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# Welcome to ΛRIX Lab.

I'm **Dr. Rahul Gulia**, a researcher and engineer exploring the intersection of **artificial intelligence, wireless communications, physics, and future technologies**.

Here, we uncover the science behind the invisible world:

* 📡 How wireless communication really works—from Wi-Fi to 6G
* 🤖 How AI is transforming engineering and scientific discovery
* ⚡ The physics behind the technologies we use every day
* 🚀 The breakthroughs shaping the future of connectivity, sensing, robotics, and beyond

Whether you're a student, engineer, researcher, or simply curious about how the modern world works, you'll find clear explanations, visual demonstrations, thought experiments, and research-inspired deep dives designed to make complex ideas intuitive.

The future isn't magic—it's science waiting to be understood.

**Welcome to ΛRIX Lab. Let's make the invisible visible.**


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Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2026-07-16T00:10:38Z`
Route: `/channel/UCIFJd350LWbSY0nSxUbashw`
Version: `2026.02.07-118d635 @ (HEAD detached at v2.20260207.0)`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /usr/share/crystal/src/hash.cr:1198:9 in '??'
  from /usr/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:524:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1035:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1082:14 in 'extract_items'
  from src/invidious/channels/videos.cr:29:22 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:127:14 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /usr/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /usr/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>