" >
<path stroke="#80e080" fill="none"
<path stroke="#00D000" fill="none"
d="
M10 253c-3.536 5.335-4.29 7.765-4.466 12.095-.139 3.405.677 6 3.3 2.094
M18 245c1.799-1.55 20.903-7.319 35.603-10.855 14.7-3.535 18.918-7.69 52.35-8.621 33.432-.93 36.037-.869 38-3
M18 245 c1.799,-1.55 20.903,-7.319 35.603,-10.855
14.7,-3.535 18.918,-7.69 52.35,-8.621 c20,0 0,-0 35.5,0
q4,-0 4,-3.5
M21 248c2.17-.372 6.744-1.343 10.792-1.736 5.858-.57 18.925-2.228 29-4.094 3.36-.728 7.673-1.492 7.618-2.812
M16.963 253.232c-.0 0 3 4 5.2 4.2 1.7 .7 4.093 .6 7-2.3
"/>
<g id="blockchain_id" >
<ellipse cx="14" cy="249" fill="#80e080" rx="8" ry="5"/>
<ellipse cx="14" cy="249" fill="#00D000" rx="8" ry="5"/>
<text fill="black">
<tspan x="11.08" y="251.265">id</tspan>
</text>
</g>
<g id="balanced merkle tree" fill="none">
<g id="height_4_tree" >
<path stroke="#F00000"
d="
M146,222 C146,217 152,217 156,219 S202,238.2 206,240
c4,2 8,3 8,-2
M146,222 C146,217 152,217 154,221
l15.5,33 l1,2 c1,2 3.5,2 3.5,-2
M146,222 C146,217 152,217 151,222
S149,264 149,266 c1,5 5,5 4,0
"/>
<!--
<path stroke="#F00000"
d="
M146,220 q2,-3 4,-2 t26,14 t34,9 t2,-1
M147,218.5 q2,-2 2,4 t-1,22 t1,22 t4,0
M146,220 c0,-1 0,-1 1,-1 c1,0 3,0 3,1 s3,0 12,26 s 14,-1 14,9
"/>
-->
<path stroke="#000000"
d="
M146, 220 c4,-20 151,2 151.5,-12
@ -890,31 +905,27 @@ solve the problem of the number of items not being a power of two?
<g id="height_3_tree">
<path stroke="#F00000"
d="
M71,234.686 s2,-1 3,0 t10,15 t15,2
M71.36 234.686s1.551-.558 2.171.186c.62.745 2.481 4.528 1.8 10.545-.683 6.016-2.854 20.719-2.854 22.577 0 2.171 1.116 2.482 2.543 1.8C76.447 269.11 76 268 77 264
M70,237 c5,-9 5,0 15,12 s11.5,7 14,3
M70,237 c5,-9 5,0 3,20 s6,10 5,8
"/>
<path stroke="#000000"
d="
M70,236 c0,-6 74,-3 76,-12
M70,237 c1,-5 9,-5 20,-5 s30,-1 39,-2.5
C146,227 144, 227, 145.5,224
m-7,12 c0,-6 9,-6 8,-12"
/>
<g id="height_2_tree">
<path stroke="#F00000"
d="
M31.3 250.83c1.054-.372 2.046-.744 2.357.31.31 1.055-.571 11.044.682 15.569C36.013 272.766 38 269.675 39 266"/>
M30,254 C33,249 35,249 35,263 S43,262 40,267"/>
<path stroke="#000000"
d="
m29.767 252c1.774-4 38.858-5.904 39.18-12
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M30,254 C33,249 35,249 50,248 s20,-9 20,-9"/>
<path id="uplink_1-2" stroke="#000000"
d="
M60 252c0-4.875 10.41-6.871 11.205-12
"/>
<g id="height_1_tree">
<path
style="stroke:#F00000"
d="M10,264 q3,-4 6,2 t4.5,2"
id="prev_leaf_link"/>
<path stroke="#000"
d="M10.09,264 q2,-4 11,-4 t9,-5
M22,264 c0,-3 9,-1.5 9,-8"/>
@ -952,7 +963,7 @@ solve the problem of the number of items not being a power of two?
<g id="merkle_chain">
<use transform="translate(0,50)" xlink:href="#blockchain_id"/>
<path
style="fill:none;stroke:#80e080;"
style="fill:none;stroke:#00D000;"
d="m 18,297 c 4,-6 4,-6 5.6,3 C 25,305 28,304 28.5,300"/>
<g id="16_leaf_links">
<g id="8_leaf_links">

10
docs/mkdocs.sh
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@ -1,5 +1,6 @@
#!/bin/bash
set -e
set -x
cd `dirname $0`
if [[ "$OSTYPE" == "linux-gnu"* ]]; then
@ -15,15 +16,19 @@ templates="./pandoc_templates"
options=$osoptions"--toc -N --toc-depth=5 --wrap=preserve --metadata=lang:en --include-in-header=$templates/icon.pandoc --include-before-body=$templates/before.pandoc --css=$templates/style.css -o"
for f in *.md
do
echo $f
len=${#f}
base=${f:0:($len-3)}
if [ $f -nt $base.html ];
then
set -x
katex=""
mine="--include-after-body=$templates/after.pandoc "
for i in 1 2 3 4 5 6
for i in 1 2 3 4
do
set -x
read line
echo $line
if [[ $line =~ katex$ ]];
then
katex=" --katex=./"
@ -40,11 +45,13 @@ if [[ $line =~ notmine$ ]];
# echo " $base.html up to date"
fi
done
echo normal exit
cd libraries
templates="../pandoc_templates"
options=$osoptions"--toc -N --toc-depth=5 --wrap=preserve --metadata=lang:en --include-in-header=$templates/icondotdot.pandoc --include-before-body=$templates/beforedotdot.pandoc --css=$templates/style.css --include-after-body=$templates/after.pandoc -o"
for f in *.md
do
echo $f
len=${#f}
base=${f:0:($len-3)}
if [ $f -nt $base.html ];
@ -68,6 +75,7 @@ cd ../..
templates=docs/pandoc_templates
for f in *.md
do
echo $f
len=${#f}
base=${f:0:($len-3)}
if [ $f -nt $base.html ];

34
docs/number_encoding.md
View File

@ -1,5 +1,5 @@
---
lang: en
# katex
title: Number encoding
---
@ -10,6 +10,38 @@ in protocols tend to become obsolete. Therefore, for future
upwards compatibility, we want to have variable precision
numbers.
Secondly, to represent integers within a patricia merkle tree representing a database index, we want all values to be left field aligned, rather than right field aligned.
## Compression algorithm preserving sort order
We want to represent integers by byte strings whose lexicographic order reflects their order as integers, which is to say, when sorted as a left aligned field, sort like integers represented as a right aligned field. (Because a Merkle patricia tree has a hard time with right aligned fields)
To do this we have a field that is a count of the number of bytes, and the size of that field is encoded in unary.
Thus a single byte value, representing integers in the range $0\le n \lt 2^7$ starts with a leading zero bit
A two byte value, representing integers in the range $2^7\le n \lt 2^{13}+2^7$ starts with the bits 100
A three byte value, representing integers in the range $2^{13}+2^7 \le n \lt 2^{21}+2^{13}+2^7$ starts with the bits 101
A four byte value representing integers in the range $2^{21}+2^{13}+2^7 \le n \lt 2^{27}+2^{21}+2^{13}+2^7$ starts with the bits 11000
A five byte value representing integers in the range $2^{21}+2^{13}+2^7 \le n \lt 2^{35}+2^{27}+2^{21}+2^{13}+2^7+2^{13}+2^7$ starts with the bits 11001
A six byte value representing integers in the range $2^{35}+2^{21}+2^{13}+2^7 \le n \lt 2^{43}+2^{35}+2^{27}+2^{21}+2^{13}+2^7+2^{13}+2^7$ starts with the bits 11010
A seven byte value representing integers in the range $2^{43}+2^{35}+2^{21}+2^{13}+2^7 \le n \lt2^{51}+2^{43}+2^{35}+2^{27}+2^{21}+2^{13}+2^7+2^{13}+2^7$ starts with the bits 11011
An eight byte value representing integers in the range $2^{51}2^{43}+2^{35}+2^{21}+2^{13}+2^7 \le n \lt2^{57}+2^{51}+2^{43}+2^{35}+2^{27}+2^{21}+2^{13}+2^7+2^{13}+2^7$ starts with the bits 1110000
A nine byte value representing integers in the range $2^{57}+2^{51}+2^{43}+2^{35}+2^{21}+2^{13}+2^7 \le n \lt2^{65}+2^{57}+2^{51}+2^{43}+2^{35}+2^{27}+2^{21}+2^{13}+2^7+2^{13}+2^7$ starts with the bits 1110001
Similarly the bits 111 0111 indicate a fifteen byte value representing 113 bit integers.
To represent signed integers so that signed integers sort correctly with each other (but not with unsigned integers) the leading bit indicates the sign, a one bit for positive signed integers, and a zero bit for negative integers, and the if the signed integer is negative, we invert the bits of the byte count. Thus signed integers in the range $-2^6\le n \lt 2^6$ are represented by the corresponding eight bit value with its leading bit inverted.
This is perhaps a little too much cleverness except for the uncommon case where we actually need a representation that sorts correctly.
## Use case
QR codes and prefix free number encoding is useful in cases where we want data to be self describing – this bunch of bits is to be interpreted in a certain way, used in a certain action, means one thing, and not another thing. At present there is no standard for self description. QR codes are given meanings by the application, and could carry completely arbitrary data whose meaning and purpose comes from outside, from the context.

10
docs/white_paper.md
View File

@ -32,6 +32,11 @@ and twist the arms of the miners to exclude transactions in those bitcoins,
with the result bitcoins cease to be fungible and thus cease to be money, as
uncut diamonds ceased to be money.
We need untraceability to prevent the blood diamonds attack. Even if you
do not need your transactions to be untraceable, if they are traceable, ham
fisted government intervention is likely to make your money disappear
under you, as the value of uncut diamonds was lost.
Bitcoin is vulnerable to the one third attack. If one third of miners exclude
“tainted” bitcoins and refuse to add to a chain ending in a block containing
“tainted” bitcoins, other miners have an incentive to exclude “tainted”
@ -65,7 +70,8 @@ recording the accumulated effect of many transactions.
A true lightning network functions as full reserve correspondence
banking with no central authority. The existing Bitcoin lightning network
functions as marginal reserve banking with good conduct enforced by central
authority.
authority. Taproot was designed to make this fixable, and plans are afoot
to fix it. At the time of writing, it was not clear to me that it has been fixed.
But even with sidechaining and the lightning network, we are going to
need the capacity to put thousands of transactions per second on the
@ -106,7 +112,7 @@ connection to the internet, or someone’s computer goes down), or, if
someone breaks the circle in a Byzantine failure suggestive of Byzantine
defection, then, and only then, it goes through on the primary blockchain.
The problem with the existing Bitcoin lightning network is that it has a
The problem with the existing Bitcoin lightning network is, or recently was, that it has a
hidden and unexplained central authority, whom you have to trust, and
which does stuff that is never explained or revealed. This is not stable, and
does not scale. Not only is it evil, it is incapable of connecting everyone

84
docs/writing_and_editing_documentation.md
View File

@ -192,14 +192,76 @@ scalable vector graphics files (`svg` files) to html can get complicated, and
interfacing the resulting complicated html to markdown can get more
complicated.
Which means that any time I want to edit the `svg`, I have to extract it into a
temporary `svg` file, edit it in Inkscape and Visual Studio Code, minify it in
Inkscape files are unreadable, and once they are cleaned up, Inkscape
cannot read them. To (irreversibly) clean up an Inkscape file, minify it in
Visual Studio Code to get rid of all confusing mystery cruft inserted by
Inkscape, edit it back into markdown compatible form, and reinsert it in
the markdown file.
Which assumes my images, once done, are rarely or never going
to change.
A sequence of straight lines is M point, L point, L point.
Z and z draw a straight line back to the beginning, use in conjunction with
`fill="#red"` , for example `fill="#FF0000"`. If the line is open, `fill="none"`
Drawing smooth curves by typing in text is painful and slow, but so is
drawing them in Inkscape. Inkscape is apt to do a series of C beziers with
sharp corners between them, and when I try to fix the sharp corners, the
bezier goes weird.
What Inkscape should do is let you manipulate a sequence of control
points, and draw an M C S S ..S bezier to the point halfway between the
final even numbered control point and the preceding control point,
creating an additional control point by mirroring if the user only provides
an odd number of control points.
What it does instead is complicated and mysterious.
To convert a sequence of straight lines into a smooth curve, you encounter
much grief matching the end of one bezier to the start of the next.\
And if you do not match them, you get corners between beziers.
* find the midpoint of each edge, or the midpoint of every second edge\
When I say midpoint, somewhere along the line, close to where
you want the turn to sharp, and far from where you want the turn to be gentle.
* A smooth curve starts a midpoint of first edge then:\
C first vertex, second vertex, next midpoint S second next vertex
next midpoint S second next vertex, next midpoint ... S second next
vertex next midpoint ...\
When I say second next vertex, I mean you skip a vertex, and thus
do not have to find the preceding midpoint. But the implied vertex
is the mirror of the preceding vertex, which if your midpoint is off,
is not where you expect it to be.\
If it fails to go through the midpoint parallel to what you think the
endpoints are, you need to tinker the control point to reduce the
discrepancy, or else it is apt to be off at subsequent midpoints.
* Or starts at midpoint of first edge then:\
Q vertex midpoint T midpoint T midpoint ....\
But the Q T T T chain is apt to act weird unless your midpoints are
near the middle, because the implied vertex is the mirror of the
preceding vertex, which may not be the vertex that you intended if
your midpoint is not near the centre of the line segment to that vertex.
Using S and T has the enormous advantage that if your midpoint is a bit
off to one side of the line segment or the other, you still get a smooth
curve, no kinks between beziers But if it is too far off from the centre,
your curve will be off from the line segments, often in weird, surprising,
and complicated ways.
On the other hand, if you have a C or a Q bezier following a previous C
or Q bezier, getting the join smooth is a bitch.
To find the midpoint of a line segment, I use `M` approximate midpoint
`v6 v-12 v6 h6 h-12 h6` to mark the location with a cross.
To draw a long twisty curve, mark your intended path with a sequence of
line segments, with your final line segment passing through your
destination, because destination will be the midpoint of that line segment.
Then do a M first point, C second point, third point, midpoint, then S
even numbered vertex, midpoint following the even numbered vertex, starting
with the fourth vertex and the midpoint to the fifth vertex. The midpoint of
the final vertex will be your destination.
Scalable vector graphics are dimensionless, and the `<svg>` tag's height,
width, and ViewBox properties translate the dimensionless quantities into
@ -221,23 +283,17 @@ take its defaults from the element selected. (which can be an entire group,
or the entire high top level group, in which case it will pick up sane and
appropriate properties from the first relevant item in the group.)
And how did you set those sane and relevant properties in the first place?
By editing that element as text, very likely in your markdown file.
The enormous advantage of scalable vector graphics is that it handles
repetitious items in diagrams beautifully, because you can define an item
by reference to another item, thus very large hierarchical structure can be
defined by very small source code.
Scalable vector graphics is best edited as text, except that one needs to
draw lines and splines graphically, and in the process, all your nicely laid out text gets mangled into soup, and has to be unmangled.
You might decide to keep it around as soup, in an `svg` file that only
Inkscape ever tries to read, but then you are going to have to edit it as text
again. And I wound up embedding my vector graphics files in markdown
rather than invoking them as separate graphics files because my last step
was apt to be editing them as text.
was apt to be editing them as text. Which irreversibly made them
uneditable by Inkscape
It is convenient to construct and position all the graphical elements in
Inkscape, then edit the resulting `svg` file in Visual Studio Code with the
@ -284,8 +340,8 @@ graphic in the markdown preview pane.
font-weight="400"
stroke-width="2">
<path fill="none" stroke="#00f000"
d="M14.629 101.381c25.856-20.072 50.69-56.814
54.433-18.37 3.742 38.443 40.484 15.309 40.484 15.309"/>
d="M14 101, c40 -20, 30 -56,
54 -18, s60 15, 40 15"/>
<ellipse cx="60" cy="85" rx="12" ry="5" style="fill:red" />
<text x="60" y="82" text-anchor="middle" style="fill:#A050C0;" >
A simple scalable vector graphic