2026-10-192026-10-19

BasicSyntax

An extremely fast Python package and project manager, written in Rust.

Installing Trio's dependencies with a warm cache.

uv Install⚓︎

uv Install

macOS and LinuxWindows

$ curl -LsSf https://astral.sh/uv/install.sh | sh

PS> powershell -ExecutionPolicy ByPass -c "irm https://astral.sh/uv/install.ps1 | iex"

Installation

Installation⚓︎

Use the following command to install uv:

python -m ensurepip && python -m pip install uv

Website HEX codes.

Website HEX codes⚓︎

I spent some time investigating and I believe any colors that follow the following HEX code will work:
- #FF0099 - 255, 0, 153 - PinkPurple
- #FF9900 - 255, 153, 0 - OrangeYellow
- #99FF00 - 153, 255, 0 - Lime Green - NOT GOOD
- #9900FF - 153, 0, 255 - PurpleViolet
- #0099FF - 0, 153, 255 - BlueCyan
- #00FF99 - 0, 255, 153 - Sea Green - NOT GOOD

This pattern places all of these color codes on the Web Safe list of colors; I was unaware of that before I started investigating this.
For a full list of all the web safe colors, check out the Web Safe Colors Chart and the HTML Color Codes Chart.

This is the website I used to check the colors (icons, not text unfortunately) on both light and dark background: Notion Icons Atlas
- #FF0099 - 255, 0, 153 - PinkPurple
- #FF9900 - 255, 153, 0 - OrangeYellow
- #66CC00 - 102, 204, 0 - GreenBlue
- #9900FF - 153, 0, 255 - PurpleViolet
- #0099FF - 0, 153, 255 - BlueCyan
- #00CC66 - 0, 204, 102 - BlueGreen

Warning

Please be aware that the names I chose to describe the colours are not official names.

Looking at the colours of the icons as you switch a theme from dark to light several times can create optical illusions in which the colours appear to be different on different themes.

Table Reference: systemctl⚓︎

Action	Command	Note
Analyzing the system state
Show system status	`systemctl status`
List running units	`systemctl` or `systemctl list-units`
List failed units	`systemctl --failed`
List installed unit files¹	`systemctl list-unit-files`
Show process status for a PID	`systemctl status pid`	cgroup slice, memory and parent
Checking the unit status
Show a manual page associated with a unit	`systemctl help unit`	as supported by the unit
Status of a unit	`systemctl status unit`	including whether it is running or not
Check whether a unit is enabled	`systemctl is-enabled unit`
Starting, restarting, reloading a unit
Start a unit immediately	`systemctl start unit` as root
Stop a unit immediately	`systemctl stop unit` as root
Restart a unit	`systemctl restart unit` as root
Reload a unit and its configuration	`systemctl reload unit` as root
Reload systemd manager configuration²	`systemctl daemon-reload` as root	scan for new or changed units
Enabling a unit
Enable a unit to start automatically at boot	`systemctl enable unit` as root
Enable a unit to start automatically at boot and start it immediately	`systemctl enable --now unit` as root
Disable a unit to no longer start at boot	`systemctl disable unit` as root
Reenable a unit³	`systemctl reenable unit` as root	i.e. disable and enable anew
Masking a unit
Mask a unit to make it impossible to start⁴	`systemctl mask unit` as root
Unmask a unit	`systemctl unmask unit` as root

Various Misc⚓︎

First ordered list item
Another item
- Unordered sub-list.
Actual numbers don't matter, just that it's a number
1. Ordered sub-list
2. Second ordered sub-item
And another item.

You can have properly indented paragraphs within list items. Notice the blank line above, and the leading spaces (at least one, but we'll use three here to also align the raw Markdown).

To have a line break without a paragraph, you will need to use two trailing spaces.
Note that this line is separate, but within the same paragraph.
(This is contrary to the typical GFM line break behaviour, where trailing spaces are not required.)

Unordered list can use asterisks
Or minuses
Or pluses

Lists ⚓︎

Click to see Code for Lists.

1. First ordered list item
2. Another item
    * Unordered sub-list.
3. Actual numbers don't matter, just that it's a number
    1. Ordered sub-list (Will automatically render as i.)
        1. ordered sub-item
        1. ordered sub-item
        1. ordered sub-item
    2. Second ordered sub-item (Will automatically render as ii.)
        1. ordered sub-item
        1. ordered sub-item
4. And another item.

    You can have properly indented paragraphs within list items. Notice the blank line above, and the leading spaces (at least one, but we'll use three here to also align the raw Markdown).

    To have a line break without a paragraph, you will need to use two trailing spaces.  
    Note that this line is separate, but within the same paragraph.
    (This is contrary to the typical GFM line break behaviour, where trailing spaces are not required.)

---

* Unordered list can use asterisks
- Or minuses
+ Or pluses

Lists.

First ordered list item
Another item
- Unordered sub-list.
Actual numbers don't matter, just that it's a number
1. Ordered sub-list (Will automatically render as i.)
  1. ordered sub-item
  2. ordered sub-item
  3. ordered sub-item
2. Second ordered sub-item (Will automatically render as ii.)
  1. ordered sub-item
  2. ordered sub-item
And another item.

You can have properly indented paragraphs within list items. Notice the blank line above, and the leading spaces (at least one, but we'll use three here to also align the raw Markdown).

To have a line break without a paragraph, you will need to use two trailing spaces.
Note that this line is separate, but within the same paragraph.
(This is contrary to the typical GFM line break behaviour, where trailing spaces are not required.)

Unordered list can use asterisks
Or minuses
Or pluses

HTML content

Press Ctrl ＋ Alt ＋ Del to log in.

Admonition after HTML

This should work with proper spacing.

Important

Admonitions, also known as <em>call-outs</em>, are an excellent choice for including side content
without significantly interrupting document flow. Material for MkDocs provides several different
types of admonitions and allows for the inclusion and nesting of arbitrary content.

Quote

Admonitions, also known as call-outs, are an excellent choice for including side content without significantly interrupting the document flow. Material for MkDocs provides several different types of admonitions and allows for the inclusion and nesting of arbitrary content.

Pied Piper

The last 3 special directories.

NB: The last 3 special directories (last, week and month) which links repectively to the last synced repository, to the last Monday and to the first of the current month.

The Title

The content is correctly parsed because it's separated by blank lines from the raw HTML block tags.

Installation

Use the following command to install uv:

python -m ensurepip && python -m pip install uv

Source	Name	Version	Description
aur	dict-gcide	0.53-4	GNU version of the Collaborative International Dictionary of English for dictd et al.
aur	openide-bin	253.28294.334.8-1	OpenID is an open source software development tool for Java, Python, and other programming languages.
aur	friidump	0.5.3.1-1	A program to dump Nintendo Wii and GameCube disc
aur	rsvndump	0.6.2-1	Remote Subversion repository dump.
aur	aurvote-utils-git	1.1.0.r7.g3e82548-1	A set of utilities for managing AUR votes

Note.

If the ESP is not mounted to /boot, make sure to not rely on the systemd automount mechanism (including that of systemd-gpt-auto-generator) during kernel upgrades. Always mount it manually prior to any system or kernel update, otherwise you may not be able to mount it after the update, locking you in the currently running kernel with no ability to update the copy of kernel on the ESP.

Alternatively preload the required kernel modules on boot, e.g.:

/etc/modules-load.d/vfat.conf
vfat nls_cp437 nls_ascii

Install Mercurial

Debian/UbuntuFedoraArch LinuxGentoomacOS (Homebrew)FreeBSDWindows (Mercurial)Windows (TortoiseHg)

apt install mercurial

dnf install mercurial

pacman -S mercurial

emerge mercurial

brew install mercurial

Binary packages can be installed using pkg:

pkg install mercurial

Alternatively, you can install from source via the ports collection:

cd /usr/ports/devel/mercurial
make install

Using the winget package manager:

winget install Mercurial.Mercurial -e

Or download from the list of binary releases.

Using the winget package manager:

winget install TortoiseHg.TortoiseHg -e

Or download from the list of binary releases.

⟶ Detailed article: Images in terminal

Terminal	Environment	Images support	Protocol
uxterm	X11	yes	Sixel
mlterm	X11	yes	Sixel
kitty	X11	yes	Kitty
wezterm	X11	yes	IIP
Darktile	X11	yes	Sixel
Jexer	X11	yes	Sixel
GNOME Terminal	X11	in-progress	Sixel
alacritty	X11	in-progress	Sixel
foot	Wayland	yes	Sixel
DomTerm	Web	yes	Sixel
Yaft	FB	yes	Sixel
iTerm2	Mac OS X	yes	IIP
mintty	Windows	yes	Sixel
Windows Terminal	Windows	in-progress	Sixel
RLogin	Windows	yes	Sixel

Internationalization and Localization⚓︎

Internationalization and Localization

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

The query string should be specified in Unicode (hex-encoded or not). Spaces in the query string must be replaced with +:

\$ curl wttr.in/станция+Восток
Weather report: станция Восток

               Overcast
      .--.     -65 – -47 °C
   .-(    ).   ↑ 23 km/h
  (___.__)__)  15 km
               0.0 mm

The language used for the output (except the location name) does not depend on the input language and it is either English (by default) or the preferred language of the browser (if the query was issued from a browser) that is specified in the query headers (Accept-Language).

wttr.in usage stats⚓︎

As of the end of August 2025, wttr.in handles 22-27 million queries per day from 170,000 to 190,000 users, according to the access logs.

Name	License	Website	Description
Max	GPL	here	A secure ripper for OS X that uses additional cdparanoia functionality
XLD	GPL	here	X Lossless Decoder(XLD) is a tool for Mac OS X that is able to decode/convert/play various 'lossless' audio files. The supported audio files can be split into some tracks with cue sheet when decoding. Can convert between many lossless and lossy formats. Plugin oriented design, for easy exchange for new encoders.

Name	License	Website	Description
CUERipper	GPL	here	A secure ripper for Windows that includes Accurate Stream functionality. Forum
dBpoweramp	commercial	here	A secure ripper for Windows that includes Accurate Stream functionality.
EAC	Free	here	A secure ripper for Windows, C2 error pointers, Accurate Stream, etc.
fre:ac	GPL	here	fre:ac is a free audio converter and CD ripper with support for various popular formats and encoders. Plus supports the CDDB/freedb online CD database which allows you query song information.

name	license	website	description
abcde	gpl	here	a command-line based ripper with cdparanoia functionality
cdparanoia	bsd, gpl	here	one of the first secure standalone rippers for the linux platform
grip	gpl	here	an open-source gnome interface ripper that uses cdparanoia functionality
Rubyripper	gpl	here	a secure ripper for linux that uses additional cdparanoia functionality
Whipper	gpl	here	a secure ripper for the linux command-line built on cdparanoia

Molecule

Molecule will remove any options matching '^[v]+$', and pass -vvv to the underlying ansible-galaxy command when executing molecule --debug.

dependency:
  name: galaxy
  options:
    ignore-certs: True
    ignore-errors: True
    role-file: requirements.yml
    requirements-file: collections.yml

Equations

The Restricted Boltzmann Machine (RBM) Set
The first and third blocks are intrinsically linked. They describe a Restricted Boltzmann Machine, a type of generative neural network.
Equation 1: The Energy Function

\[ E(\mathbf{v}, \mathbf{h}) = -\sum_{i,j}w_{ij}v_i h_j - \sum_i b_i v_i - \sum_j c_j h_j \]

Equation 2: Basic Inequality

\[[3 < 4]\]

This is a simple mathematical truth (three is less than four). In this context, it is a separate entity and likely just a placeholder or a syntax test in your document.

Equation 3: Conditional Probabilities (The Activation Functions)

\[\begin{align} p(v_i=1|\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\ p(h_j=1|\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right) \end{align}\]

These go directly with the Energy Function. They show how to update the state of one layer given the other, which is the core of the RBM's learning and sampling process.

Equation 4: Bayes' Theorem

$p(x|y) = \frac{p(y|x)p(x)}{p(y)}$ + $p(x|y) = \frac{p(y|x)p(x)}{p(y)}$.

This is Bayes' Rule, the foundation of Bayesian statistics. While RBMs are probabilistic models, this specific equation is a general law of probability used across almost all of science and math. It stands alone as its own fundamental concept.

Click to see Code for Equation Below

\begin{align}
    p(v_i=1|\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\
    p(h_j=1|\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right)
\end{align}

\[\begin{align} p(v_i=1|\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\ p(h_j=1|\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right) \end{align}\]

Lorem ipsum dolor sit amet: Sed sagittis eleifend rutrum. Donec vitae suscipit est. Nullam tempus tellus non sem sollicitudin, quis rutrum leo facilisis.

Cras arcu libero: Aliquam metus eros, pretium sed nulla venenatis, faucibus auctor ex. Proin ut eros sed sapien ullamcorper consequat. Nunc ligula ante.

Duis mollis est eget nibh volutpat, fermentum aliquet dui mollis.
Nam vulputate tincidunt fringilla.
Nullam dignissim ultrices urna non auctor.

Lorem ipsum dolor sit amet, consectetur adipiscing elit
Vestibulum convallis sit amet nisi a tincidunt
In hac habitasse platea dictumst
In scelerisque nibh non dolor mollis congue sed et metus
Praesent sed risus massa
Aenean pretium efficitur erat, donec pharetra, ligula non scelerisque

Mathematical Pillars⚓︎

1. The Gaussian Integral⚓︎

The Gaussian Integral

What it is: A fundamental result in calculus showing the area under a bell curve.

Why it matters: Even though $e^{-x^2}$ has no standard antiderivative, its total area across the entire real line is exactly $\sqrt{\pi}$. This is the backbone of statistics and probability, forming the basis of the Normal Distribution.

$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$

2. The Quadratic Formula⚓︎

The Quadratic Formula

What it is: The standard method for finding the roots of any quadratic equation $ax^2 + bx + c = 0$

Why it matters: It tells you exactly where a parabola crosses the horizontal axis using the formula $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$. It’s the "Swiss Army Knife" of algebra.

$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

3. Matrix-Vector Multiplication⚓︎

Matrix-Vector Multiplication

What it is: A core operation where a matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ transforms a vector.

Why it matters: It results in a new vector $\begin{pmatrix} ax+by \\ cx+dy \end{pmatrix}$. This is how computers handle graphics and AI; it’s the math of moving and stretching space.

$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax+by \\ cx+dy \end{pmatrix}$

4. The Schrödinger Equation⚓︎

The Schrödinger Equation

What it is: The fundamental equation of Quantum Mechanics.

Why it matters: It describes how the "wave function" $\Psi$ of a system changes over time. It’s the reason we understand how atoms behave.

$i\hbar\frac{\partial}{\partial t}\Psi = \left[-\frac{\hbar^2}{2m}\nabla^2+V\right]\Psi$

The above equations listed together

The Gaussian Integral $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$

Click to see Code

\[
\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}
\]

The Quadratic Formula $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

Click to see Code

$$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$$

Matrix-Vector Multiplication $\begin{pmatrix} a & b \\ c & d\end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax+by \\ cx+dy \end{pmatrix}$

Click to see Code

\[
\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax+by \\ cx+dy \end{pmatrix}
\]

The Schrödinger Equation $i\hbar\frac{\partial}{\partial t}\Psi = \left[-\frac{\hbar^2}{2m}\nabla^2+V\right]\Psi$

Click to see Code

$$i\hbar\frac{\partial}{\partial t}\Psi = \left[-\frac{\hbar^2}{2m}\nabla^2+V\right]\Psi$$

Second Law of Thermodynamics

The mathematical expression of the Second Law of Thermodynamics is often presented in terms of the change in entropy ($\Delta S$) for an isolated system or the universe.
Here are examples of the MathJax code for common formulations of the Second Law: General Statement (Entropy of the Universe) The most common and general mathematical statement is that the total entropy of an isolated system (the universe) can never decrease.

MathJax Code (inline):
Renders as: $\Delta S_{\text{univ}} \ge 0$

\[\Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0\]

For a System and its Surroundings:

The total entropy change is the sum of the changes in the system and the surroundings, which must be greater than or equal to zero.

MathJax Code (display mode):
Renders as: $\Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0$

For any process, the change in entropy of a system is greater than or equal to the heat transfer ($Q$) divided by the absolute temperature ($T$). The equality holds for reversible processes, and the inequality for irreversible (real spontaneous) processes.

MathJax Code (inline)
Renders as: $dS \ge \frac{\delta Q}{T}$

Click to see Code

!!! recommendation "Second Law of Thermodynamics"

    - The mathematical expression of the Second Law of Thermodynamics is often presented in terms of the change in entropy (\(\Delta S\)) for an isolated system or the universe.

    - Here are examples of the MathJax code for common formulations of the Second Law: General Statement (Entropy of the Universe) The most common and general mathematical statement is that the total entropy of an isolated system (the universe) can never decrease.

    ---

    MathJax Code (inline):

    Renders as: $\Delta S_{\text{univ}} \ge 0$

    ---

    $$\Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0$$

    ---

    For a System and its Surroundings:

    The total entropy change is the sum of the changes in the system and the surroundings, which must be greater than or equal to zero.

    MathJax Code (display mode):

    Renders as:  $\Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}} \geq 0$

    ---

    For any process, the change in entropy of a system is greater than or equal to the heat transfer (\(Q\)) divided by the absolute temperature (\(T\)). The equality holds for reversible processes, and the inequality for irreversible (real spontaneous) processes.

    MathJax Code (inline)

    Renders as: $dS \ge \frac{\delta Q}{T}$

Probabilistic Models

Restricted Boltzmann Machines⚓︎

While RBMs are probabilistic models, these specific equations define the conditional layer activation probabilities using the sigmoid function ($\sigma$) rather than Bayes' rule directly.

Inline equation code: $p(v_i=1\vert{}\mathbf{h}) = \sigma\left(\sum_j w_{ij}h_j + b_i\right), \ p(h_j=1\vert{}\mathbf{v}) = \sigma\left(\sum_i w_{ij}v_i + c_j\right)$ for Restricted Boltzmann Machines (RBMs)

$\begin{flalign} p(v_i=1\vert{}\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) & \\ p(h_j=1\vert{}\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right) & \end{flalign}$

Code

\begin{align}
p(v_i=1|\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\
p(h_j=1|\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right)
\end{align}

\begin{flalign}
p(v_i=1|\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) & \\
p(h_j=1|\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right) &
\end{flalign}

\(p(v_i=1\vert{}\mathbf{h}) = \sigma\left(\sum_j w_{ij}h_j + b_i\right)\), \(p(h_j=1\vert{}\mathbf{v}) = \sigma\left(\sum_i w_{ij}v_i + c_j\right)\)

Bayes' Theorem

Bayes' Theorem⚓︎

This is Bayes' Rule, the foundation of Bayesian statistics. This specific equation is a general law of probability used across almost all of science and math. It stands alone as its own fundamental concept.

Bayes' Rule with two different rendering methods, one: $p(x|y) = \frac{p(y|x)p(x)}{p(y)}$, and two: $p(x|y) = \frac{p(y|x)p(x)}{p(y)}$, see the code below showing the difference.

Click to see code

$p(x|y) = \frac{p(y|x)p(x)}{p(y)}$

\(p(x|y) = \frac{p(y|x)p(x)}{p(y)}\)

Molecule

Molecule will remove any options matching ^[v]+$, and pass -vvv to the underlying ansible-galaxy command when executing molecule --debug.

dependency:
  name: galaxy
  options:
    ignore-certs: True
    ignore-errors: True
    role-file: requirements.yml
    requirements-file: collections.yml

Molecule

Molecule will remove any options matching ^[v]+$, and pass -vvv to the underlying ansible-galaxy command when executing molecule --debug.

dependency:
  name: galaxy
  options:
    ignore-certs: True
    ignore-errors: True
    role-file: requirements.yml
    requirements-file: collections.yml

name	license	website	description
abcde	gpl	here	a command-line based ripper with cdparanoia functionality
cdparanoia	bsd, gpl	here	one of the first secure standalone rippers for the linux platform
grip	gpl	here	an open-source gnome interface ripper that uses cdparanoia functionality
Rubyripper	gpl	here	a secure ripper for linux that uses additional cdparanoia functionality
Whipper	gpl	here	a secure ripper for the linux command-line built on cdparanoia

Two Solutions

When $a \ne 0$, there are two solutions to $(ax^2 + bx + c = 0)$ and they are: $\ x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

This sentence uses $ delimiters to show math inline: $\sqrt{3x-1}+(1+x)^2$

The Cauchy-Schwarz Inequality

The Cauchy-Schwarz Inequality

$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

The $\sqrt{\$4}$ and the True Inequality

In the initial text dump provided, the raw fragment reads as follows:

$E(\mathbf{v}, \mathbf{h}) = -\sum_{i,j}w_{ij}v_i h_j - \sum_i b_i v_i - \sum_j c_j h_j$

$3 < 4$

$\begin{align} p(v_i=1\vert{}\mathbf{h}) & = \sigma\left(\sum_j w_{ij}h_j + b_i\right) \\ p(h_j=1\vert{}\mathbf{v}) & = \sigma\left(\sum_i w_{ij}v_i + c_j\right) \end{align}$

The string $[3 < 4]$ sits explicitly between the global energy definition and the local node update equations. It has zero mathematical or conceptual connection to the structural physics of Restricted Boltzmann Machines or neural networks. It operates purely as an arbitrary, detached example of an inequality statement sitting mid-document.

Why These Strange Fragments Exist

The inclusion of these specific elements points directly to a LaTeX syntax stress test or a formatting template. Document developers frequently mix these exact symbols to test parser edge cases for three specific reasons:

Delimiter Escape Validation: Putting a literal dollar sign ($\$$) inside a square root ($\sqrt{\$4}$) checks if the rendering engine can distinguish between currency symbols and mathematical math-mode triggers.
HTML Tag Conflict Testing: The less-than sign in $[3 < 4]$ is used to see ifan aggressive Markdown or HTML parser will accidentally interpret $<$ as the start of an invalid code tag and break the display.
Bracket Priority Checks: Combining standard square brackets $[...]$ right next to LaTeX display math brackets $\backslash[...\backslash]$ verifies if the layout engine properly separates normal document text from centered equations.

Essentially, they serve as a diagnostic checklist to ensure the formatting software does not break when encountering complex real-world text.

The direct mathematical relationship between them is structured as follows:

The Energy Equation ($E(\mathbf{v}, \mathbf{h})$): This defines a single scalar value measuring the total "compatibility" or "badness" of the entire system state across all nodes simultaneously. It is a global calculation.
The Probability Equations ($p(v_i = 1|\mathbf{h})$ and $p(h_j = 1|\mathbf{v})$)

These calculate the probability of a single specific neuron turning on (setting its binary state to 1) given what the other layer is currently doing.

The Derivation Link

The conditional probabilities are mathematically derived directly out of the global energy function using the Boltzmann distribution formula:

$\displaystyle p(\mathbf{v}, \mathbf{h}) = \frac{e^{-E(\mathbf{v}, \mathbf{h})}}{\sum_{\mathbf{v}', \mathbf{h}'} e^{-E(\mathbf{v}', \mathbf{h}')}}$

Because there are no connections between nodes within the same layer of an RBM, taking the conditional probability rules of standard statistics ($p(\mathbf{v},\mathbf{h}) / p(\mathbf{v})$) and expanding that fraction causes almost all variables to cancel out perfectly. The algebraic remainder simplifies down to exactly the logistic sigmoid function ($\sigma $) shown in your inline equations. In practice, the network uses the Energy equation to score its overall state, and uses the Probability equations as a localized blueprint to actually update its nodes one by one during training.

Auto-generated code

This repository is auto-generated from the Immich OpenAPI specification.
Pull requests are welcome, but modifications to auto-generated code will be rejected. See Contributing for more details.

Auto-synced with Immich

This project is auto-synced with the latest Immich release.

Not affiliated with Immich

This project is not affiliated with or endorsed by Immich.

Everybody should know Euler's formula: $e^{ \pm i\theta } = \cos \theta \pm i\sin \theta$

These are Euler's most famous equations:

\[ \begin{aligned} e^{ \pm i\theta } & = \cos \theta \pm i\sin \theta \\ e^{i \pi} & = -1 \end{aligned} \]

Table 2. Orbital Elements of S2 and S4716⚓︎

Source	a (mpc)	e	i (deg)	ω (deg)	Ω (deg)	t_closest (yr)
S2	5.09 ± 0.01	0.886 ± 0.002	133.49 ± 0.40	65.89 ± 0.75	227.46 ± 1.03	2018.37 ± 0.02
S4716 (estimated)	1.93 ± 0.02	0.756 ± 0.02	161.24 ± 2.80	0.073 ± 0.02	151.54 ± 1.54	2017.41 ± 0.004
S4716 (max. likelihood)	1.94 ± 0.02	0.756 ± 0.02	161.13 ± 2.80	2.25 ± 0.02	153.55 ± 1.54	2017.41 ± 0.004

Note. The estimated values for S4716 are based on a Keplerian fit model, while the maximum likelihood stems from the MCMC simulation. See Appendix B for a discussion of these values.

Table 2. Orbital Elements of S2 and S4716⚓︎

Source	a (mpc)	e	i (deg)	ω (deg)	Ω (deg)	t_closest (yr)
S2	5.09 ± 0.01	0.886 ± 0.002	133.49 ± 0.40	65.89 ± 0.75	227.46 ± 1.03	2018.37 ± 0.02
S4716 (est)	1.93 ± 0.02	0.756 ± 0.02	161.24 ± 2.80	0.073 ± 0.02	151.54 ± 1.54	2017.41 ± 0.004
S4716 (ML)	1.94 ± 0.02	0.756 ± 0.02	161.13 ± 2.80	2.25 ± 0.02	153.55 ± 1.54	2017.41 ± 0.004

Note. The estimated values for S4716 are based on a Keplerian fit model, while the maximum likelihood stems from the MCMC simulation. See Appendix B for a discussion of these values.

Here is the Complete Summary Guide for your "Related Pages" link system.
You can copy and save this as a local text file.

Part 1: Folder Structure & Config⚓︎

Ensure your project directory looks like this:

Folder Structure.

my-project/
├── mkdocs.yml
├── docs/
│  ├── UV.md
│  └── UV_Style/
│     └── STYLE.md
└── overrides/
   └── main.html

In your mkdocs.yml, add the custom_dir setting to the theme:

theme:
  name: material
  custom_dir: overrides

Part 2: The Logic Template (overrides/main.html)⚓︎

Create this file and paste the code below. This handles two scenarios:

Manual: You specify a link in a specific file.
Automatic: Any file in the MkDocs-Material/ folder automatically gets a link back to its main page.

html

html for Site Logic Summary

Site Logic Summary⚓︎

To create your overrides/main.html file, copy the code block below:

{% extends "base.html" %}

{% block content %}
  {# 1. Check for manual links in page metadata #}
  {% if page.meta.related_link %}
    <p>
      <strong>Related:</strong> 
      <a href="{{ page.meta.related_link | url }}">{{ page.meta.related_title | default('Click here') }}</a>
    </p>
    <hr>

  {# 2. Auto-link for the MkDocs-Material folder #}
  {% elif "MkDocs-Material/" in page.file.src_uri and page.file.src_uri != "MkDocs-Material/setting-up-tags.md" %}
    <p>
      <strong>Return to:</strong> 
      <a href="{{ 'MkDocs-Material/setting-up-tags.md' | url }}">Main Setup Guide</a>
    </p>
    <hr>

  {# 3. Auto-link for the Arch_OS_Docs folder #}
  {% elif "Arch_OS_Docs/" in page.file.src_uri and page.file.src_uri != "DOCS.md" %}
    <p>
      <strong>Return to:</strong> 
      <a href="{{ 'DOCS.md' | url }}">Main Arch OS Index</a>
    </p>
    <hr>

  {# 4. Auto-link for the UV_Style folder #}
  {% elif "UV_Style/" in page.file.src_uri %}
    <p>
      <strong>Return to:</strong> 
      <a href="{{ 'UV.md' | url }}">Main UV Documentation</a>
    </p>
    <hr>

  {% endif %}

  {{ super() }}
{% endblock %}

Part 3: How to Use in Your Markdown Files⚓︎

Method A: For Unique Pages

Method A: For Unique Pages (e.g., UV and Style)

Add this "Front Matter" (the YAML block) to the very top of your .md files.
In docs/UV.md:

---
related_link: UV_Style/STYLE.md
related_title: "View UV Style Guide"
---

UV Main Page

In docs/UV_Style/STYLE.md:

---
related_link: UV.md
related_title: "Return to UV Main"
---

Style Guide

Method B: For Bulk Folders (e.g., MkDocs-Material)

You don't have to do anything. Because of the code in Part 2 (Scenario 2), every page inside the MkDocs-Material/ folder will automatically display a "Return to Main Setup Guide" link at the top, except for the main guide page itself.

Troubleshooting Tips:

The "not_in_nav" pages:

These pages will still show the link box! As long as the file exists in the folder, the template will find it and display the link.

Paths: If a link doesn't work, try using the path relative to the docs/ folder (e.g., Folder/Subfolder/file.md).

Icons: If the icons don't show up, make sure you have python-markdown extensions enabled in your mkdocs.yml, specifically pymdownx.emoji.

Would you like me to generate a similar "Bulk Rule" for any other folders you have (like "Arch OS Docs") before you go?

Summary of how to add more Bulk Rules later:⚓︎

Bulk Folder More Than One .md File

If you find another folder (e.g., Networking/) and want all 20 pages in it to link back to Networking_Home.md, just add another {% elif ... %} block before the final {% endif %}:

1. Check the path: "Folder_Name/" in page.file.src_uri
2. Exclude the main page: and page.file.src_uri != "Folder_Name/Main_Page.md"
   (This prevents the link from appearing on the main page itself).
3. Set the link: <a href="{{ 'Path/to/Main.md' | url }}">

Quick Checklist for your local setup:

1. mkdocs.yml: Ensure custom_dir: overrides is present.
2. overrides/main.html: Paste the code above.
3. Icons: If icons don't show, ensure you have this in your mkdocs.yml under markdown_extensions:

flowchart LR
    config["Mkdocs config file\n(extra section)\nunit_price: 10"] --> variable
    variable["Variable in the page\n{{ unit_price }}"] --> renderer
    renderer(("Template Renderer")) --> text
    text("Markdown text\n10")

smxi/inxi⚓︎

Home Page

Home Page :: inxi smxi sgfxi svmi rbxi

smxi

Winner of the Distrowatch.com March 2009 award donation.

Welcome to the smxi/sgfxi/svmi + inxi + rbxi group of tools main site. Documentation is being updated and improved routinely, so check out the various sections and see if what you needed to know has been answered already.

Donations are always welcome! The smallest amount is still more than nothing.

Script Documentation Resources⚓︎

There are a range of help and end user resources available, as well as more developer oriented materials.

You can find them here:

1 - General documentation (manuals, options, how-to's).
2 - Inxi Docs. (manuals, options, how-to's).
3 - About-tools. A brief introduction to what smxi, sgfxi, svmi, inxi, and rbxi do.
4 - The smxi-story. The story of smxi. How it started, what it does, and its current options.
5 - Install-tools. How to install tools (smxi, sgfxi, svmi, inxi, and rbxi).
6 - FAQs FAQs. Answers to questions about the tools in general.
7 - FAQs-smxi smxi FAQs. Smxi specific questions.
8 - FAQs-sgfxi sgfxi FAQs. Sgfxi specific questions (video drivers etc).
9 - smxi-change-blog smxi change log/blog. Random thoughts and change notes, nothing exciting.

Script Forums and Contact Resources⚓︎

The tools have support forums, which I encourage you to use to file bug reports, feature requests, and so on. Also note the changeblog, which is sometimes up-to date.

Please use the existing bug report or feature requests threads to report issues for the tool in question. That helps keep the forums reasonably uncluttered and readable for other users. Thanks.

1 - user-forums, where you can post bugs, issues, questions.
2 - Dev-forums, talk about code and other more dev oriented things.
3 - Contact project. But generally use forums, IRC, or git repo issues.
4 - Follow on fosstodon.org/@smxi (nope, not on twitter, never).

Code Repositories⚓︎

Code Repositories

The tools all have their own code repositories, where you can check out the code (and see if you can figure out how it all works), file issues, or checkout documentation.

Here's what's available:

Code Repositories

The tools all have their own code repositories, where you can check out the code (and see if you can figure out how it all works), file issues, or checkout documentation.

Here's what's available:

1. smxi — Check out the main tool code, file issues, or read the docs.
2. sgfxi — Graphics driver installer for Debian and Ubuntu based systems.
3. svmi — VirtualBox helper script for managing VM installations.
4. rbxi — A specialized tool for managing Ruby-on-Rails environments.
5. inxi — The classic full-featured CLI system information tool.
6. pinxi — The development (preview) version of the inxi system tool.
7. acxi — Audio convert script for FLAC, MP3, OGG and more.

Test 2 Mermaid Flow Chart⚓︎

flowchart TD
    Start((Start)) --> Q1{Condition A?}

    subgraph Main_Flow [Main Logic]
        Q1 -- Yes --> Q2{Condition B?}
        Q2 -- Yes --> Q3{Condition C?}
    end

    subgraph Alt_Flow [Secondary Logic]
        OptionB([Option B Path]) --> Q4{Condition D?}
    end

    %% Routing to Outcomes
    Q1 -- No ----> OutA
    Q2 -- No ----> OutA
    Q3 -- No ----> OutA

    Q3 -- Yes ---> OutB
    Q4 -- Yes ---> OutB
    Q4 -- No ----> OutC

    OutA([Outcome A])
    OutB([Outcome B])
    OutC([Outcome C])

flowchart LR
    Start((Start)) --> Q1{Condition A?}

    %% Main Path
    Q1 -- Yes --> Q2{Condition B?}
    Q2 -- Yes --> Q3{Condition C?}
    Q3 -- Yes --> OutB([Outcome B])

    %% Secondary Path
    OptionB([Option B Path]) --> Q4{Condition D?}
    Q4 -- Yes --> OutB
    Q4 -- No --> OutC([Outcome C])

    %% Shared Exit Path
    Q1 -- No --> OutA([Outcome A])
    Q2 -- No --> OutA
    Q3 -- No --> OutA

flowchart TD
    Start((Start)) --> Q1{Condition A?}

    subgraph Main_Path [Main Process]
        Q1 -- Yes ---> Q2{Condition B?}
        Q2 -- Yes ---> Q3{Condition C?}
    end

    subgraph Alt_Path [Secondary Process]
        OptionB([Option B Path]) --> Q4{Condition D?}
    end

    %% Routing to shared outcomes
    Q1 -- No ----> OutA
    Q2 -- No ----> OutA
    Q3 -- No ----> OutA
    Q4 -- No ----> OutC

    Q3 -- Yes ---> OutB
    Q4 -- Yes ---> OutB

    %% Outcomes
    OutA([Outcome A])
    OutB([Outcome B])
    OutC([Outcome C])

flowchart LR
    Start((Start)) --> Q1{Condition A?}

    Q1 -- Yes --> Q2{Condition B?}
    Q2 -- Yes --> Q3{Condition C?}
    Q3 -- Yes --> OutB([Outcome B])

    OptionB([Option B Path]) --> Q4{Condition D?}
    Q4 -- Yes --> OutB
    Q4 -- No --> OutC([Outcome C])

    %% Shared No Path
    Q1 -- No --> OutA([Outcome A])
    Q2 -- No --> OutA
    Q3 -- No --> OutA

flowchart TD
    %% Starting the process
    Start((🚀 Project Launch)) --> Q1{Code Review <br/>Passed?}

    subgraph Standard_Pipeline [Quality Gates]
        Q1 -- "✅ Yes" ---> Q2{All Unit Tests <br/>100% Green?}
        Q2 -- "✅ Yes" ---> Q3{Stakeholder <br/>Sign-off?}
    end

    subgraph Emergency_Pipeline [Hotfix Logic]
        OptionB([🛠️ Emergency Patch]) --> Q4{Is it a <br/>Security Fix?}
    end

    %% The "Kill Switch" Logic (Routing all failures to one place)
    Q1 -- "❌ No" ----> OutA
    Q2 -- "❌ No" ----> OutA
    Q3 -- "❌ No" ----> OutA

    %% Success Routing
    Q3 -- "✅ Yes" ---> OutB
    Q4 -- "✅ Yes" ---> OutB

    %% The "Fail-Safe" for non-critical patches
    Q4 -- "❌ No" ----> OutC

    %% Outcomes with high-contrast text and theme-friendly styling
    OutA([🛑 ABORT <br/>Return to Dev])
    OutB([🎉 DEPLOY <br/>Live to Prod])
    OutC([⏳ QUEUE <br/>Wait for Sprint])

    %% Minimal border styling to keep MkDocs happy
    style OutA stroke:#e74c3c,stroke-width:3px
    style OutB stroke:#2ecc71,stroke-width:3px
    style OutC stroke:#3498db,stroke-width:3px

flowchart TD
    %% --- MAIN LOGIC ---
    Start((Start)) --> Q1{Condition A?}

    Q1 -- Yes ---> Q2{Condition B?}
    Q2 -- Yes ---> OutB

    Q1 -- No ----> OutA
    Q2 -- No ----> OutA

    %% --- OUTCOMES ---
    OutA([Outcome A])
    OutB([Outcome B])

    %% --- THE LEGEND (Hidden Logic) ---
    %% We use a 'dummy' link with 0px width to tether the legend to the bottom
    OutA ~~~ Legend

    subgraph Legend [Diagram Key]
        direction LR
        L1(( )) --- T1[Entry Point]
        L2{ } --- T2[Decision]
        L3([ ]) --- T3[Success/Final]
        L4([ ]) --- T4[Warning/Exit]
    end

    %% --- STYLING ---
    %% Styles for the main chart
    style OutB stroke:#2ecc71,stroke-width:3px
    style OutA stroke:#e74c3c,stroke-width:3px

    %% Styles for the legend to match
    style L3 stroke:#2ecc71,stroke-width:3px
    style L4 stroke:#e74c3c,stroke-width:3px

    %% Making the legend box look distinct
    style Legend fill:transparent,stroke-dasharray: 5 5

flowchart TD
    %% --- MAIN LOGIC ---
    Start((Start)) --> Q1{Condition A?}
    Q1 -- Yes ---> Q2{Condition B?}
    Q2 -- Yes ---> OutB

    Q1 -- No ----> OutA
    Q2 -- No ----> OutA

    OutA([Outcome A])
    OutB([Outcome B])

    %% --- THE CLEAN LEGEND ---
    %% Invisible link to keep it at the bottom
    OutA ~~~ Legend

    Legend[<b>DIAGRAM KEY</b><br/>━━━━━━━━━━━━━━<br/>○ Entry Point<br/>◇ Decision Diamond<br/>▭ Outcome / Result]

    %% --- STYLING ---
    %% High-contrast borders for MkDocs
    style OutB stroke:#2ecc71,stroke-width:3px
    style OutA stroke:#e74c3c,stroke-width:3px

    %% Style the legend to look like a separate 'sticker'
    style Legend fill:transparent,stroke:#888,stroke-dasharray: 5 5,text-align:left

flowchart TD
    %% --- MAIN LOGIC ---
    Start((Start)) --> Q1{Condition A?}

    subgraph Main_Path [Main Process]
        Q1 -- Yes ---> Q2{Condition B?}
        Q2 -- Yes ---> Q3{Condition C?}
    end

    subgraph Alt_Path [Secondary Process]
        OptionB([Option B Path]) --> Q4{Condition D?}
    end

    %% Routing to shared outcomes
    Q1 -- No ----> OutA
    Q2 -- No ----> OutA
    Q3 -- No ----> OutA
    Q4 -- No ----> OutC

    Q3 -- Yes ---> OutB
    Q4 -- Yes ---> OutB

    %% Outcomes
    OutA([Outcome A])
    OutB([Outcome B])
    OutC([Outcome C])

    %% --- THE CLEAN LEGEND ---
    %% Invisible link to anchor it at the bottom
    OutA ~~~ Legend

    Legend[<b>DIAGRAM KEY</b><br/>━━━━━━━━━━━━━━<br/>○ Entry Point<br/>◇ Decision Diamond<br/>▭ Outcome / Result]

    %% --- STYLING ---
    %% Outcome Colors (Theme-friendly borders)
    style OutA stroke:#e74c3c,stroke-width:3px
    style OutB stroke:#2ecc71,stroke-width:3px
    style OutC stroke:#3498db,stroke-width:3px

    %% Legend Box Styling
    style Legend fill:transparent,stroke:#888,stroke-dasharray: 5 5,text-align:left

flowchart TD
    %% --- MAIN LOGIC ---
    Start((Start)) --> Q1{Condition A?}

    subgraph Main_Path [Main Process]
        Q1 -- Yes ---> Q2{Condition B?}
        Q2 -- Yes ---> Q3{Condition C?}
    end

    subgraph Alt_Path [Secondary Process]
        OptionB([Option B Path]) --> Q4{Condition D?}
    end

    %% Routing
    Q1 -- No ----> OutA
    Q2 -- No ----> OutA
    Q3 -- No ----> OutA
    Q4 -- No ----> OutC
    Q3 -- Yes ---> OutB
    Q4 -- Yes ---> OutB

    %% Outcomes
    OutA([Outcome A])
    OutB([Outcome B])
    OutC([Outcome C])

    %% --- THE COMPLETE INTERACTIVE LAYER ---
    %% Syntax: click ID "URL" "Tooltip"
    %% (Use "#" as a placeholder for the URL to avoid 404s while testing)

    click Start "#" "Entry point for the standard workflow."
    click Q1 "#" "Check logs for Condition A criteria."
    click Q2 "#" "Verify Condition B requirements."
    click Q3 "#" "Final quality gate for the main path."

    click OptionB "#" "Alternative entry point for ad-hoc requests."
    click Q4 "#" "Specific check for the secondary path logic."

    click OutA "#" "Exit Path A: Redirection to troubleshooting."
    click OutB "#" "Success Path B: Proceed to final delivery."
    click OutC "#" "Exit Path C: Hold for further review."

    %% --- STYLING ---
    style OutA stroke:#e74c3c,stroke-width:3px
    style OutB stroke:#2ecc71,stroke-width:3px
    style OutC stroke:#3498db,stroke-width:3px

%%{init: {"securityLevel": "loose"}}%%
flowchart TD
    Start((Start)) --> Q1{Condition A?}

    subgraph Main_Path [Main Process]
        Q1 -- Yes ---> Q2{Condition B?}
        Q2 -- Yes ---> Q3{Condition C?}
    end

    subgraph Alt_Path [Secondary Process]
        OptionB([Option B Path]) --> Q4{Condition D?}
    end

    %% Routing
    Q1 -- No ----> OutA
    Q2 -- No ----> OutA
    Q3 -- No ----> OutA
    Q4 -- No ----> OutC
    Q3 -- Yes ---> OutB
    Q4 -- Yes ---> OutB

    %% Outcomes
    OutA([Outcome A])
    OutB([Outcome B])
    OutC([Outcome C])

    %% --- THE TOOLTIPS ---
    %% Note: You must provide a link (even just #) for tooltips to trigger
    click Start "#" "This is the start of the journey!"
    click Q1 "#" "Hovering over Q1 works now."
    click OutB "#" "You found the success path!"
    click OutA "#" "This is a failure path."

    %% Styling
    style OutA stroke:#e74c3c,stroke-width:3px
    style OutB stroke:#2ecc71,stroke-width:3px
    style OutC stroke:#3498db,stroke-width:3px

%%{init: {"securityLevel": "loose"}}%%
flowchart TD
    Start((Start)) --> Q1{Condition A?}
    Q1 -- No --> OutA([Outcome A])

    %% THE TOOLTIP LAYER
    %% You need a '#' (placeholder link) for the tooltip to trigger
    click Start "#" "This is the start of the journey!"
    click Q1 "#" "Check logs for Condition A."
    click OutA "#" "This is a failure path."

---
config:
  layout: elk
---
flowchart TB
 subgraph Main_Path["Main Process"]
        Q2{"Condition B?"}
        Q1{"Condition A?"}
        Q3{"Condition C?"}
  end
 subgraph Alt_Path["Secondary Process"]
        Q4{"Condition D?"}
        OptionB(["Option B Path"])
  end
    Start(("Start")) --> Q1
    Q1 -- Yes ---> Q2
    Q2 -- Yes ---> Q3
    OptionB --> Q4
    Q1 -- No ----> OutA(["Outcome A"])
    Q2 -- No ----> OutA
    Q3 -- No ----> OutA
    Q4 -- No ----> OutC(["Outcome C"])
    Q3 -- Yes ---> OutB(["Outcome B"])
    Q4 -- Yes ---> OutB

    style OutA stroke:#e74c3c,stroke-width:3px
    style OutC stroke:#3498db,stroke-width:3px
    style OutB stroke:#2ecc71,stroke-width:3px
    click Start "/"
    click Q1 "/"
    click Q2 "/"
    click Q3 "/"
    click OptionB "/"
    click Q4 "/"
    click OutA "/"
    click OutC "/"
    click OutB "/"

Enlightenment Lao Tse 1.⚓︎

graph TD
    %% Title with a "Zen" Hexagon shape
    Title{{<b>✨ ENLIGHTENMENT ✨</b><br/>Lao Tse}}

    %% Intro Section
    P1["<i>The enlightened possess understanding<br/>so profound they cannot be understood.</i>"]
    P2["<i>Because they cannot be understood,<br/>I can only describe their appearance:</i>"]

    Title --> P1
    P1 --> P2

    %% THE FIX: Bridge Node for Qualities
    P2 --> H1["<i>The Seven Qualities</i>"]

    subgraph Qualities [" "]
        direction TB
        H1 --> C1
        C1["<b>❄️ Cautious</b> as one crossing thin ice"]
        C2["<b>⚠️ Undecided</b> as one surrounded by danger"]
        C3["<b>🤝 Modest</b> as one who is a guest"]
        C4["<b>🌊 Unbounded</b> as melting ice"]
        C5["<b>🌲 Genuine</b> as unshaped wood"]
        C6["<b>⛰️ Broad</b> as a valley"]
        C7["<b>☁️ Seamless</b> as muddy water"]

        C1 --> C2 --> C3 --> C4 --> C5 --> C6 --> C7
    end

    %% THE FIX: Bridge Node for Actions
    C7 --> H2["<i>The Way of the Sage</i>"]

    subgraph Actions [" "]
        direction TB
        H2 --> A1
        A1["Stills the water that the mud may settle"]
        A2["Seeks to stop that he may travel on"]
        A3["Desires less than what may transpire"]
        A4["Decays, but will not renew"]

        A1 --> A2 --> A3 --> A4
    end

    %% --- THE "GHOST BOX" STYLING ---
    classDef head stroke:#d4af37,stroke-width:4px,fill:#8882;
    classDef intro stroke:#888,stroke-width:2px,fill:#8882;
    classDef quality stroke:#5b6d5b,stroke-width:2px,fill:#8882;
    classDef action stroke:#4e5d6c,stroke-width:2px,fill:#8882;

    %% Frame for the Sub-headings (Bordered, No Fill)
    classDef header fill:none,stroke:#888,stroke-width:1px,stroke-dasharray: 5 5;

    class Title head;
    class P1,P2 intro;
    class C1,C2,C3,C4,C5,C6,C7 quality;
    class A1,A2,A3,A4 action;
    class H1,H2 header;

    %% Subgraph Outlines
    style Qualities fill:none,stroke:#888,stroke-dasharray: 5 5;
    style Actions fill:none,stroke:#888,stroke-dasharray: 5 5;

Enlightenment Lao Tse 2.⚓︎

---
config:
  look: classic
  layout: dagre
---
graph TD
    Title{{"<b>✨ ENLIGHTENMENT ✨</b><br/>Lao Tse"}}
    P1["<i>The enlightened possess understanding<br/>so profound they cannot be understood.</i>"]
    P2["<i>Because they cannot be understood,<br/>I can only describe their appearance:</i>"]

    Title --> P1 
    P1 --> P2

    %% The Bridge Headers
    P2 --> H1["<i>The Seven Qualities</i>"]

    subgraph Qualities [" "]
        direction TB
        H1 --> C1
        C1["<b>❄️ Cautious</b> as one crossing thin ice"]
        C2["<b>⚠️ Undecided</b> as one surrounded by danger"]
        C3["<b>🤝 Modest</b> as one who is a guest"]
        C4["<b>🌊 Unbounded</b> as melting ice"]
        C5["<b>🌲 Genuine</b> as unshaped wood"]
        C6["<b>⛰️ Broad</b> as a valley"]
        C7["<b>☁️ Seamless</b> as muddy water"]

        C1 --> C2 --> C3 --> C4 --> C5 --> C6 --> C7
    end

    C7 --> H2["<i>The Way of the Sage</i>"]

    subgraph Actions [" "]
        direction TB
        H2 --> A1
        A1["Stills the water that the mud may settle"]
        A2["Seeks to stop that he may travel on"]
        A3["Desires less than what may transpire"]
        A4["Decays, but will not renew"]

        A1 --> A2 --> A3 --> A4
    end

    %% STYLING
    classDef head fill:#cc9900,stroke:#997300,color:#fff,stroke-width:2px;
    classDef intro fill:#666666,stroke:#444444,color:#fff;
    classDef quality fill:#4e7a5b,stroke:#34523d,color:#fff;
    classDef action fill:#456a8e,stroke:#2e475f,color:#fff;

    %% Updated Header: Bordered, No Fill, Dashed for style
    classDef header fill:none,stroke:#888,stroke-width:1px,stroke-dasharray: 5 5,color:#888;

    class Title head;
    class P1,P2 intro;
    class C1,C2,C3,C4,C5,C6,C7 quality;
    class A1,A2,A3,A4 action;
    class H1,H2 header;

    style Qualities fill:none,stroke:#888,stroke-dasharray: 5 5;
    style Actions fill:none,stroke:#888,stroke-dasharray: 5 5;

Pro-Tips

The "Micro-Update" Method: If we are working on a long project (like your cheat-sheet), feel free to ask me to provide updates in smaller, bite-sized sections. It’s easier to copy-paste as we go!
The Resume Command:
A: If a response hangs or vanishes mid-sentence, just type "Continue from [last line]".
B: I can usually pick up the thread right where we left off.
Version Control:
A: Whenever we hit a milestone, I can give you a "Clean Export" version of everything we've covered so you have a fresh master copy to save.
Handy Tools for your Cheat-Sheet:
A: Backup & Sync:
B: If you are using Obsidian, check out the Obsidian Git plugin to automatically back up your notes so nothing gets lost.
Note Organisation: Use the Periodic Notes plugin to keep track of when you added specific tips to your sheet.
CSS Troubleshooting: If your custom colors aren't showing up, the Obsidian Forum is the best place to find specific CSS fixes for different themes.

HTML Code for the table below

<div class="isolated-table-container">
  <style>
    /* Use CSS Variables instead of hardcoded colors for dynamic theming */
    .isolated-table-container .table.table-bordered {
      border-collapse: collapse;
      width: 100%;
      max-width: 800px;
      margin: 20px auto;
      /* Use theme default border color */
      border: 1px solid var(--md-default-fg-color--light); 
      font-size: 16px;
      /* Default background color */
      background-color: var(--md-default-bg-color); 
      /* Default text color */
      color: var(--md-default-fg-color);
    }
    .isolated-table-container .table.table-bordered th,
    .isolated-table-container .table.table-bordered td {
      /* Use theme default border color */
      border: 1px solid var(--md-default-fg-color--light); 
      padding: 8px;
      text-align: left;
    }
    .isolated-table-container .table.table-bordered thead th {
      /* Use primary theme color for header background */
      background-color: var(--md-primary-fg-color); 
      font-weight: bold;
      /* Ensure header text is readable against primary color */
      color: var(--md-primary-bg-color); 
    }
    .isolated-table-container .table.table-bordered tbody tr:nth-child(odd) {
        /* Add some striping using a slightly different background color variable */
        background-color: var(--md-default-bg-color--light);
    }
    .isolated-table-container .table.table-bordered a {
      /* Use theme accent color for links */
      color: var(--md-accent-fg-color); 
      text-decoration: underline;
    }
  </style>

  <!-- Your original HTML table code starts here -->
  <table class="table table-bordered">
    <thead class="thead-light">
      <tr>
        <th>Markdown</th>
        <th>HTML</th>
        <th>Rendered Output</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td><code class="highlighter-rouge"># Heading level 1</code></td>
        <td><code class="highlighter-rouge">&lt;h1&gt;Heading level 1&lt;/h1&gt;</code></td>
        <td><h1 class="no-anchor" data-toc-skip="" id="heading-level-1">Heading level 1</h1></td>
      </tr>
      <tr>
        <td><code class="highlighter-rouge">## Heading level 2</code></td>
        <td><code class="highlighter-rouge">&lt;h2&gt;Heading level 2&lt;/h2&gt;</code></td>
        <td><h2 class="no-anchor" data-toc-skip="" id="heading-level-2">Heading level 2</h2></td>
      </tr>
      <tr>
        <td><code class="highlighter-rouge">### Heading level 3</code></td>
        <td><code class="highlighter-rouge">&lt;h3&gt;Heading level 3&lt;/h3&gt;</code></td>
        <td><h3 class="no-anchor" data-toc-skip="" id="heading-level-3">Heading level 3</h3></td>
      </tr>
      <tr>
        <td><code class="highlighter-rouge">#### Heading level 4</code></td>
        <td><code class="highlighter-rouge">&lt;h4&gt;Heading level 4&lt;/h4&gt;</code></td>
        <td><h4 class="no-anchor" id="heading-level-4">Heading level 4</h4></td>
      </tr>
      <tr>
        <td><code class="highlighter-rouge">##### Heading level 5</code></td>
        <td><code class="highlighter-rouge">&lt;h5&gt;Heading level 5&lt;/h5&gt;</code></td>
        <td><h5 class="no-anchor" id="heading-level-5">Heading level 5</h5></td>
      </tr>
      <tr>
        <td><code class="highlighter-rouge">###### Heading level 6</code></td>
        <td><code class="highlighter-rouge">&lt;h6&gt;Heading level 6&lt;/h6&gt;</code></td>
        <td><h6 class="no-anchor">Heading level 6</h6></td>
      </tr>
    </tbody>
  </table>
</div>

Markdown	HTML	Rendered Output
`# Heading level 1`	`<h1>Heading level 1</h1>`	Heading level 1
`## Heading level 2`	`<h2>Heading level 2</h2>`	Heading level 2
`### Heading level 3`	`<h3>Heading level 3</h3>`	Heading level 3
`#### Heading level 4`	`<h4>Heading level 4</h4>`	Heading level 4
`##### Heading level 5`	`<h5>Heading level 5</h5>`	Heading level 5
`###### Heading level 6`	`<h6>Heading level 6</h6>`	Heading level 6

Table converted from html to markdown as a ref.⚓︎

Table converted from html to markdown as a ref.

| Markdown | HTML | Rendered Output |
| :--- | :--- | :--- |
| `# Heading level 1` | `<h1>Heading level 1</h1>` | <h1>Heading level 1</h1> |
| `## Heading level 2` | `<h2>Heading level 2</h2>` | <h2>Heading level 2</h2> |
| `### Heading level 3` | `<h3>Heading level 3</h3>` | <h3>Heading level 3</h3> |
| `#### Heading level 4` | `<h4>Heading level 4</h4>` | <h4>Heading level 4</h4> |
| `##### Heading level 5` | `<h5>Heading level 5</h5>` | <h5>Heading level 5</h5> |
| `###### Heading level 6` | `<h6>Heading level 6</h6>` | <h6>Heading level 6</h6> |

Markdown	HTML	Rendered Output
`# Heading level 1`	`<h1>Heading level 1</h1>`	Heading level 1
`## Heading level 2`	`<h2>Heading level 2</h2>`	Heading level 2
`### Heading level 3`	`<h3>Heading level 3</h3>`	Heading level 3
`#### Heading level 4`	`<h4>Heading level 4</h4>`	Heading level 4
`##### Heading level 5`	`<h5>Heading level 5</h5>`	HEADING LEVEL 5
`###### Heading level 6`	`<h6>Heading level 6</h6>`	Heading level 6

Configure Cybersmart email with Gmail⚓︎

Configure Cybersmart email

To configure Cybersmart email with Gmail using POP and SMTP (for sending and receiving), use the following settings. Note that Cybersmart has transitioned to requiring SSL for secure connections.

Cybersmart Email Settings (For Gmail)⚓︎

Cybersmart Email Settings (For Gmail)

Incoming Mail Server (POP3): mail.yourdomainname (e.g., mail.example.co.za)
Incoming Port (POP3): 995 (SSL enabled)
Outgoing Mail Server (SMTP): mail.yourdomainname (e.g., mail.example.co.za)
Outgoing Port (SMTP): 587 (requires authentication) or 465 (SSL/TLS)
Username: Your full email address
Password: Your email password
Authentication: Required for outgoing mail (use same settings as incoming)

Steps to Add Cybersmart to Gmail (POP3)⚓︎

Steps to Add

Open Gmail on a computer.
Click the Settings gear icon in the top right, then See all settings.
Go to the Accounts and Import tab.
Under "Check mail from other accounts," click Add a mail account.
Enter your Cybersmart email address and click Next.
Select "Import emails from my other account (POP3)" and click Next.

Enter the settings:
Username: Full email address.
Password: Your email password.
POP Server: mail.yourdomainname | Port: 995.
Check Always use a secure connection (SSL).
Click Add Account.
Select "Yes, I want to be able to send mail as..." to configure SMTP for sending.

To Send Through Cybersmart (SMTP) in Gmail
When asked to send mail through your SMTP server, enter:
SMTP Server: mail.yourdomainname
Port: 587 (or 465 if 587 fails)
Username/Password: Same as incoming.
Select Secured connection using TLS (for 587) or SSL (for 465).

Note

If you are using a very old domain, pop3.cybersmart.co.za might be used, but generally, mail.yourdomainname is recommended.

Adaptive Rendering-Insufficient Space

If there's insufficient space to render grid items next to each other, the items will stretch to the full width of the viewport, e.g. on mobile viewports. If there's more space available, grids will render in items of 3 and more, e.g. when hiding both sidebars.

Block Syntax⚓︎

Block Syntax. Click to see Code!

The block syntax allows for arranging cards in grids together with other elements, as explained in the section on [generic grids]. Just add the card class to any block element inside a grid:

Card grid, blocks

<div class="grid" markdown>

:fontawesome-brands-html5: __HTML__ for content and structure
{ .card }

:fontawesome-brands-js: __JavaScript__ for interactivity
{ .card }

:fontawesome-brands-css3: __CSS__ for text running out of boxes
{ .card }

> :fontawesome-brands-internet-explorer: __Internet Explorer__ ... huh?

</div>

HTML for content and structure

JavaScript for interactivity

CSS for text running out of boxes

Internet Explorer ... huh?

Syntax Above: ⤴️

While this syntax may seem unnecessarily verbose at first, the previous example shows how card grids can now be mixed with other elements that will also stretch to the grid.

Using Generic Grids⚓︎

Using Generic Grids

Generic grids allow for arranging arbitrary block elements in a grid, including admonitions, code blocks, content tabs and more. Just wrap a set of blocks by using a div with the grid class:

Click to see Code

Generic Grid

<div class="grid" markdown>

=== "Unordered list"

    * First Normal Form (1NF)
    * Second Normal Form (2NF)
    * Third Normal Form (3NF)

=== "Ordered list"

    1. HTML5 (Structure)
    2. CSS3 (Styling)
    3. JavaScript (Behavior)

!!! recommendation "⚖️"

    ``` markdown title="Content Tabs"
    === "Unordered list"

        * First Normal Form (1NF)
        * Second Normal Form (2NF)
        * Third Normal Form (3NF)

    === "Ordered list"

        1. HTML5 (Structure)
        2. CSS3 (Styling)
        3. JavaScript (Behavior)
    ```

</div>

Unordered listOrdered list

First Normal Form (1NF)
Second Normal Form (2NF)
Third Normal Form (3NF)

HTML5 (Structure)
CSS3 (Styling)
JavaScript (Behavior)

⚖️

Content Tabs

=== "Unordered list"

    * First Normal Form (1NF)
    * Second Normal Form (2NF)
    * Third Normal Form (3NF)

=== "Ordered list"

    1. HTML5 (Structure)
    2. CSS3 (Styling)
    3. JavaScript (Behavior)

The Quick Version

This article explores how custom CSS can transform boring documentation into a high-end user interface.

Save 50% more time
Higher reader retention
Looks significantly cooler

Deep Dive/Core Concepts: Technical Details

This text will use a monospace-style header to signal it's for the "techies" and will have a nice dark grey beaker icon.

Important

Seeing what this does!

Recommendation

Seeing what this does!

Instruction

Seeing what this does!

Decision

Seeing what this does!

Assumption

Seeing what this does!

Dollar

Seeing What This Does!

Grey

Seeing What This Does!

Education

Seeing What This Does!

version-added

Seeing What This Does!

version-changed

Seeing What This Does!

version-removed

Seeing What This Does!

Git

New Git

New copyright

soundcloud

New soundcloud

lyrics

New lyrics

heart

New heart!

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

Unordered listOrdered list

First Normal Form (1NF)
Second Normal Form (2NF)
Third Normal Form (3NF)

HTML5 (Structure)
CSS3 (Styling)
JavaScript (Behavior)

⚖️

Content Tabs

=== "Unordered list"

    * First Normal Form (1NF)
    * Second Normal Form (2NF)
    * Third Normal Form (3NF)

=== "Ordered list"

    1. HTML5 (Structure)
    2. CSS3 (Styling)
    3. JavaScript (Behavior)

Test

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

Test

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

Test

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

Test

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

Test

wttr.in supports multilingual locations names that can be specified in any language in the world (it may be surprising, but many locations in the world don't have an English name).

erDiagram
    SCHEMA ||--o{ ENTITY : defines
    ENTITY ||--o{ ATTRIBUTE : contains
    ENTITY ||--o{ RELATIONSHIP : participates_in
    ENTITY ||--o{ CONSTRAINT : governed_by
    RELATIONSHIP }o--|| ENTITY : connects
    DEPENDENCY }o--|| ENTITY : impacts

    SCHEMA {
        string name
        string version
    }

    ENTITY {
        string name
        string type
    }

    ATTRIBUTE {
        string name
        string data_type
        boolean required
    }

    RELATIONSHIP {
        string name
        string cardinality
    }

    CONSTRAINT {
        string rule
        string scope
    }

    DEPENDENCY {
        string description
    }

graph TD
    SgrA["Sagittarius A* (Supermassive Black Hole)"]
    S62["S62 Star"]
    S2["S2 Star"]
    S55["S55 Star"]
    S29["S29 Star"]

    %% Connected Labels to guarantee alignment
    S29 --- L1(["Sometimes confused in observations"]) --> S62

    S62 --- L2["Orbits (≈9.9-year period)"] --> SgrA
    S62 --- L3["Extreme close approach (~16 AU)"] --> SgrA

    S2 --- L4["Orbits (≈16-year period)"] --> SgrA
    S55 --- L5["Orbits (≈12.8-year period)"] --> SgrA

erDiagram
    SCHEMA ||--o{ ENTITY : defines
    ENTITY ||--o{ ATTRIBUTE : contains

    SCHEMA {
        string name PK "Unique name of the schema"
        string version
    }

    ENTITY {
        string name PK
        string type
    }

    ATTRIBUTE {
        string name PK
        string data_type
        boolean required
    }

erDiagram
    DATABASE ||--o{ TABLE : contains
    TABLE {
        string name
        string type
    }

erDiagram
    SCHEMA ||--o{ ENTITY : defines
    ENTITY ||--o{ ATTRIBUTE : contains
    ENTITY ||--o{ RELATIONSHIP : participates_in
    ENTITY ||--o{ CONSTRAINT : governed_by
    RELATIONSHIP }o--|| ENTITY : connects
    DEPENDENCY }o--|| ENTITY : impacts

    SCHEMA {
        varchar name PK
        varchar version
    }

    ENTITY {
        varchar name PK
        varchar schema_name FK
        varchar type
    }

    ATTRIBUTE {
        varchar name PK
        varchar entity_name FK
        varchar data_type
        boolean required
    }

    RELATIONSHIP {
        varchar name PK
        varchar cardinality
    }

    CONSTRAINT {
        varchar rule PK
        varchar entity_name FK
        varchar scope
    }

    DEPENDENCY {
        varchar entity_name PK, FK
        varchar description
    }

erDiagram
  CUSTOMER {
    string name
  }
  DELIVERY-ADDRESS {
    string address
  }
  LINE-ITEM {
    string product
    int pricePerUnit
  }
  CUSTOMER ||--o{ DELIVERY-ADDRESS : uses
  CUSTOMER ||--o{ LINE-ITEM : contains

block
columns 1
  db(("DB"))
  blockArrowId6<["&nbsp;&nbsp;&nbsp;"]>(down)
  block:ID
    A
    B["A wide one in the middle"]
    C
  end
  space
  D
  ID --> D
  C --> D
  style B fill:#969,stroke:#333,stroke-width:4px

architecture-beta
    group api(cloud)[API]

    service db(database)[Database] in api
    service disk1(disk)[Storage] in api
    service disk2(disk)[Storage] in api
    service server(server)[Server] in api

    db:L -- R:server
    disk1:T -- B:server
    disk2:T -- B:db

architecture-beta
    service left_disk(disk)[Disk]
    service top_disk(disk)[Disk]
    service bottom_disk(disk)[Disk]
    service top_gateway(internet)[Gateway]
    service bottom_gateway(internet)[Gateway]
    junction junctionCenter
    junction junctionRight

    left_disk:R -- L:junctionCenter
    top_disk:B -- T:junctionCenter
    bottom_disk:T -- B:junctionCenter
    junctionCenter:R -- L:junctionRight
    top_gateway:B -- T:junctionRight
    bottom_gateway:T -- B:junctionRight

classDiagram
  Person <|-- Student
  Person <|-- Professor
  Person : +String name
  Person : +String phoneNumber
  Person : +String emailAddress
  Person : +purchaseParkingPass()
  Address "1" <-- "0..1" Person : lives at
  class Student{
    +int studentNumber
    +int averageMark
    +isEligibleToEnrol()
    +getSeminarsTaken()
  }
  class Professor{
    +int salary
  }
  class Address{
    +String street
    +String city
    +String state
    +int postalCode
    +String country
    -validate()
    +outputAsLabel()
  }

classDiagram
  Person <|-- Professor
  Person : +String name
  Person : +String phoneNumber
  Person : +String emailAddress
  Person : +purchaseParkingPass()
  Address "1" --> "0..1" Person : lives at
  class Student{
s1}
  class Professor{
s2}
  class Address{
s3}

🖋️ Playwrite AR Guides (Arch Linux System Integration) ⚓︎

A summary documentation page tracking the installation, filesystem diagnostics, and OpenType rendering features for the Playwrite AR Guides typeface.

📋 Quick Status Summary⚓︎

Package Source: Upstream Google Fonts / TypeTogether GitHub repository.
Installation Scope: Local User (~/.local/share/fonts/PlaywriteARGuides-Regular.ttf).
System Integrity: Verified. System-wide fc-cache anomalies (looped directory detected) are identified as safe, superficial Fontconfig engine duplication warnings. Fonts are caching successfully.

🔍 System Verification & Diagnostics⚓︎

1. Confirm Font Recognition

1. Confirm Font Recognition⚓︎

To verify that the system successfully registers and indexes the font family, run:

fc-list : family | grep -i "Playwrite"

Expected Output: Playwrite AR Guides

2. Suppress/Ignore Fontconfig Cache Artifacts

2. Suppress/Ignore Fontconfig Cache Artifacts⚓︎

If fc-cache -fv outputs skipping, looped directory detected errors for /usr/share/fonts/ subdirectories, it can be safely ignored.

The Cause: Fontconfig triggers a false-positive tracking flag during its second-pass explicit array check after completing its initial recursive filesystem scan.
The Proof: Ensure the final engine line outputs: fc-cache: succeeded.

🛠️ Enabling Cursive Connections (OpenType Features)⚓︎

🛠️ Enabling Cursive Connections (OpenType Features)

Because Playwrite is a highly specialized primary school education font, it relies heavily on OpenType feature tags to dynamically link letters together into seamless cursive scripts. Without these features enabled, letters will appear disconnected.

🌐 Web & MkDocs Custom CSS⚓︎

🌐 Web & MkDocs Custom CSS

To use this font natively on a website or custom MkDocs theme, ensure you load the local file or standard web font, and explicitly declare the standard ligatures layout:

.playwrite-cursive {
    font-family: 'Playwrite AR Guides', sans-serif;

    /* Mandatory properties for cursive script linking */
    font-feature-settings: "liga" 1, "calt" 1;
    font-variant-ligatures: common-ligatures contextual;

    /* Optional: Optimizes rendering speed vs legibility */
    text-rendering: optimizeLegibility;
}

📄 LibreOffice / OpenOffice⚓︎

📄 LibreOffice / OpenOffice

To use the font inside office suites with proper connecting lines, append the mandatory feature tags directly inside the Font Name selector box:

Click on the Font Name drop-down menu.
Type or change the string to exactly match this syntax:
Playwrite AR Guides:liga=1&calt=1
Press Enter. The system will now actively link the characters as you type.

🎨 Graphic Design Tools (Inkscape / GIMP)⚓︎

🎨 Graphic Design Tools (Inkscape / GIMP)

Inkscape: Open the Text and Font sidebar (Ctrl+Shift+T), click the Features tab, and ensure Standard Ligatures (liga) and Contextual Alternates (calt) are ticked.
GIMP: Standard ligatures are turned on by default in the text tool layer options.

Produces { .centered }Text Plus Colour

Text `{. centered}`⚓︎

This pertains to "Remarkable" and MkDocs-MaterialX using 'GFM'

OK so with this example heading:

### <font style="color:pink"> 🖋️ Playwrite AR Guides (<font style="color:cornflowerblue">Arch Linux System Integration</font>) </font> { .centered }

With the added custom css below, { .centered } works on any heading level, # through ######, and it's the same one-word class each time:

.md-typeset .admonition pre > code,
.md-typeset details pre > code {
  white-space: pre-wrap;
  overflow-wrap: anywhere;
  padding-right: 3.5rem;
}

.md-typeset .admonition pre > code > span,
.md-typeset details pre > code > span {
  min-width: 0 !important;
}

Is the working solution!

Blogs⚓︎

Basics Inc. Post Metadata
View Guide

Covers basics of setting up a blog, including post metadata. (20 min)
Nav, Pgn, et al. Authors
View Config

Describes how to make it easier for your readers to find content. (30 min)
Eng. and Dissemination
View Guide

Walks you through ways of increasing engagement with your content. (30 min)
Template Repository

Basics
View Guide

Shows how to configure MaterialX to create social cards for your content. (20 min)
Custom Cards
View Guide

Shows you how to design your own custom social cards. (15 min)
Template Repository

Basics
View Guide

Shows how to configure MaterialX to create social cards for your content. (20 min)
Custom Cards
View Guide

Shows you how to design your own custom social cards. (15 min)
Template Repository

Linux GTK/WebKit "Nothing Renders" Checklist

Operational Diagnostic Guide

`Operational Diag Guide`⚓︎

An Operational Diagnostic Guide for troubleshooting instances where GTK/WebKit-based applications (e.g., Remarkable, Devhelp, Yelp, GNOME Help) launch successfully but render a completely blank content pane.

⚡ Quick Triage (The 2-Minute Version)⚓︎

Quick Triage

Before executing the full diagnostic tree, run these four commands to immediately isolate the root cause.

pkill WebKitWebProcess

fc-match monospace

coredumpctl list WebKitWebProcess | tail

LIBGL_ALWAYS_SOFTWARE=1 devhelp

🔍 Immediate Indicator Matrix⚓︎

Diagnostic Signal	Identified Subsystem	Immediate Action
`pkill` resolves issue	Stale Render Process	Document incident; restart application.
`fc-match` fails/hangs	Font Config Subsystem	Proceed directly to Step 5 (Cache Reset).
`coredumpctl` shows fresh logs	WebKit Core Crash	Proceed to Step 2 (Crash Analysis).
`LIBGL` variable resolves issue	GPU / Mesa Driver	Proceed to Step 6 (Hardware Isolation).

Core Diagnostic Rule

If multiple WebKitGTK applications suddenly render blank content simultaneously, suspect the shared WebKit rendering stack before troubleshooting the individual applications.

🎮 Cross-Hardware Graphics Triage⚓︎

Cross-Hardware Graphics Triage

When an application works under LIBGL_ALWAYS_SOFTWARE=1, the issue lies within your hardware acceleration pipeline. Select your active GPU architecture below to run targeted environment overrides before resorting to full software fallback.

AMD Radeon (My Setup)Nvidia GeForceIntel Iris / Arc

Because you are running an AMD Radeon RX 580 via the open-source Mesa drivers, rendering issues are often caused by WebKit fighting with hardware acceleration, WebGL, or driver compilation layers.

Disable GPU Sandboxing (WebKit Flag)
```
devhelp --disable-gpu-sandbox
```
Use Case: WebKit's security sandbox often clashes with AMD driver memory allocation. If this works, the issue is sandboxing, not your GPU.
Bypass Driver Shaders (Mesa Toggles)
```
R600_DEBUG=nocall devhelp
# OR (For newer Vulkan-based WebKit paths)
RADV_DEBUG=nocache devhelp
```
Use Case: Disables specific hardware-level optimization steps in the AMD driver to see if a driver bug is misdrawing the app window.
Disable Compositing Mode
```
WEBKIT_DISABLE_COMPOSITING_MODE=1 devhelp
```
Use Case: Forces WebKit to draw the window layout using standard rendering instead of hardware acceleration, bypassing deep driver layers entirely.

The proprietary Nvidia driver stack utilizes a completely different rendering path than Mesa. WebKit failures here usually relate to GLX contexts, thread management, or power-saving states.

Force Legacy GLX Indirect Rendering
```
__GLX_FORCE_VENDOR_LIBRARY_0=1 devhelp
```
Use Case: Bypasses Nvidia's direct rendering infrastructure if there is a context mismatch between GTK and the display server.
Disable Threaded Optimizations
```
__GL_THREADED_OPTIMUS=0 devhelp
```
Use Case: Resolves timing-related race conditions where WebKit threads collapse while communicating with the Nvidia binary driver.
Force WebKit WebGL Disabling
```
WEBKIT_DISABLE_DMABUF_RENDERER=1 devhelp
```
Use Case: Fixes blank screens on Nvidia setups caused by broken DMA-BUF memory sharing protocols between the GPU and WebKit processes.

Intel graphics rely heavily on the modern iris driver within Mesa. Under production stress, it can experience severe rendering sync drops or memory caching faults.

Force Older Intel Driver Generation
```
MESA_LOADER_DRIVER_OVERRIDE=i965 devhelp
```
Use Case: Forces the system to fall back from the modern Iris driver to the mature, stable legacy i965 driver path.
Disable Performance Cache Compilations
```
INTEL_DEBUG=nocache devhelp
```
Use Case: Instructs the Intel driver to bypass the internal shader cache, clearing up pipeline errors caused by corrupted system shader trees.

📋 Comprehensive Diagnostic Steps⚓︎

Step 0 — Isolate Scope⚓︎

Isolate Scope

Determine if the rendering failure is isolated or system-wide by testing at least two independent WebKit applications (e.g., remarkable and devhelp).

Step 0 ExecutionScope Analysis

Run the following test suite in your terminal:

remarkable & devhelp &

Observation	Diagnostic Deductible	Operational Focus
One application broken	App-Specific Configuration Error	Check local app configs, dotfiles, or extensions.
Both applications broken	Shared Stack Corruption	Target shared libraries (WebKit, GTK, Fonts, GPU).

Step 1 — Check for WebKit Crashes⚓︎

Check for Webkit Crashes

Inspect the system core dump manager to verify if the underlying WebKit process is actively terminating.

coredumpctl list WebKitWebProcess

Analysis of Outputs

If fresh entries are populated in the list, extract the specific crash metadata using the Process ID (PID):

coredumpctl info <PID>

* Critical Signal to Look For: Signal: 6 (ABRT) or any explicit WebKitWebProcess failure tracking.
* Verdict: If present, the WebKit engine itself is unstable. Proceed to package integrity validation.

Step 2 — Trace Terminal Standard Outputs⚓︎

Trace Terminal Standard Outputs

Launch the affected application directly from an active terminal session to capture real-time stdout and stderr diagnostic streams.

devhelp
# OR
remarkable

Error Signature Branching

Signature: Segmentation fault
👉 Verdict: Memory corruption or binary incompatibility. Skip rendering checks; review system memory or package versions.
Signature: References to GLib, WebKit, or JavaScriptCore
👉 Verdict: Broken rendering stack. Proceed with the checklist sequentially.

Step 3 — Terminate Stale WebKit Renderers⚓︎

Terminate Stale WebKit Renderers

Stale background rendering processes can lock shared resources and prevent new instances from drawing GUI surfaces.

pkill WebKitWebProcess

Validation

Relaunch the target application. If the interface renders correctly, a stale or orphaned renderer state was blocking execution.

Step 4 — Verify Font Subsystem Integrity⚓︎

Verify Font Subsystem Integrity

A corrupted, missing, or hanging system font configuration can completely block text-heavy WebKit canvas initialization.

fc-match monospace

fc-list | head

Output Evaluation

Positive Indicators: Clean, instant stdout mapping to local fonts (e.g., Noto Sans, DejaVu).
Negative Indicators: Missing output, explicitly logged errors, or a terminal hang. Proceed immediately to Step 5.

Step 5 — Rebuild Font Subsystem Caches⚓︎

Rebuild Font Subsystem Caches

Force a complete purge and regeneration of the font configuration binaries. Execute this if Step 4 yielded any anomalies.

rm -rf ~/.cache/fontconfig

fc-cache -rv

Post-Execution Action

Relaunch your WebKit applications to verify if the fresh font map resolves the rendering block.

Step 6 — Isolate GPU and Mesa Driver Conflicts⚓︎

Isolate GPU and Mesa Driver Conflicts

Determine if hardware acceleration or the graphics driver stack is causing rendering failures by forcing a pure software rendering fallback.

LIBGL_ALWAYS_SOFTWARE=1 devhelp
# OR
LIBGL_ALWAYS_SOFTWARE=1 remarkable

Deductible Outcomes

Resolved: A direct incompatibility exists between the user-space driver, kernel GPU module, and WebKit's hardware pipeline. Move to the Cross-Hardware Graphics Triage section to find an architectural workaround.
Unchanged: The hardware acceleration pipeline is highly unlikely to be the root cause.

Step 7 — Validate Package Integrity⚓︎

Validate Package Integrity

Verify that the shared WebKit libraries and components are complete, uncorrupted, and synchronized via pacman.

Verify versions

pacman -Q webkit2gtk-4.1 javascriptcoregtk-4.1

Verify file hashes and permissions

pacman -Qkk webkit2gtk-4.1

Package Discrepancies

Look closely for warnings concerning Missing files, Modified files, or Partial upgrades. If any are found, force-reinstall the packages:

sudo pacman -S webkit2gtk-4.1 javascriptcoregtk-4.1

Step 8 — Query System Logs for Component Failures⚓︎

Query System Logs for Component Failures

Filter user and system journals specifically for WebKit engine events generated during the current boot cycle.

journalctl -b --user | grep -i webkit

journalctl -b | grep -i webkit

Log Analysis

This step regularly surfaces hidden segmentation faults, pointer errors, or system library linkage omissions not printed to the application's standard terminal output.

Step 9 — Isolate Local User Profile Corruption⚓︎

Isolate Local User Profile Corruption

Determine if the root cause resides within user configuration directories (~/.config, ~/.local) or is a persistent system-wide fault.

sudo useradd -m testwebkit

sudo passwd testwebkit

Test Protocol

Log out of your desktop environment.
Log in as the newly created testwebkit user profile.
Execute devhelp from a terminal window.

Result Profile	Root Cause Domain
Interface Renders Successfully	Dotfile/Cache corruption within your primary home directory.
Interface Remains Blank	System-wide package, library, or hardware driver failure.

Step 10 — Nuclear User Cache Reset⚓︎

Nuclear User Cache Reset

If Step 9 proved the issue is isolated to your primary user profile, execute a complete clearance of local transient caches.

rm -rf ~/.cache/*

Precautionary Step

Ensure all work is saved. Log completely out of your desktop session, then log back in to force all background user processes to re-initialize clean caches.

📝 Incident Data Collection Protocol⚓︎

Incident Data Collection Protocol

When anomalous rendering behaviors occur, immediately dump the system state metrics. Preserving this timeline context prevents trial-and-error debugging later.

Capture operational snapshot

date > issue.log

uname -a >> issue.log

pacman -Q webkit2gtk-4.1 javascriptcoregtk-4.1 mesa >> issue.log

Extract the recent delta of the system log

journalctl -b --since "10 minutes ago" >> issue.log

Lessons Learned Notebook

Always record the exact packages updated in the transaction preceding a WebKit crash event. Correlating package rollouts to application behavior reduces diagnostic mazes into predictable, 2-minute resolutions.

👉 Advanced-Configuration

⚖️

Content Tabs

Unordered listOrdered list

First Normal Form (1NF)
Second Normal Form (2NF)
Third Normal Form (3NF)

HTML5 (Structure)
CSS3 (Styling)
JavaScript (Behavior)

Power Bus Results

The power flow bus results are defined as:

$\begin{aligned} &vm\_pu_{phase} = \lvert \underline{V_{phase}}_{bus} \rvert \\ &va\_degree_{phase} = \angle \underline{V_{phase}}_{bus} \\ &p\_mw_{phase} = Re(\sum_{n=1}^N \underline{S_{phase}}_{bus, n}) \\ &q\_mvar_{phase} = Im(\sum_{n=1}^N \underline{S_{phase}}_{bus, n}) \end{aligned}$

Power Bus Results

net.res_bus

$\begin{align*} &vm\_pu = \lvert \underline{V}_{bus} \rvert \\ &va\_degree = \angle \underline{V}_{bus} \\ &p\_mw = Re(\sum_{n=1}^N \underline{S}_{bus, n}) \\ &q\_mvar = Im(\sum_{n=1}^N \underline{S}_{bus, n}) \end{align*}$

Power Equation

The power equation in each phase is therefore given as $S_{ph-e} = \frac{V_{ph-ph} \cdot I_{ph-ph}}{\sqrt3 }$

$\begin{align*} S_{ph-e} = \frac{V_{ph-ph} \cdot I_{ph-ph}}{\sqrt3 } \end{align*}$

MathJax & MaterialX Configuration Summary⚓︎

A complete, neat summary of everything finalized for the MaterialX for MkDocs (v9.7.0) site.

1. Updated JavaScript Configuration File⚓︎

Replace the entire contents of your javascripts/mathjax.js file with this clean, optimized version. It fixes the trailing pipe regex bug, preserves your dynamic page-switching hooks, and forces your single-click zoom layout for everyone sitewide.

MathJax .js config

window.MathJax = {
  tex: {
    inlineMath: [["\\(", "\\)"]],
    displayMath: [["\\[", "\\]"]],
    processEscapes: true,
    processEnvironments: true
  },
  options: {
    ignoreHtmlClass: ".*", // FIXED: Cleaned up the trailing pipe '|' to prevent parsing bugs
    processHtmlClass: "arithmatex",

    // LOCKS USER ZOOM PREFERENCES SITEWIDE FOR ALL VISITORS
    menuOptions: {
      settings: {
        zoom: 'Click',     // Forces a simple left-mouse click to trigger the zoom window
        zscale: '200%'     // Sets the default zoom scaling level to 200%
      }
    }
  }
};

// CRITICAL FOR MATERIALX / MKDOCS: Handles dynamic theme changes and SPA page switches
document\$.subscribe(() => { 
  MathJax.startup.output.clearCache()
  MathJax.typesetClear()
  MathJax.texReset()
  MathJax.typesetPromise()
})

2. Streamlined mkdocs.yml Settings⚓︎

Configuration blocks are clean and perfectly structured. Active components load immediately, while unused options are safely preserved as plain comments for future reference without causing layout compile errors:

yaml restructure

extra_css:
  # Future Reference (KaTeX Toggle):
  # https://unpkg.com/katex@0/dist/katex.min.css
  - styles/custom.css

extra_javascript:
  - javascripts/mathjax.js
  - javascripts/expand-code.js
  - https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js
  # Future Reference (MathJax Toggles):
  # https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
  - javascripts/theme_extra.js
  # Future Reference (KaTeX Toggles):
  # javascripts/katex.js
  # https://unpkg.com/katex@0/dist/katex.min.js
  # https://unpkg.com/katex@0/dist/contrib/auto-render.min.js
  - https://unpkg.com/tablesort@5.3.0/dist/tablesort.min.js
  - https://unpkg.com/tablesort@5.3.0/dist/sorts/tablesort.number.min.js
  - javascripts/tablesort.js
  - javascripts/iconsearch.js

3. Page Layout Cheat Sheet (The 3 Math Situations)⚓︎

Use these exact Markdown syntax patterns depending on the alignment and sizing goals for page sections:

Situation 1

Situation 1: Inline Math (Inside a Text Sentence)

Goal: Blend equations directly into sentences without disrupting regular line heights.
How to write it: Use single dollar signs ($) on the same line as your text.

Rogers-Ramanujan Identity 1

Placed inside a sentence, $1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \dots = \prod_{j=0}^{\infty} \frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad \text{for } |q| < 1$ this is what a Rogers-Ramanujan Identity looks like.

Situation 1

Situation 1: Inline Math (Inside a Text Sentence)

Goal: Blend equations directly into sentences without disrupting regular line heights.
How to write it: Use single dollar signs ($) on the same line as your text.

Inline Equation Example

The famous Euler identity, $e^{i\pi} + 1 = 0$, connects five fundamental mathematical constants seamlessly within a single sentence.

Situation 2

Situation 2: Left-Aligned Display Math (Full Sized)

Goal: Display mathematical symbols at full scale (large fractions, stacked summation/product symbols) but align them neatly with your left text margin.
How to write it: Put your formula on a new line, open with a single $, and immediately lead with \displaystyle.

Rogers-Ramanujan Identity 2

A Rogers-Ramanujan Identity:

$\displaystyle 1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \dots = \prod_{j=0}^{\infty} \frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad \text{for } |q| < 1$

Situation 3

Situation 3: Centered Display Math (Standalone)

Goal: Give highly important formulas full breathing room by centering them standalone on their own structural block.
How to write it: Isolate the equation completely on its own line wrapped in double dollar signs ($$).

Rogers-Ramanujan Identity 3

A Rogers-Ramanujan Identity:

\[ 1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \dots = \prod_{j=0}^{\infty} \frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad \text{for } |q| < 1 \]

The Chandrasekhar Limit & Supernova Catalysts⚓︎

🌌 The Chandrasekhar Limit⚓︎

The Chandrasekhar Limit

The Chandrasekhar limit is the maximum mass a white dwarf star can support against its own gravity.

The Threshold: Exactly 1.44 solar masses.
The Mechanism: Electron degeneracy pressure provides the outward push.
The Trigger: Exceeding this mass destroys the star's structural equilibrium.
The Outcome: Runaway carbon fusion triggers a catastrophic Type Ia supernova.

🔥 Core-Collapse Candidates⚓︎

Massive, active stars bypass the white dwarf stage entirely and end their lives in violent collapses.
* The Threshold: Stars born with at least 8 to 10 solar masses.
* The Mechanism: Iron buildup in the core stops energy production.
* The Trigger: Gravity instantly crushes the unsupported core.
* The Outcome: A violent rebound flings the outer layers into a Type II, Ib, or Ic supernova.
* The Targets: Red and blue supergiants like Betelgeuse and Antares are prime active candidates.

Next Steps to Explore⚓︎

1. Core Fusion Sequences⚓︎

Track how massive stars transition from burning Hydrogen to Helium.
Explore the creation of heavy cosmic elements up to Iron.

2. Supernova Classification⚓︎

Learn how light spectrums differentiate Type Ia from core-collapse explosions.
Discover why the presence or absence of Hydrogen lines matters to astronomers.

3. Supergiant Life Cycles⚓︎

Examine the final, volatile evolutionary stages of massive stars.
See how stellar winds and mass loss affect their ultimate explosive fate.

Customised Tables⚓︎

Please note that ALL tables below are rendered 1^st, with the collapsed admonition BELOW it, containing the markdown code within a code box.

Basic Table⚓︎

First Header	Second Header
Content Cell	Content Cell

Basic Table - Click To See Code

First Header  | Second Header
------------- | -------------
Content Cell  | Content Cell

Alignment Table⚓︎

Item	Value
Centered	Right

Alignment - Click To See Code

| Item      | Value  |
| :-------: | -----: |
| Centered  | Right  |

Column Spanning⚓︎

	Grouping
Header	A	B
Data	spans

Column Spanning - Click To See Code

|            | Grouping ||
| Header     | A        | B        |
| ---------- | :------: | -------: |
| Data       | spans    ||

Row Spanning⚓︎

A	B	C
tall	1	x
tall	2	y

Row Spanning (rowspan: true) - Click To See Code

| A      | B  | C  |
| ------ | -- | -- |
| tall   | 1  | x  |
| ^^     | 2  | y  |

Caption With Label⚓︎

Sales Data
Q1	Q2
R100 000	R120 000

Caption With Label - Click To See Code

[Sales Data][sales]
| Q1   | Q2   |
| ---- | ---- |
| R100 000  | R120 000  |

Multiline Cells⚓︎

Code	Output
`print("hello")`	hello

Multiline Cells (multiline: true) - Click To See Code

| Code            | Output  |
| --------------- | ------- |
| ```python      |         |\
| print("hello") | hello   |\
| ```            |         |

Headerless Table⚓︎

No header

here

Headerless Table (headerless: true) - Click To See Code

| -------- | ----- |
| No header| here  |

Attribute Lists Cells Rows⚓︎

Header
plain cell
styled cell
id cell
full

Attribute Lists on Cells and Rows (attr_list: true) - Click To See Code

| Header                        |
| ----------------------------- |
| plain cell                    |
| styled cell {.highlight}      |
| id cell {#cell-1}             |
| full {#c2 .bold data-x="1"}   |

Row Attributes - append⚓︎

A	B
x	y
p	q

Row Attributes - append {…} after the last | of a row: Click To See Code

| A | B |
| - | - |
| x | y |{.even}
| p | q |{.odd #row-2}

Cell Row Attribs used together⚓︎

H
cell

Combined Cell and Row Attribs can be used together - Click To See Code

| H                  |
| ------------------ |
| cell {.myclass} |{.myrow}

Multiline⚓︎

Markdown	Rendered HTML
Italic	Italic
Item 1 Item 2	Item 1 Item 2
`.1 + .2`	`.1 + .2`

Multiline

|   Markdown   | Rendered HTML |
|--------------|---------------|
|    *Italic*  | *Italic*      | \
|              |               |
|    - Item 1  | - Item 1      | \
|    - Item 2  | - Item 2      |
|    ```python | ```python       \
|    .1 + .2   | .1 + .2         \
|    ```       | ```           |

Rowspan⚓︎

Net ATP yields per hexose
Stage	Direct Products	ATP Yields
Glycolysis: Fundamental Metabolic pathway breaks down Glucose into two molecules of Pyruvate.	2 ATP
	2 NADH	3--5 ATP
Pyruvate Oxidation	2 NADH	5 ATP
Citric Acid Cycle	2 ATP
	6 NADH	15 ATP
	2 FADH2	3 ATP
30--32 ATP

Rowspan

Stage | Direct Products | ATP Yields
----: | --------------: | ---------:
Glycolysis | 2 ATP ||
^^ | 2 NADH | 3--5 ATP |
Pyruvate oxidation | 2 NADH | 5 ATP |
Citric acid cycle | 2 ATP ||
^^ | 6 NADH | 15 ATP |
^^ | 2 FADH2 | 3 ATP |
**30--32** ATP |||
[Net ATP yields per hexose]

Headerless 2⚓︎

♜		♝	♛	♚	♝	♞	♜
	♟	♟	♟		♟	♟	♟
♟		♞
	♗			♟
				♙
					♘
♙	♙	♙	♙		♙	♙	♙
♖	♘	♗	♕	♔			♖

Headerless

|--|--|--|--|--|--|--|--|
|♜|  |♝|♛|♚|♝|♞|♜|
|  |♟|♟|♟|  |♟|♟|♟|
|♟|  |♞|  |  |  |  |  |
|  |♗|  |  |♟|  |  |  |
|  |  |  |  |♙|  |  |  |
|  |  |  |  |  |♘|  |  |
|♙|♙|♙|♙|  |♙|♙|♙|
|♖|♘|♗|♕|♔|  |  |♖|

👉 Advanced-Configuration

Data table, columns aligned to left

| Method      | Description                          |
| :---------- | :----------------------------------- |
| `GET`       | :material-check:     Fetch resource  |
| `PUT`       | :material-check-all: Update resource |
| `DELETE`    | :material-close:     Delete resource |

Method	Description
`GET`	Fetch resource
`PUT`	Update resource
`DELETE`	Delete resource

Data table, columns centered

| Method      | Description                          |
| :---------: | :----------------------------------: |
| `GET`       | :material-check:     Fetch resource  |
| `PUT`       | :material-check-all: Update resource |
| `DELETE`    | :material-close:     Delete resource |

Method	Description
`GET`	Fetch resource
`PUT`	Update resource
`DELETE`	Delete resource

Data table, columns aligned to right

| Method      | Description                          |
| ----------: | -----------------------------------: |
| `GET`       | :material-check:     Fetch resource  |
| `PUT`       | :material-check-all: Update resource |
| `DELETE`    | :material-close:     Delete resource |

Method	Description
`GET`	Fetch resource
`PUT`	Update resource
`DELETE`	Delete resource

Method	Description
`GET`	Fetch resource
`PUT`	Update resource
`DELETE`	Delete resource

🚀 GitHub Deployment⚓︎

Afridyne Systems: GitHub Pages Deployment

Follow this step-by-step guide to completely reset your repository and configure automated Markdown building via GitHub Actions.

Local Backup Dir.⚓︎

Part 1: Local Project Root

Ensure your local project root directory matches this exact structure. Note that files like mathjax.js must live inside the docs/ subdirectory.

Afridyne-Systems/ (Your local project root)
├── .github/
│   └── workflows/
│       └── deploy.yml
├── docs/
│   ├── index.md
│   ├── MathJax.md
│   ├── [your other .md files/folders...]
│   └── javascripts/
│       └── mathjax.js
└── mkdocs.yml

Asset Code Files⚓︎

Part 2: Configuration & Asset Code Files 📂 File 1: mkdocs.yml

Place this in your project root folder. Make sure the site_url points to your project subfolder.

site_url: https://johnpiers.github.io/Afridyne-Systems
site_name: Afridyne Systems

theme:
  name: materialx  # Swap to 'materialx' if using the specific MaterialX package

extra_javascript:
  - javascripts/mathjax.js
  - https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js
  - javascripts/expand-code.js
  - javascripts/theme_extra.js
  - https://unpkg.com/tablesort@5.3.0/dist/tablesort.min.js
  - javascripts/tablesort.js
  - javascripts/iconsearch.js

`mathjax.js`⚓︎

📂 File 2:docs/javascripts/mathjax.js Click To See Code

Place this inside your docs/javascripts/ directory. It contains the Material lifecycles and your specific user menu preferences.

window.MathJax = {
  tex: {
    inlineMath: [["\\(", "\\)"]],
    displayMath: [["\\[", "\\]"]],
    processEscapes: true,
    processEnvironments: true
  },
  options: {
    ignoreHtmlClass: ".*",
    processHtmlClass: "arithmatex",
    menuOptions: {
      settings: {
        zoom: 'Click',     // Locks left-mouse click as the zoom trigger
        zscale: '200%'     // Zoom scale default
      }
    }
  }
};

// Lifecycles for Material theme SPA dynamic page loading switching
document\$.subscribe(() => { 
  if (typeof MathJax !== "undefined" && MathJax.startup) {
    MathJax.startup.output.clearCache();
    MathJax.typesetClear();
    MathJax.texReset();
    MathJax.typesetPromise();
  }
});

`deploy.yml`⚓︎

📂 File 3:.github/workflows/deploy.yml Click To See Code

Place this exactly in the subfolder path .github/workflows/ relative to your project root. This manages your compiler.

name: ci
on:
  push:
    branches:
      - main

permissions:
  contents: write

jobs:
  deploy:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v4

      - uses: actions/setup-python@v5
        with:
          python-version: 3.x

      - run: echo "cache_id=\((date +\%Y\%m\%d)" >> \)GITHUB_ENV

      - uses: actions/cache@v4
        with:
          key: mkdocs-materialx-\${{ env.cache_id }}
          path: .cache

      - name: Install pngquant system package
        run: sudo apt-get update && sudo apt-get install -y pngquant

      # Sets up uv cleanly on GitHub Actions
      - name: Install uv
        uses: astral-sh/setup-uv@v5

      # Installs every plugin and MaterialX using uv straight from your requirements.txt
      - name: Install MaterialX Dependencies
        run: |
          uv pip install --system --upgrade pip
          uv pip install --system -r requirements.txt

      - run: mkdocs build --clean

      - run: sed -i 's|/assets/local_icons/|/Afridyne-Systems/assets/local_icons/|g' site/search/search_index.json site/assets/javascripts/*.js 2>/dev/null || true

      - uses: peaceiris/actions-gh-pages@v4
        with:
          github_token: \${{ secrets.GITHUB_TOKEN }}
          publish_dir: ./site

Delete Repo.⚓︎

Part 3: 📂Step 1: Delete old GitHub Repo

Go to your repo at https://johnpiers.github.io/Afridyne-Systems.
Click Settings (the gear icon on the top tab row).
Scroll all the way down to the bottom Danger Zone.
Click Delete this repository.
Type out the required repository path confirmation string and authorize the deletion.

New Repo.⚓︎

Step 2: Create a New Repository

On GitHub, click New repository (or go to https://github.com).
Name it exactly: Afridyne-Systems.
Set visibility to Public.
CRITICAL: Do NOT initialize with a README, .gitignore, or License. Keep it completely empty.
Click Create repository.

Push (Actions)⚓︎

Part 4: Push Your Backup Files (Terminal Actions)

Open your terminal or command prompt, navigate into your clean local project backup root directory (Afridyne-Systems/), and run these commands to push your project files for the first time:

Initialize a clean git tree local tracker.
```
git init
```
Add all local files (docs/, .github/, mkdocs.yml) into stage tracking.
```
git add
```

Commit your changes.

git commit -m "Initial automated MkDocs structure setup"

Target the main default branch.
```
git branch -M main
```
Link your local project directory to your new remote GitHub repository.
```
git remote add origin https://github.com.git
```
Push to main (this will automatically launch the GitHub Actions compiler!).
```
git push -u origin main
```

GitHub Setup⚓︎

Part 5: One-Time GitHub Pages Setup (Web Dashboard)

Once you push your code, the GitHub Action workflow will compile your site and automatically generate a background branch named gh-pages. To activate the public URL route:

Go back to your new repository on GitHub.com.
Go to Settings -> Pages (in the left sidebar configuration panel).
Under Build and deployment -> Source, make sure it says Deploy from a branch.
Under Branch, change the dropdown selection from None to gh-pages.
Keep the folder path field set to /(root) and hit Save.

Your clean, interactive site will load live at https://github.io in under 2 minutes!

Phase 1⚓︎

Phase 1: Overcoming the Pipeline Obstacles.

This phase covers how you resolved the environment conflicts between your cutting-edge Arch Linux machine and GitHub's virtual runner environment.

1. The Core Issue⚓︎

The Core Issue

Your local project relies on a modern, independent fork called mkdocs-materialx.
GitHub's clean servers did not possess your specialized plugins or system-level dependencies.
The standard mkdocs gh-deploy script repeatedly crashed due to automated Git fast-import permission restrictions.

2. The Resolutions⚓︎

The Resolutions

Namespace Fixes: Updated plugin names in mkdocs.yml from material/ (e.g., blog, social, optimize) to materialx/ for direct compatibility.
Typographic Errors: Removed the non-existent - material/typeset plugin line entirely.
System Packages: Added a native Linux layer command to the pipeline to automatically install pngquant for image compression.
Dependency Chain: Explicitly listed all standalone utilities (glightbox, table-reader, markdown-exec, section-index, open-in-new-tab, schema-reader, caption, minify-plugin) so the server downloads them instantly.
Deployment Engine Swap: Replaced the broken gh-deploy script with a native GitHub Actions direct-upload plugin (peaceiris/actions-gh-pages), bypassing the Git transfer limits completely.

Phase 2⚓︎

Phase 2: Final Synchronization & Repository Protection.

This phase details how you secured your project and synchronized your local workstation with the live cloud framework.

1. Protection⚓︎

Intellectual Property Protection

Action: Overwrote the boilerplate repository text by editing README.md directly via your web browser.
Result: Cleared the default configuration noise and established a clear, public notice asserting your copyright over all explicit data, branding profiles, and proprietary assets relating directly to Afridyne Systems.

2. Workstation Synchronization⚓︎

Workstation Synchronization

Action: Ran git pull origin main in your local Tilix terminal.
Result: Downloaded the updated copyright file to your hard drive, locking your Arch PC and GitHub in a 100% matched state.

3. Future Update Workflow⚓︎

Future Update Workflow

To publish new documentation files or update equations moving forward, run this streamlined sequence:

git add
git commit -m "Your description here"
git push

Note: GitHub Actions automatically triggers, compiles your MaterialX code, and deploys your fully interactive MathJax pages to the web completely on its own.

🗺️ Afridyne Project Synchronization Blueprint⚓︎

Current System Status: Fully Synchronized

This reference covers the seamless sync workflow across your 4 active deployment legs:

💻 Working Site: Local real-time engine (http://127.0.0.1:8000/)
🗂️ Git Site: Local synchronization hub (/mnt/sdb/AfridyneSystems)
🚀 Cloud Pipeline: GitHub Actions Runner (https://github.com/johnpiers/Afridyne-Systems/actions)
🌐 Live Website: Public Production Front (https://johnpiers.github.io/Afridyne-Systems/)

🔄 The 3-Step Update Workflow🛡️ Safety Checklist

📦 Step 1: Copy Assets Across⚓︎

Copy your updated .md file or image asset from your Working directory into the exact same path inside your Git directory:

Working/docs/your-page.md ➔ 📁 Overwrite ➔ Git/docs/your-page.md

💻 Step 2: Navigate to Git Hub⚓︎

Open your terminal window and pivot cleanly into your active tracking repository:

cd /mnt/sdb/AfridyneSystems

🚀 Step 3: Run the Git Pipeline⚓︎

Execute the core sequence to stage your files, log your message, and deploy to the cloud:

git add docs/your-page.md
git commit -m "docs: update content page assets"
git push origin main

⚠️ Rule #1: The Pre-Work Pull⚓︎

Always run a local pull inside your Git Site folder before dragging new files over. This prevents cloud sync conflicts if you ever make adjustments directly on the GitHub web interface:

cd /mnt/sdb/AfridyneSystems && git pull origin main

🎯 Rule #2: File Hygiene⚓︎

Ensure your target file name layout contains no unexpected space bars or double extensions. Your active file structure requires lowercase, standard syntax naming rules.

⚡ Pro Automation: The One-Line Mirror Command

If you want to completely skip dragging and dropping individual files through your file manager, you can use this lightning-fast terminal syncing script inside your terminal. It will instantly wipe, mirror, and synchronize your entire workspace folder structure in a split second:

rsync -av --delete --exclude='.git/' --exclude='.github/' /home/johnpc/path/to/your/primary/AfridyneSystems/ /mnt/sdb/AfridyneSystems/

🎛️ MaterialX Environment Layout Matrix⚓︎

Core Dependency Engine (requirements.txt)

This matrix tracks the lean, high-speed documentation compilation engine running on your system. It is stripped of all local Linux system bloat to prevent GitHub Actions runner crashes.

📦 The 10 Core Packages🔌 Advanced Layout Extensions

Package Name	Purpose / Functionality	Role in Ecosystem
`mkdocs-materialx==10.1.8`	Primary Theme Fork	Handles total layout rendering & modern UI
`mkdocs==1.6.1`	Base Framework	Core static site engine
`markdown==3.10.2`	Core Processor	Converts raw `.md` files into valid web pages
`jinja2`	Template Engine	Generates underlying HTML document patterns
`pymdown-extensions`	Markdown Extras	Supercharges text formatting (Icons, Admonitions)
`mkdocs-document-dates`	Metadata Automation	Automatically extracts page modification times
`mkdocs-include-markdown-plugin`	Page Inheritance	Allows nesting markdown documents inside other pages
`mkdocs-autorefs`	Cross-Linking	Resolves linking conflicts across subfolders automatically
`mkdocstrings`	Code Documentation	Automatically formats programmatic structures
`pymdown-multimd-table`	Complex Matrixes	Renders advanced rows and custom table spacing

mkdocs-click                 # Compiles command-line text layouts and interactive code help blocks
mkdocs-rss-plugin            # Generates dynamic syndication feeds for your Blog index layout
mkdocs-table-reader-plugin   # Dynamically imports live CSV/Excel data arrays onto pages
mkdocs-glightbox             # Image zoom overlay lightbox system for pictures
markdown-exec                # Enables code execution blocks natively inside documentation pages
mkdocs-section-index         # Transforms static folder drop-downs into active, clickable index links
mkdocs-open-in-new-tab       # Forces external links to process securely in a fresh browser page
mkdocs-schema-reader         # Structured data data injector for optimized web visibility
mkdocs-caption               # Automates numeric labeling for your images and figures
pillow                       # Python image manipulation pipeline needed for dynamic asset building
cairosvg                     # Specialized asset vector compiler for rendering icons

Critical Enforcement Rule

NEVER run a blanket global pip freeze > requirements.txt command inside this repository directory. Doing so will dump your local Arch Linux system utilities back into the file and instantly break the automated GitHub runner again!

🎨 MaterialX Content Formatting & Grid Card Blocks⚓︎

Component Library

Use these pre-formatted snippets inside your Markdown files to build visually stunning layouts with modern grid frameworks and interactive cards.

🎴 Responsive Grid Cards💡 Custom Admonition Variants🎨 Inline Text Magic

### 🛠️ Core Project Frameworks

<div class="grid cards" markdown>

-   :material-language-markdown:{ .lg .middle } __Markdown Engine__

    ---

    Clean, highly formatted documentation layout utilizing standard theme
    structures.

    [:octicons-arrow-right-24: Open Workspace Component](#)

-   :material-github:{ .lg .middle } __Automated Deployments__

    ---

    Powered natively by `uv` and high-speed cloud build compilation runners.

    [:octicons-arrow-right-24: Check Actions Log](https://github.com)

-   :material-magnify:{ .lg .middle } __Precious Icon Search__

    ---

    Seamless interactive local indexing engine with deeply optimized search path
    layers.

    [:octicons-arrow-right-24: Open Finder Control](#)

</div>

!!! danger "System Failure Point (Red Highlight)"
    This block indicates critical pipeline errors, broken dependency names, or unresolvable path flags.

!!! warning "General Warning (Orange Highlight)"
    Use this specific container variant to document just about any warning or alert to potential pitfalls in your code.  

!!! bug "Visual or Syntax Mismatch (Red Highlight)"
    Use this specific container variant to document trailing file-extension typos or formatting glitches.

!!! quote "System Verbatim Output (Grey Border Accent)"
    Perfect for framing exact code responses or tracebacks directly from terminal log dumps.

* Add crisp keyboard shortcut styling tags: ++ctrl+alt+del++
* Apply clean colored badges to text segments: Deletions look red and
  Insertions look green
* Utilize precise inline styling markers: `#!yaml nav:` { .annotate }

✍️ MaterialX Blog Post & Metadata Blueprint⚓︎

Blog Optimization Engine

MaterialX compiles blog pages using a highly specialized Front Matter configuration block. By declaring explicit keys (like authors, dates, and categories) inside the top dashed lines ---, the theme automatically structures your layouts, generates summary snippets, and links tag archives.

📝 Fresh Post Template👥 Global Authors Profile Configuration🎨 Blog Accent UI Components

---
title: Modern System Synchronization Architectures
description: A deep-dive exploration into aligning multi-leg local storage
             environments with automated cloud compilation builders.
date: 2026-06-26
authors: [johnpiers]
categories:
  - Infrastructure
  - Git Operations
tags:
  - MaterialX
  - Environment Sync
  - Terminal Automation
---

# Modern System Synchronization Architectures

When dealing with separate development environments, maintaining a strict tracking
rhythm is paramount. Today we take a look at stabilizing active project trunks.

<!-- more -->

Everything written below this explicit divider line acts as the main content body.
Everything above it serves as the short summary text card displayed directly on
your primary blog index page index layout!

### Key Discoveries
* High-speed `uv` deployment execution cuts processing limits down instantly.
* Modular requirements tracking isolates native system utilities completely.

To keep your post headers clean without typing out your full bio every time, place this structure directly inside your main project configuration file mkdocs.yml under the active blog section:

plugins:
  - blog:
      authors:
        johnpiers:
          name: John Piers
          description: Chief Systems Architect & Lead Platform Developer
          avatar: https://github.com
          url: https://github.com

### 🏷️ Content Tag Badges
Inject custom color accents directly into your blog inline paragraphs:
* Highlight active code blocks: [MaterialX]{ .md-tag }
* Highlight stable state releases: [v10.1.7]{ .md-tag .md-tag--green }
* Highlight alert conditions: [Critical System Phase]{ .md-tag .md-tag--red }

### 📌 Custom Sidebar Callouts
```yaml
# To change how your archive sidebars render, tweak these flags in mkdocs.yml
plugins:
  - blog:
      archive_format: MMMM YYYY  # Displays "June 2026" instead of "2026/06"
      pagination_per_page: 5     # Keeps your scroll heights tightly compact
      categories_allowed: true   # Activates the structural grouping layout

⚡ MaterialX Native Interactive Hover Previews (Rich Tooltips)⚓︎

The Native Preview System

No extra Python packages are required! MaterialX features built-in Rich Tooltips that automatically turn standard Markdown page links and anchor tags into beautiful interactive hover popup cards site-wide.

⚙️ Global Configuration (mkdocs.yml)🔗 Writing Scannable Links💡 Manual Annotations Feature

Add the content.tooltips feature flag directly inside your main theme settings block to turn on hover previews globally:

theme:
  name: materialx
  features:
    - content.tooltips  # <-- Add this line to activate automatic hover cards

Write standard, natural Markdown links. The native theme engine automatically scans the target page's title and top text blocks to render the popup layout:

Make sure to activate your tracking parameters inside the core configuration
file. 
You can easily verify the active nesting boundaries using the site's [SuperFences]
(#) module architecture.

* Links targeting section headers work perfectly too: [Check Table Settings](#)

To append numbered, clickable dropdown comment buttons directly inside code blocks (like the screen snippet markers), ensure pymdownx.superfences is turned on under your markdown extensions list:

```yaml
nav:
  - blog/ # (1)

This special notation marker instructs the theme engine to compile folder structures as dynamic blogs.
```

Click To See Code for Table below

| Right oriented rendering |
|-------------------------:|
| 150.0                    |
| or text                  |

Right oriented rendering
150.0
or text

Click To See Code for Table below

| Left oriented rendering |
| :---------------------- |
| 150.0                   |
| or text                 |

Left oriented rendering
150.0
or text

Click To See Code for Table below

| Centered rendering |
| :----------------: |
|       150.0        |
|      or text       |

Centered rendering
150.0
or text

Ref: GreyStone Theme⚓︎

Reference: Fixing Broken/Tiny Nautilus Sidebar Icons (GreyStone Theme)

Issue Description⚓︎

Issue Description

Modern GNOME/Nautilus (GTK4) requires specific symbolic variants (-symbolic.svg) to render sidebar icons properly. If these SVGs are malformed, misconfigured internally, or missing standard dimensions, GNOME fails to scale them, resulting in tiny dots or generic placeholders for folders like Documents, Pictures, and Videos.

Solution⚓︎

Solution

Override the faulty theme icons by symlinking standard, dark-optimized symbolic folder assets from the upstream dependency (Papirus) directly into the active theme paths, then refresh the system icon cache.

(Optional) Audit the theme's internal symbolic folder inventory

find ~/.local/share/icons/GreyStone/ -name "*symbolic.svg" | grep -i "folder"

Create a backup subdirectory for the broken SVGs

mkdir -p ~/.local/share/icons/GreyStone/places/symbolic/backup

Move the faulty symbolic folder icons into the backup folder

mv ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/
mv ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/
mv ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/

Symlink working symbolic icons from Papirus to override GreyStone's versions

ln -s /usr/share/icons/Papirus/scalable/places/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg

Rebuild the GTK icon cache to force system recognition:

gtk-update-icon-cache -f ~/.local/share/icons/GreyStone/

Kill all active Nautilus processes to force a clean GUI reload:
```
nautilus -q
```

Now you have a permanent blueprint saved whenever an icon update reverts your changes! Let me know if you want help generating:

A quick automated Bash script variant of this code that you can execute in one click.
Custom MaterialX admonition tags (like notes or warnings) to make this log pop out visually on your site.

Sidebar Icon Fix

Override faulty theme icons by symlinking dark-optimized symbolic folder assets from Papirus directly into active theme paths.

Step-by-Step GuideQuick One-Liner ScriptFresh Install Blueprint

(Optional) Audit the theme's internal symbolic folder inventory:

find ~/.local/share/icons/GreyStone/ -name "*symbolic.svg" | grep -i "folder"

Create a backup subdirectory for the broken SVGs:

mkdir -p ~/.local/share/icons/GreyStone/places/symbolic/backup

Move the faulty symbolic folder icons into the backup folder:

mv ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/
mv ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/
mv ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/

Symlink working symbolic icons from Papirus:

ln -s /usr/share/icons/Papirus/scalable/places/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg

Rebuild the GTK icon cache:

gtk-update-icon-cache -f ~/.local/share/icons/GreyStone/

Kill all active Nautilus processes to force a clean GUI reload:
```
nautilus -q
```

mkdir -p ~/.local/share/icons/GreyStone/places/symbolic/backup && \
mv ~/.local/share/icons/GreyStone/places/symbolic/folder-{documents,pictures,videos}-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/ 2>/dev/null; \
ln -s /usr/share/icons/Papirus/scalable/places/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg && \
ln -s /usr/share/icons/Papirus/scalable/places/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg && \
ln -s /usr/share/icons/Papirus/scalable/places/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg && \
gtk-update-icon-cache -f ~/.local/share/icons/GreyStone/ && \
nautilus -q

# 1. Download and extract the latest repository directly to the local icons folder
mkdir -p ~/.local/share/icons
curl -L https://github.com | tar -xz -C ~/.local/share/icons/
mv ~/.local/share/icons/GreyStone-main ~/.local/share/icons/GreyStone

# 2. Apply the missing symbolic folder fixes from Papirus
mkdir -p ~/.local/share/icons/GreyStone/places/symbolic/backup
mv ~/.local/share/icons/GreyStone/places/symbolic/folder-{documents,pictures,videos}-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/ 2>/dev/null
ln -s /usr/share/icons/Papirus/scalable/places/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg

# 3. Clear caches and reload Nautilus
gtk-update-icon-cache -f ~/.local/share/icons/GreyStone/
nautilus -q

Manual Installation⚓︎

Fresh Manual Installation Blueprint

If migrating to a new machine or rebuilding the local environment, fetch the repo directly and apply the symlink fixes in one go:

Download and extract the latest repository directly to the local icons folder

mkdir -p ~/.local/share/icons
curl -L https://github.com | tar -xz -C ~/.local/share/icons/
mv ~/.local/share/icons/GreyStone-main ~/.local/share/icons/GreyStone

Apply the missing symbolic folder fixes from Papirus

mkdir -p ~/.local/share/icons/GreyStone/places/symbolic/backup

mv ~/.local/share/icons/GreyStone/places/symbolic/folder-{documents,pictures,videos}-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/backup/ 2>/dev/null

ln -s /usr/share/icons/Papirus/scalable/places/folder-documents-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-documents-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-pictures-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-pictures-symbolic.svg
ln -s /usr/share/icons/Papirus/scalable/places/folder-videos-symbolic.svg ~/.local/share/icons/GreyStone/places/symbolic/folder-videos-symbolic.svg

Clear caches and reload Nautilus

gtk-update-icon-cache -f ~/.local/share/icons/GreyStone/

nautilus -q

Renaming a .md File⚓︎

General Pattern Renaming a .md file

This is the general pattern for any "rename a file safely" job: find → read → search for references → confirm real vs. false matches → rename → fix references → test locally → deploy.

Step 1. Finding a .md File

Find where a suspicious file actually lives

find /home/johnpc/AfridyneSystems/docs -iname contributing.md

Step 2.

See what's inside it, to understand what it actually is:

cat /home/johnpc/AfridyneSystems/docs/CONTRIBUTING.md

Step 3.

Check if anything references it by name, anywhere in the site:

grep -rln "CONTRIBUTING.md" /home/johnpc/AfridyneSystems/docs/ /home/johnpc/AfridyneSystems/mkdocs.yml

Step 4.

Look at the exact lines matched, not just filenames — separates real links from unrelated mentions

grep -n "CONTRIBUTING.md" /home/johnpc/AfridyneSystems/docs/ALPM.md /home/johnpc/AfridyneSystems/mkdocs.yml

Step 5.

Rename the file itself:

mv "/home/johnpc/AfridyneSystems/docs/CONTRIBUTING.md" "/home/johnpc/AfridyneSystems/docs/ALPM-Contributing.md"

Step 6.

Fix every real reference to match the new name:

sed -i 's/CONTRIBUTING\.md/ALPM-Contributing.md/g' /home/johnpc/AfridyneSystems/docs/ALPM.md

Step 7.

sed -i 's/^  CONTRIBUTING.md$/  ALPM-Contributing.md/' /home/johnpc/AfridyneSystems/mkdocs.yml

Step 8.

Verify locally before trusting it

mkdocs serve --clean

Then manually click through the affected link in the browser

Deploy for real, once confirmed clean

cd ~/Deploy && ./deploy.sh

graph TD
A["Sagittarius A* (supermassive black hole)"] --> B["Orbit of Star S62"]
B --> C["Periapsis (closest approach): 17.8 AU\n(AU = Astronomical Units, 1 AU ≈ Earth-Sun distance)"]
B --> D["Apoapsis (farthest distance): 1,462.2 AU\n(AU = Astronomical Units, 1 AU ≈ Earth-Sun distance)"]
style A fill:#7a7878,stroke:#948686,stroke-width:4px
style B fill:#4d6aa1,stroke:#747474,stroke-width:2px
style C fill:#f05b5b,stroke:#000,stroke-width:2px
style D fill:#4d964d,stroke:#000,stroke-width:2px

M-Theory: The Mother of all SuperStrings

M-Theory & Matrix Theory Foundations⚓︎

M-Theory & Matrix Theory Foundations

M-Theory is the unifying framework of all five consistent ten-dimensional superstring theories and eleven-dimensional supergravity, linked by dualities like S-duality and T-duality, with low-energy dynamics governed by 11-dimensional supergravity and fundamental excitations including 2-branes and 5-branes.

11-Dimensional Supergravity Action⚓︎

11-Dimensional Supergravity Action
The low-energy effective field theory of M-theory is 11-dimensional supergravity. Its bosonic sector includes the metric $g_{\mu\nu}$ and a 3-form gauge field $C_3$ with a 4-form field strength $G_4 = dC_3$.

\[\color{#4da6ff}{S_{11}} = \frac{1}{2\kappa_{11}^2} \int d^{11}x \sqrt{-g} \left( \color{#ff6666}{R} - \frac{1}{2} |\color{#ffcc00}{G_4}|^2 \right) - \frac{1}{6} \int \color{#33cc33}{C_3} \wedge \color{#ffcc00}{G_4} \wedge \color{#ffcc00}{G_4}\]

Where:
* $\color{#4da6ff}{S_{11}}$ is the 11D Supergravity Action.
* $\color{#ff6666}{R}$ is the Ricci scalar curvature.
* $\color{#ffcc00}{G_4}$ is the 4-form field strength defined as $\color{#ffcc00}{G_4} = d\color{#33cc33}{C_3}$.
* $\color{#33cc33}{C_3}$ is the 3-form gauge potential.

Brane Tensions⚓︎

Brane Tensions

M-theory contains dynamical extended objects called branes. The fundamental membrane is the M2-brane, and its magnetic dual is the M5-brane. Their tensions depend on the 11D Planck length $l_p$:

M2-Brane Tension:
$\color{#ffb366}{T_{M2}} = \frac{1}{(2\pi)^2 \color{#cc99ff}{l_p}^3}$
M5-Brane Tension:
$\color{#ff80df}{T_{M5}} = \frac{1}{(2\pi)^5 \color{#cc99ff}{l_p}^6}$

Compactification to Type IIA String Theory⚓︎

Compactification to Type IIA String Theory

Compactifying M-theory on a circle $S^1$ of radius $R_{10} = g_s l_s$ yields Type IIA string theory. The 11D metric splits into the 10D metric $g_{\mu\nu}^{(10)}$, a graviphoton gauge field $A_\mu$, and the dilaton $\phi$:

\[ds_{11}^2 = e^{-2\color{#00fa9a}{\phi}/3} g_{\mu\nu}^{(10)} dx^\mu dx^\nu + e^{4\color{#00fa9a}{\phi}/3} \left( dx^{10} + A_\mu dx^\mu \right)^2\]

The string coupling constant $\color{#e0cda9}{g_s}$ is directly related to the radius of the 11^th dimension:

\[\color{#e0cda9}{g_s} = e^{\langle \color{#00fa9a}{\phi} \rangle} = \left( \frac{R_{10}}{l_s} \right)^{3/2}\]

Matrix Theory (BFSS Model) Formulations⚓︎

Matrix Theory (BFSS Model) Formulations

The BFSS Matrix Theory describes M-theory in the infinite momentum frame as the quantum mechanics of $N \times N$ Hermitian matrices. The variables are nine spatial matrices $\color{#20b2aa}{X^i}$ ($i=1, \dots, 9$) and their fermionic superpartners $\color{#dda0dd}{\Psi}$.

BFSS Matrix Model Lagrangian:
$\color{#ee82ee}{L} = \text{Tr} \left( \frac{1}{2R}\sum_{i=1}^9 \color{#4da6ff}{\dot{X}^i}^2 + \frac{R}{4} \sum_{i,j=1}^9 [\color{#20b2aa}{X^i}, \color{#20b2aa}{X^j}]^2 + i \color{#dda0dd}{\Psi}^T \color{#4da6ff}{\dot{\Psi}} - R\color{#dda0dd}{\Psi}^T \sum_{i=1}^9 \gamma_i [\color{#20b2aa}{X^i}, \color{#dda0dd}{\Psi}] \right)$
Gauss Constraint (Matrix Gauge Invariance):
$\sum_{i=1}^9 [\color{#20b2aa}{X^i}, \color{#4da6ff}{\dot{X}^i}] - \frac{i}{2} \{\color{#dda0dd}{\Psi}, \color{#dda0dd}{\Psi}^T\} = \color{#ff6666}{0}$
Supersymmetry Generators (Supercharges):
$\color{#ffb366}{Q} = \text{Tr} \left( \sum_{i=1}^9 \color{#4da6ff}{\dot{X}^i} \gamma_i \color{#dda0dd}{\Psi} + \frac{i}{2} \sum_{i,j=1}^9 [\color{#20b2aa}{X^i}, \color{#20b2aa}{X^j}] \gamma_{ij} \color{#dda0dd}{\Psi} \right)$

IKKT Matrix Model (Type IIB Matrix Theory)

IKKT Matrix Model (Type IIB Matrix Theory)⚓︎

IKKT Matrix Model (Type IIB Matrix Theory)

The IKKT Matrix Model (Ishibashi, Kawai, Kitazawa, and Tsuchiya) is a non-perturbative formulation of Type IIB Superstring Theory, providing a dual perspective to the BFSS model (which describes M-Theory). Unlike the quantum-mechanical BFSS model, IKKT is a zero-dimensional matrix model (a reduced regularized field theory) where spacetime coordinates themselves emerge dynamically from eigenvalues of large $N \times N$ matrices.

The IKKT Action⚓︎

The IKKT Action

The action is highly symmetric and beautifully compact, composed of a bosonic commutator term and a fermionic inner product:

\[\color{#4da6ff}{S_{\text{IKKT}}} = -\frac{1}{4g^2} \text{Tr} \left( \sum_{\mu,\nu=0}^9 [\color{#20b2aa}{A_\mu}, \color{#20b2aa}{A_\nu}]^2 \right) - \frac{1}{2g^2} \text{Tr} \left( \color{#dda0dd}{\bar{\Psi}} \sum_{\mu=0}^9 \Gamma^\mu [\color{#20b2aa}{A_\mu}, \color{#dda0dd}{\Psi}] \right)\]

Where:
* $\color{#4da6ff}{S_{\text{IKKT}}}$ is the total Euclidean or Lorentzian IKKT action.
* $\color{#20b2aa}{A_\mu}$ represents ten $N \times N$ Hermitian matrices ($\mu = 0, \dots, 9$) representing spacetime points.
* $\color{#dda0dd}{\Psi}$ is a 10D Majorana-Weyl fermionic matrix superpartner.
* $g$ is the matrix coupling constant.

Relationship and Duality to BFSS (M-Theory)⚓︎

Relationship and Duality to BFSS (M-Theory)

The IKKT model can be directly related to the BFSS model derived previously via dimensional reduction and regularization:

Dimensional Reduction: By recovering time dependence, the BFSS model's Lagrangian can be seen as a 1D version of the 0D IKKT structure.
The T-Duality Link: While the BFSS model computes the discrete lightcone quantization of M-Theory (Type IIA limit), IKKT represents the configuration space of Type IIB string theory via a lattice-free matrix regularization of the worldsheet action.

Equations of Motion⚓︎

Equations of Motion

Varying the IKKT action with respect to the bosonic coordinates yields the classical matrix field equations:

\[\sum_{\nu=0}^9 [\color{#20b2aa}{A^\nu}, [\color{#20b2aa}{A_\mu}, \color{#20b2aa}{A_\nu}]] + \frac{1}{2} \{\color{#dda0dd}{\bar{\Psi}}, \Gamma_\mu \color{#dda0dd}{\Psi}\} = \color{#ff6666}{0}\]

Deep Dive: BFSS & IKKT Matrix Formulations

BFSS & IKKT Matrix Formulations⚓︎

1. The BFSS Model (M-Theory in Lightcone Gauge)⚓︎

1. The BFSS Model (M-Theory in Lightcone Gauge)

The BFSS model establishes that the non-perturbative degrees of freedom of M-theory are uncompactified $D0$-branes. In the infinite momentum frame ($P^+ \to \infty$), the theory reduces to a $U(N)$ Super Yang-Mills quantum mechanics in $1+0$ dimensions.

The Complete BFSS Hamiltonian⚓︎

The Complete BFSS Hamiltonian

Derived from the matrix Lagrangian via Legendre transformation, the quantum mechanical Hamiltonian governs the dynamics of nine $N \times N$ spatial matrices $\color{#20b2aa}{X^i}$ and their canonical conjugate momenta $\color{#4da6ff}{P^i} = \frac{1}{R}\dot{X}^i$:

\[\color{#ee82ee}{H_{\text{BFSS}}} = R \;\text{Tr} \left( \frac{1}{2} \sum_{i=1}^9 (\color{#4da6ff}{P^i})^2 - \frac{1}{4} \sum_{i,j=1}^9 [\color{#20b2aa}{X^i}, \color{#20b2aa}{X^j}]^2 + \color{#dda0dd}{\bar{\Psi}} \sum_{i=1}^9 \gamma_i [\color{#20b2aa}{X^i}, \color{#dda0dd}{\Psi}] \right)\]

Large-$N$ Limit and Continuous Membrane Emergence⚓︎

Large-$N$ Limit and Continuous Membrane Emergence

In the $N \to \infty$ limit, the discrete matrix commutators map to continuous Poisson brackets on a 2-dimensional worldvolume topology $\Sigma$ (the M2-brane membrane configuration):

\[\lim_{N \to \infty} (-iN) [\color{#20b2aa}{X^i}, \color{#20b2aa}{X^j}] = \{\color{#20b2aa}{X^i}(\sigma_1, \sigma_2), \color{#20b2aa}{X^j}(\sigma_1, \sigma_2)\}_{\text{P.B.}} = \frac{\partial \color{#20b2aa}{X^i}}{\partial \sigma_1}\frac{\partial \color{#20b2aa}{X^j}}{\partial \sigma_2} - \frac{\partial \color{#20b2aa}{X^i}}{\partial \sigma_2}\frac{\partial \color{#20b2aa}{X^j}}{\partial \sigma_1}\]

2. The IKKT Model (Emergent Spacetime & Type IIB)⚓︎

2. The IKKT Model (Emergent Spacetime & Type IIB)

Unlike BFSS, the IKKT model lacks a fundamental time parameter. It is a strictly 0-dimensional statistical/quantum mechanical system where time and space emerge on equal footing from the eigenvalue distributions of the matrices.

Lorentzian vs. Euclidean Action Signatures⚓︎

Lorentzian vs. Euclidean Action Signatures

The path integral behavior changes drastically depending on the chosen global metric signature. The structural transformation is governed by the switch in the bosonic commutator footprint:

Euclidean Signature Action ($A_0 \to iA_{10}$):
$\color{#4da6ff}{S_{\text{E}}} = -\frac{1}{g^2} \text{Tr} \left( \frac{1}{4} \sum_{\mu,\nu=1}^{10} [\color{#20b2aa}{A_\mu}, \color{#20b2aa}{A_\nu}]^2 + \frac{1}{2} \color{#dda0dd}{\bar{\Psi}} \sum_{\mu=1}^{10} \Gamma^\mu [\color{#20b2aa}{A_\mu}, \color{#dda0dd}{\Psi}] \right)$
Lorentzian Signature Action (Physical Spacetime):
$\color{#4da6ff}{S_{\text{L}}} = \frac{1}{g^2} \text{Tr} \left( -\frac{1}{2} [\color{#20b2aa}{A_0}, \color{#20b2aa}{A_i}]^2 + \frac{1}{4} [\color{#20b2aa}{A_i}, \color{#20b2aa}{A_j}]^2 + \frac{1}{2} \color{#dda0dd}{\bar{\Psi}} \Gamma^0 [\color{#20b2aa}{A_0}, \color{#dda0dd}{\Psi}] + \frac{1}{2} \color{#dda0dd}{\bar{\Psi}} \sum_{i=1}^9 \Gamma^i [\color{#20b2aa}{X^i}, \color{#dda0dd}{\Psi}] \right)$

Extraction of the Emergent Spacetime Metric⚓︎

Extraction of the Emergent Spacetime Metric

Smooth geometric space manifests by analyzing the expectation values of the matrix blocks. An effective local spacetime metric $\color{#ff6666}{g_{\mu\nu}(x)}$ is extracted using the non-commutative coordinates defined by the components of $\color{#20b2aa}{A_\mu}$:

\[\color{#ff6666}{g^{\mu\nu}(x)} \sim \lim_{N \to \infty} \left\langle \frac{1}{N} \text{Tr} \left( \phi(x) [\color{#20b2aa}{A^\mu}, \color{#20b2aa}{A_\lambda}][\color{#20b2aa}{A^\nu}, \color{#20b2aa}{A^\lambda}] \right) \right\rangle\]

Where $\phi(x)$ is a localized state checking scale structures in the matrix eigenvalue space.

3. Gauge Invariant Observables (Wilson Loops)⚓︎

3. Gauge Invariant Observables (Wilson Loops)

To probe physical geometry and find graviton scattering states without referencing coordinate frames, gauge-invariant operators must be mapped out.

The primary non-local observable in IKKT is the generalized Wilson Loop, defined via an exponentiated source field $k^\mu$:

\[\color{#ffcc00}{W(k)} = \text{Tr} \left( \exp \left( i \sum_{\mu=0}^9 \color{#ffb366}{k^\mu} \color{#20b2aa}{A_\mu} \right) \right)\]

In the continuum limit, expanding $\color{#ffcc00}{W(k)}$ in powers of $\color{#ffb366}{k^\mu}$ yields a complete set of local operators corresponding to off-shell supergravity fields, establishing the exact link back to 10D and 11D effective field actions.

M-Theory & Matrix Theory Foundations

M-Theory & Matrix Theory Foundations⚓︎

M-Theory & Matrix Theory Foundations

11-Dimensional Supergravity Action⚓︎

11-Dimensional Supergravity Action

The low-energy effective field theory of M-theory is 11-dimensional supergravity. Its bosonic sector includes the metric $\color{#20b2aa}{g_{\mu\nu}}$ and a 3-form gauge field $\color{#33cc33}{C_3}$ with a 4-form field strength $\color{#ffcc00}{G_4} = d\color{#33cc33}{C_3}$.

\[\begin{flalign*} \color{#4da6ff}{S_{11}} = \frac{1}{2\kappa_{11}^2} \int d^{11}x \sqrt{-g} \left( \color{#ff6666}{R} - \frac{1}{2} |\color{#ffcc00}{G_4}|^2 \right) - \frac{1}{6} \int \color{#33cc33}{C_3} \wedge \color{#ffcc00}{G_4} \wedge \color{#ffcc00}{G_4} && \end{flalign*}\]

Where:
* Action: $\color{#4da6ff}{S_{11}}$ is the 11D Supergravity Action.
* Curvature: $\color{#ff6666}{R}$ is the Ricci scalar curvature.
* Field Strength: $\color{#ffcc00}{G_4}$ is the 4-form field strength defined as $\color{#ffcc00}{G_4} = d\color{#33cc33}{C_3}$.
* Potential: $\color{#33cc33}{C_3}$ is the 3-form gauge potential.

Brane Tensions⚓︎

Brane Tensions

M-theory contains dynamical extended objects called branes. The fundamental membrane is the M2-brane, and its magnetic dual is the M5-brane. Their tensions depend on the 11D Planck length $\color{#cc99ff}{l_p}$:

M2-Brane Tension:

\[\begin{flalign*} \color{#ffb366}{T_{M2}} = \frac{1}{(2\pi)^2 \color{#cc99ff}{l_p}^3} && \end{flalign*}\]

M5-Brane Tension:

\[\begin{flalign*} \color{#ff80df}{T_{M5}} = \frac{1}{(2\pi)^5 \color{#cc99ff}{l_p}^6} && \end{flalign*}\]

Compactification to Type IIA String Theory⚓︎

Compactification to Type IIA String Theory

Compactifying M-theory on a circle $\color{#f08c00}{S^1}$ of radius $\color{#f08c00}{R_{10}} = \color{#e0cda9}{g_s} \color{#cc99ff}{l_s}$ yields Type IIA string theory. The 11D metric splits into the 10D metric $\color{#20b2aa}{g_{\mu\nu}^{(10)}}$, a graviphoton gauge field $\color{#4da6ff}{A_\mu}$, and the dilaton $\color{#00fa9a}{\phi}$:

\[\begin{flalign*} ds_{11}^2 = e^{-2\color{#00fa9a}{\phi}/3} g_{\mu\nu}^{(10)} dx^\mu dx^\nu + e^{4\color{#00fa9a}{\phi}/3} \left( dx^{10} + A_\mu dx^\mu \right)^2 && \end{flalign*}\]

The string coupling constant $\color{#e0cda9}{g_s}$ is directly related to the radius of the 11^th dimension:

\[\begin{flalign*} \color{#e0cda9}{g_s} = e^{\langle \color{#00fa9a}{\phi} \rangle} = \left( \frac{R_{10}}{l_s} \right)^{3/2} && \end{flalign*}\]

Matrix Theory (BFSS Model) Formulations⚓︎

Matrix Theory (BFSS Model) Formulations

BFSS Matrix Model Lagrangian:

$\color{#ee82ee}{L} = \text{Tr} \left( \frac{1}{2R}\sum_{i=1}^9 \color{#4da6ff}{\dot{X}^i}^2 + \frac{R}{4} \sum_{i,j=1}^9 [\color{#20b2aa}{X^i}, \color{#20b2aa}{X^j}]^2 + i \color{#dda0dd}{\Psi}^T \color{#4da6ff}{\dot{\Psi}} - R\color{#dda0dd}{\Psi}^T \sum_{i=1}^9 \gamma_i [\color{#20b2aa}{X^i}, \color{#dda0dd}{\Psi}] \right)$

Gauss Constraint (Matrix Gauge Invariance):

\[\begin{flalign*} \color{#ee82ee}\sum_{i=1}^9 [\color{#20b2aa}{X^i}, \color{#4da6ff}{\dot{X}^i}] - \frac{i}{2} \{\color{#dda0dd}{\Psi}, \color{#dda0dd}{\Psi}^T\} = \color{#ff6666}{0} && \end{flalign*}\]

Supersymmetry Generators (Supercharges):

\[\begin{flalign*} \color{#ffb366}{Q} = \text{Tr} \left( \sum_{i=1}^9 \color{#4da6ff}{\dot{X}^i} \gamma_i \color{#dda0dd}{\Psi} + \frac{i}{2} \sum_{i,j=1}^9 [\color{#20b2aa}{X^i}, \color{#20b2aa}{X^j}] \gamma_{ij} \color{#dda0dd}{\Psi} \right) && \end{flalign*}\]

IKKT Matrix Model (Type IIB Matrix Theory)

IKKT Matrix Model (Type IIB Theory⚓︎

The IKKT Matrix Model (Ishibashi, Kawai, Kitazawa, and Tsuchiya) is a non-perturbative formulation of Type IIB Superstring Theory, providing a dual perspective to the BFSS model (which describes M-Theory). Unlike the quantum-mechanical BFSS model, IKKT is a zero-dimensional matrix model where spacetime coordinates themselves emerge dynamically from eigenvalues of large $N \times N$ matrices.

The IKKT Action⚓︎

The IKKT Action

The action is composed of a bosonic commutator term and a fermionic inner product:

Where:
* Action: $\color{#4da6ff}{S_{\text{IKKT}}}$ is the total Euclidean or Lorentzian IKKT action.
* Coordinates: $\color{#20b2aa}{A_\mu}$ represents ten $N \times N$ Hermitian matrices ($\mu = 0, \dots, 9$) representing spacetime points.
* Fermions: $\color{#dda0dd}{\Psi}$ is a 10D Majorana-Weyl fermionic matrix superpartner.
* Coupling: $g$ is the matrix coupling constant.

Relationship and Duality to BFSS (M-Theory)⚓︎

Relationship and Duality to BFSS (M-Theory)
The IKKT model can be directly related to the BFSS model derived previously via dimensional reduction and regularization:
* Dimensional Reduction: By recovering time dependence, the BFSS model's Lagrangian can be seen as a 1D version of the 0D IKKT structure.
* The T-Duality Link: While the BFSS model computes the discrete lightcone quantization of M-Theory (Type IIA limit), IKKT represents the configuration space of Type IIB string theory via a lattice-free matrix regularization of the worldsheet action.

Equations of Motion⚓︎

Equations of Motion

Varying the IKKT action with respect to the bosonic coordinates yields the classical matrix field equations:

\[\sum_{\nu=0}^9 [\color{#20b2aa}{A^\nu}, [\color{#20b2aa}{A_\mu}, \color{#20b2aa}{A_\nu}]] + \frac{1}{2} \{\color{#dda0dd}{\bar{\Psi}}, \Gamma_\mu \color{#dda0dd}{\Psi}\} = \color{#ff6666}{0}\]

Hover rows⚓︎

Add .table-hover to enable a hover state on table rows within a <tbody>.

#	First Name	Last Name	Username
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2	Jacob	Thornton	@fat
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Sublime Text 4 Build 4215⚓︎

Build 4215

Sublime Text 4 Build 4215 can be patched using hex modifications widely documented in GitHub Gists, as shared license keys are frequently blocked by network verification.

Update / Install Build 4215 on Arch Linux

Add GPG Key

curl -O https://download.sublimetext.com/sublimehq-pub.gpg && sudo pacman-key --add sublimehq-pub.gpg && sudo pacman-key --lsign-key 8A8F901A && rm sublimehq-pub.gpg

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echo -e "\n[sublime-text]\nServer = https://download.sublimetext.com/arch/stable/x86_64" | sudo tee -a /etc/pacman.conf

Synchronize and update

sudo pacman -Syu sublime-text

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Alternative: Multi-Build Method (Gsed)

If your environment lacks an initialized perl runtime profile, you can accomplish the exact same binary adjustment using sed matching the build 4215 specific array offset:

sudo sed -i 's/\x0f\xb6\x51\x0c\x83\xf2\x01/\xc6\x41\x0c\x01\x31\xd2\x90/g' /opt/sublime_text/sublime_text

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