Fix typos and broken links in documentation (correct GitHub URL, fix variable names, and grammar corrections)

Author: sanketsabharwal

docs/index.md

@@ -18,7 +18,7 @@ Movement Analysis Toolkit
 :material-school: **Apply in science, health, and the arts**  
 :material-handshake: **Developed with the partial support of the [EU ICT STARTS Resilence Project](https://resilence.eu/)**
 
-[:octicons-book-24: Get Started](getting_started/getting_started.md){ .md-button .md-button--primary } [:material-github: GitHub Repository](https://github.com/InfoMusCP/InfoMove){ .md-button }  
+[:octicons-book-24: Get Started](getting_started/getting_started.md){ .md-button .md-button--primary } [:material-github: GitHub Repository](https://github.com/InfoMusCP/PyEyesWeb){ .md-button }  
 
 </div>
 
@@ -102,7 +102,7 @@ This framework models an observer of a dance performance through four interconne
     ![InfoMus Lab Logo](assets/cp-logo.png){ width=512 }
     </div>
 
-PyEyesWeb is developed the partial support of the [EU ICT STARTS Resilence Project](https://resilence.eu/),
+PyEyesWeb is developed with the partial support of the [EU ICT STARTS Resilence Project](https://resilence.eu/),
 funded by the European Union’s Horizon programme.  
 
 <div align="center">

docs/user_guide/integrations.md

@@ -4,7 +4,7 @@ PyEyesWeb aims to provide seamless integration with popular tools in the creativ
 
 ## TouchDesigner
 
-We provide a [plugin](https://github.com/InfoMusCP/PyEyesWebTD) consisting of set of TouchDesigner custom components (i.e., `.tox` files).
+We provide a [plugin](https://github.com/InfoMusCP/PyEyesWebTD) consisting of a set of TouchDesigner custom components (i.e., `.tox` files).
 Each `.tox` component implements a movement feature as outlined in the [documentation](theoretical_framework/index.md).
 
 Example usage of the plugin is available in the [examples folder](https://github.com/InfoMusCP/PyEyesWeb/tree/main/examples).

docs/user_guide/theoretical_framework/analysis_primitives/synchronization.md

@@ -69,9 +69,9 @@ $$
 **Output:** \( \text{PLV} \in [0,1] \)
 
 !!! tip "Interpretation"
-    - \( PLV > 0.7 \): strong phase coupling  
-    - \( 0.4 < \rho_{\max} \leq 0.7 \): moderate phase coupling   
-    - \( \rho_{\max} \leq 0.4 \): weak phase coupling 
+    - \( PLV > 0.7 \): strong phase coupling
+    - \( 0.4 < PLV \leq 0.7 \): moderate phase coupling
+    - \( PLV \leq 0.4 \): weak phase coupling 
 
 ## Usage Examples
 

docs/user_guide/theoretical_framework/low_level/smoothness.md

@@ -106,7 +106,7 @@ $$
 $$
 
 !!! tip
-    The measurment units is (length unit)/s³ (e.g., m/s³).  
+    The measurement units is (length unit)/s³ (e.g., m/s³).  
     Lower RMS values indicate smoother movement, but the scale depends on movement amplitude and units.
 
 ## Usage Examples