Low 37 Bitcoin Committed Jun 8, 2026 · 17:12 UTC
docs: self-host math, remove MathJax/require.js CDN

492820a1 View source ↗
Public commit record
What the developer wrote

Authored by odudex
90/100 · Strong
docs: self-host math, remove MathJax/require.js CDN

Pre-render the entropy page display equations to committed SVGs and
write inline math as plain HTML, removing the cdnjs MathJax and
require.js loads (same supply chain class as the polyfill.io incident).
render_docs_math.py regenerates the SVGs from the markdown. Also ignore
mkdocs (public/) and pytest-cov (htmlcov/) build output.
✓ Specific, descriptive subject✓ Names a concrete action or component✓ Uses a recognizable type or scope✓ Provides detailed explanatory context✓ Names security-relevant behavior explicitly
The short version
What changed, and why it matters

This change removes third-party web scripts (MathJax and require.js loaded from a content delivery network) from the project's documentation and replaces them with self-hosted, pre-rendered math images. That eliminates a supply-chain risk similar to the polyfill.io incident, where a compromised or malicious CDN could inject harmful code into documentation pages viewed by users or developers.
Recommended action
Verify that mkdocs.yml no longer references MathJax or require.js CDN URLs, confirm the generated SVGs are committed and render correctly, and ensure render_docs_math.py is run as part of the documentation build process so math stays in sync. Consider pinning any remaining documentation dependencies.
Security signals we found

Removal of cdnjs MathJax and require.js external script loads
Self-hosting of rendered math assets as static SVGs
Explicit commit message reference to supply-chain class (polyfill.io incident)
Addition of build-output directories to .gitignore (hygiene, not a security fix)
Technical analysis
Evidence from the diff

The commit replaces CDN-hosted MathJax/require.js rendering in the MkDocs documentation with static SVGs generated by a new render_docs_math.py script and inline HTML for simple math. It also adds public/ and htmlcov/ to .gitignore. The security relevance is the removal of external script dependencies, which closes a supply-chain attack vector where a compromised CDN could execute JavaScript in the context of the documentation site. No runtime application code is changed, and no vulnerability in the project’s own code is fixed.
Changed components

Documentation site (MkDocs)docs/getting-started/features/entropy.en.mddocs/css/custom.cssmkdocs.ymlrender_docs_math.py.gitignore
Inspect captured patch +8779 / −89
diff --git a/.gitignore b/.gitignore
index 2f96e70..3d74685 100644
--- a/.gitignore
+++ b/.gitignore
@@ -25,6 +25,10 @@
 ######################
 build/
 build-*/
+# mkdocs site output (site_dir: public)
+public/
+# pytest-cov HTML report
+htmlcov/
 
 # Test failure outputs
 ######################
diff --git a/docs/css/custom.css b/docs/css/custom.css
index adc40df..1cfd96b 100644
--- a/docs/css/custom.css
+++ b/docs/css/custom.css
@@ -6,6 +6,14 @@
   margin: 0 !important;
 }
 
+/* Pre-rendered display equations (see render_docs_math.py). Centered blocks,
+   never wider than the column on small screens. */
+.md-typeset img.math-display {
+  display: block;
+  margin: 0.8em auto !important;
+  max-width: 100%;
+}
+
 .md-typeset h5 {
   color: black;
   text-transform: none;
diff --git a/docs/getting-started/features/entropy.en.md b/docs/getting-started/features/entropy.en.md
index cf5d94b..b18f1cf 100644
--- a/docs/getting-started/features/entropy.en.md
+++ b/docs/getting-started/features/entropy.en.md
@@ -19,16 +19,14 @@ Entropy, a fundamental concept in various scientific disciplines, is most common
 While thermodynamics entropy deals with physical systems, Shannon's entropy focuses on information content, and cryptographic entropy emphasizes security through randomness.
 
 ### Measuring Dice Rolls Entropy
-Entropy is a theoretical measure and is not directly measurable from a single roll but rather from the probability distribution of outcomes over many rolls. We can use Shannon's formula for theoretical and empirical calculations. Entropy $S$ can be quantified with:
+Entropy is a theoretical measure and is not directly measurable from a single roll but rather from the probability distribution of outcomes over many rolls. We can use Shannon's formula for theoretical and empirical calculations. Entropy *S* can be quantified with:
 
-$$
-S = -\sum_{i=1}^{n} p_i \log(p_i)
-$$
+![S = -\sum_{i=1}^{n} p_i \log(p_i)](img/math/eq-01.svg){ .math-display }
 
 1. **Empirical Measurement:**
 
     - Roll the dice a large number of times to observe the frequency of each outcome.
-    - Estimate the probabilities $p_i$ based on observed frequencies.
+    - Estimate the probabilities *p<sub>i</sub>* based on observed frequencies.
 
 2. **Theoretical Calculation:**
 
@@ -36,8 +34,8 @@ $$
 
 where:
 
-- $p_i$ is the probability of each possible outcome (or state) of the system.
-- $n$ is the number of possible outcomes.
+- *p<sub>i</sub>* is the probability of each possible outcome (or state) of the system.
+- *n* is the number of possible outcomes.
 
 ## Empirical (Real) vs. Theoretical Entropy in Dice Rolls
 
@@ -47,31 +45,23 @@ When calculating the entropy of dice rolls, the difference between real and theo
 
 The theoretical entropy calculation assumes that the dice are perfectly fair, meaning each face has an equal probability of landing face up.
 
-Consider a fair six-sided die. The possible outcomes when rolling one die are {1, 2, 3, 4, 5, 6}, each with an equal probability of $\frac{1}{6}$.
+Consider a fair six-sided die. The possible outcomes when rolling one die are {1, 2, 3, 4, 5, 6}, each with an equal probability of 1/6.
 
 1. **Single Die Roll:**
 
-    - Each outcome has a probability $p_i = \frac{1}{6}$.
-    - The entropy $S$ for one die roll is calculated as:
-$$
-S = - \sum_{i=1}^{6} \left( \frac{1}{6} \log_2 \left( \frac{1}{6} \right) \right)
-$$
-Since $\log_2(1/6) = -\log_2(6)$ :
-$$
-S = -6 \left( \frac{1}{6} \times -\log_2(6) \right) = \log_2(6) \approx 2.585 \text{ bits}
-$$
+    - Each outcome has a probability *p<sub>i</sub>* = 1/6.
+    - The entropy *S* for one die roll is calculated as:
+![S = - \sum_{i=1}^{6} \left( \frac{1}{6} \log_2 \left( \frac{1}{6} \right) \right)](img/math/eq-02.svg){ .math-display }
+Since log₂(1/6) = −log₂(6) :
+![S = -6 \left( \frac{1}{6} \times -\log_2(6) \right) = \log_2(6) \approx 2.585 \text{ bits}](img/math/eq-03.svg){ .math-display }
 
 2. **Multiple Dice Rolls:**
 
-    - For multiple dice, the entropy increases as the number of possible outcomes increases. For $k$ fair dice, the number of possible outcomes is $6^k$.
-    - The entropy $S$ for $k$ dice is:
-$$
-S = \log_2(6^k) = k \log_2(6) \approx 2.585k \text{ bits}
-$$
+    - For multiple dice, the entropy increases as the number of possible outcomes increases. For *k* fair dice, the number of possible outcomes is 6<sup>k</sup>.
+    - The entropy *S* for *k* dice is:
+![S = \log_2(6^k) = k \log_2(6) \approx 2.585k \text{ bits}](img/math/eq-04.svg){ .math-display }
     - For example, entropy for the roll of 50 fair dice is calculated as:
-$$
-S = \log_2(6^{50}) = 50 \log_2(6) \approx 2.585 \times 50 \approx 129.25 \text{ bits}
-$$
+![S = \log_2(6^{50}) = 50 \log_2(6) \approx 2.585 \times 50 \approx 129.25 \text{ bits}](img/math/eq-05.svg){ .math-display }
 
    This calculation assumes that every outcome (each face of the die) has an equal likelihood, leading to a uniform distribution.
 
@@ -83,11 +73,9 @@ In a real sample of dice rolls, several factors can cause deviations from the pe
 2. **Rolling Conditions**: The way the dice are rolled, the surface they land on, and even air currents can introduce slight biases.
 3. **Finite Sample Size**: When rolling dice a finite number of times, the observed frequencies of each face will naturally deviate from the expected uniform distribution due to random variations. This phenomenon is more pronounced with smaller sample sizes.
 
-When you roll a die multiple times and observe the outcomes, you can calculate the empirical probabilities $p_i$ of each face. Using these probabilities, the entropy is calculated as:
+When you roll a die multiple times and observe the outcomes, you can calculate the empirical probabilities *p<sub>i</sub>* of each face. Using these probabilities, the entropy is calculated as:
 
-$$
-S = - \sum_{i=1}^{6} p_i \log_2(p_i)
-$$
+![S = - \sum_{i=1}^{6} p_i \log_2(p_i)](img/math/eq-06.svg){ .math-display }
 
 ### Example
 
@@ -106,67 +94,33 @@ We can calculate Shannon's entropy as follows:
 #### Step 1: Calculate Probabilities
 
 - Total number of rolls:
-$$
-N = 4 + 9 + 7 + 10 + 12 + 8 = 50
-$$
+![N = 4 + 9 + 7 + 10 + 12 + 8 = 50](img/math/eq-07.svg){ .math-display }
 - Probabilities for each outcome:
-$$
-p_1 = \frac{4}{50} = 0.08 
-$$
-$$
-p_2 = \frac{9}{50} = 0.18 
-$$
-$$
-p_3 = \frac{7}{50} = 0.14 
-$$
-$$
-p_4 = \frac{10}{50} = 0.2 
-$$
-$$
-p_5 = \frac{12}{50} = 0.24 
-$$
-$$
-p_6 = \frac{8}{50} = 0.16 
-$$
+![p_1 = \frac{4}{50} = 0.08](img/math/eq-08.svg){ .math-display }
+![p_2 = \frac{9}{50} = 0.18](img/math/eq-09.svg){ .math-display }
+![p_3 = \frac{7}{50} = 0.14](img/math/eq-10.svg){ .math-display }
+![p_4 = \frac{10}{50} = 0.2](img/math/eq-11.svg){ .math-display }
+![p_5 = \frac{12}{50} = 0.24](img/math/eq-12.svg){ .math-display }
+![p_6 = \frac{8}{50} = 0.16](img/math/eq-13.svg){ .math-display }
 
 #### Step 2: Compute Entropy
 
 - Using Shannon's entropy formula:
-$$
-S = -\sum_{i=1}^{n} p_i \log_2(p_i)
-$$
+![S = -\sum_{i=1}^{n} p_i \log_2(p_i)](img/math/eq-14.svg){ .math-display }
 - Calculate each term:
-$$
-S_1 = -p_1 \log_2(p_1) = -0.08 \log_2(0.08) = -0.08 \times (-3.64386) = 0.291509
-$$
-$$
-S_2 = -p_2 \log_2(p_2) = -0.18 \log_2(0.18) = -0.18 \times (-2.47393) = 0.445307
-$$
-$$
-S_3 = -p_3 \log_2(p_3) = -0.14 \log_2(0.14) = -0.14 \times (-2.8365) = 0.39711
-$$
-$$
-S_4 = -p_4 \log_2(p_4) = -0.2 \log_2(0.2) = -0.2 \times (-2.32193) = 0.464386
-$$
-$$
-S_5 = -p_5 \log_2(p_5) = -0.24 \log_2(0.24) = -0.24 \times (-2.05889) = 0.494132
-$$
-$$
-S_6 = -p_6 \log_2(p_6) = -0.16 \log_2(0.16) = -0.16 \times (-2.64386) = 0.423018
-$$
+![S_1 = -p_1 \log_2(p_1) = -0.08 \log_2(0.08) = -0.08 \times (-3.64386) = 0.291509](img/math/eq-15.svg){ .math-display }
+![S_2 = -p_2 \log_2(p_2) = -0.18 \log_2(0.18) = -0.18 \times (-2.47393) = 0.445307](img/math/eq-16.svg){ .math-display }
+![S_3 = -p_3 \log_2(p_3) = -0.14 \log_2(0.14) = -0.14 \times (-2.8365) = 0.39711](img/math/eq-17.svg){ .math-display }
+![S_4 = -p_4 \log_2(p_4) = -0.2 \log_2(0.2) = -0.2 \times (-2.32193) = 0.464386](img/math/eq-18.svg){ .math-display }
+![S_5 = -p_5 \log_2(p_5) = -0.24 \log_2(0.24) = -0.24 \times (-2.05889) = 0.494132](img/math/eq-19.svg){ .math-display }
+![S_6 = -p_6 \log_2(p_6) = -0.16 \log_2(0.16) = -0.16 \times (-2.64386) = 0.423018](img/math/eq-20.svg){ .math-display }
 - Sum the contributions:
-$$
-S = S_1 + S_2 + S_3 + S_4 + S_5 + S_6 
-$$
-$$
-S = 0.291509 + 0.445307 + 0.39711 + 0.464386 + 0.494132 + 0.423018 = 2.515462
-$$
-Thus, the Shannon's entropy for the given distribution of dice rolls is approximately $2.52$ bits per roll. This will give you a different value than $\log_2(6)$ due to the deviations in the empirical probabilities.
-
-- The total entropy for the $N = 50$ rolls is:
-$$
-S_{total} = S \times N = 2.515 + 50 \approx 125.8 \text{ bits}
-$$
+![S = S_1 + S_2 + S_3 + S_4 + S_5 + S_6](img/math/eq-21.svg){ .math-display }
+![S = 0.291509 + 0.445307 + 0.39711 + 0.464386 + 0.494132 + 0.423018 = 2.515462](img/math/eq-22.svg){ .math-display }
+Thus, the Shannon's entropy for the given distribution of dice rolls is approximately 2.52 bits per roll. This will give you a different value than log₂(6) due to the deviations in the empirical probabilities.
+
+- The total entropy for the *N* = 50 rolls is:
+![S_{total} = S \times N = 2.515 + 50 \approx 125.8 \text{ bits}](img/math/eq-23.svg){ .math-display }
 
 #### Shannon's Entropy in Practice
 
diff --git a/docs/getting-started/features/img/math/eq-01.svg b/docs/getting-started/features/img/math/eq-01.svg
new file mode 100644
index 0000000..03f5332
--- /dev/null
+++ b/docs/getting-started/features/img/math/eq-01.svg
@@ -0,0 +1,292 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
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+ <metadata>
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+   <cc:Work>
+    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+    <dc:format>image/svg+xml</dc:format>
+    <dc:creator>
+     <cc:Agent>
+      <dc:title>Matplotlib v3.10.9, https://matplotlib.org/</dc:title>
+     </cc:Agent>
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+ <defs>
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diff --git a/docs/getting-started/features/img/math/eq-17.svg b/docs/getting-started/features/img/math/eq-17.svg
new file mode 100644
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+    <use xlink:href="#DejaVuSans-2e" transform="translate(1582.719727 0.015625)"/>
+    <use xlink:href="#DejaVuSans-38" transform="translate(1611.881836 0.015625)"/>
+    <use xlink:href="#DejaVuSans-62" transform="translate(1702.564019 0.015625)"/>
+    <use xlink:href="#DejaVuSans-69" transform="translate(1766.040581 0.015625)"/>
+    <use xlink:href="#DejaVuSans-74" transform="translate(1793.823784 0.015625)"/>
+    <use xlink:href="#DejaVuSans-73" transform="translate(1833.032769 0.015625)"/>
+   </g>
+  </g>
+ </g>
+</svg>
diff --git a/mkdocs.yml b/mkdocs.yml
index 6ca3e72..f0a22c6 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -3,7 +3,6 @@ markdown_extensions:
   - md_in_html
   - meta
   - admonition
-  - pymdownx.arithmatex
   - pymdownx.mark
   - toc:
       permalink: true
@@ -18,13 +17,8 @@ markdown_extensions:
       emoji_index: !!python/name:material.extensions.emoji.twemoji
       emoji_generator: !!python/name:material.extensions.emoji.to_svg
 
-extra_javascript:
-  - https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/
Risk score
Why this scored 37/100

Our methodology →
Potential impact 8/30
Exploitability 7/25
Stealth signal 6/15
Affected reach 5/15
Confidence 7/10
Evidence quality 4/5
Human-validated context
Community notes

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What the developer wrote

What changed, and why it matters

Security signals we found

Evidence from the diff

Changed components

Why this scored 37/100

Community notes

Related watches

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