Bibliography:
Ultimate explanation: math.stackexchange.com/questions/776039/intuition-behind-normal-subgroups/3732426#3732426
Does not have to be isomorphic to a subgroup:
This is one of the reasons why the analogy between simple groups of finite groups and prime numbers is limited.
To some extent, the ultimate achievement of a TAS is to achieve arbitrary code execution (ACE) on a game, although this has been becoming rarer and rarer in newer consoles. The Nintendo 64 is the current interesting ACE discovery frontier as of 2020.
Post ACE, you then get into more subtle categories which tend to be more geometric clipping through wall glitches, but those can still be fun.
The most beautiful TAS content ever made are:
- Super Mario 64
- Super Mario 64 A press challenge
- 1-key any percent run:
- 2016 emulator run: www.youtube.com/watch?v=TkOkJvLKxUY
- AGDQ 2018 commented TASBOT console verification: www.youtube.com/watch?v=xvWOLT9G6tM
- Why we need one key: gaming.stackexchange.com/questions/249969/in-mario-64-speedruns-why-are-the-keys-necessary/351595#351595
- related: Super Mario 64 reverse engineering project
- Super Mario World for the SNES arbitrary code execution
- www.youtube.com/watch?v=OPcV9uIY5i4 with in-game programmed Pong and Snake, 2014
- www.youtube.com/watch?v=HxFh1CJOrTU Seth Bling does the credit warp manually in about 3 minutes, 2015. Later reduced to less than 1 minute: www.youtube.com/watch?v=Jf9i7MjViCE
- www.youtube.com/watch?v=voL3e0iqugo ACE was initially not forbidden in 11 exit rules, so Seth made an in-game manual ACE that programs an in-game accessible "exit stage now" functionality!!! This was later forbidden of course, but it was fun while it lasted.
- then he injected a Flappy Bird clone manually!!! www.youtube.com/watch?v=hB6eY73sLV0, 2016
- Ocarina of Time
- 2020 ACE via use after free including a non-TAS credit warp faster than the 2016 wrong glitch: www.polygon.com/2020/1/24/21080568/zelda-ocarina-of-time-arwing-spawn-video-speedrun-credits-ace-cheat-code ACE later reproduced in Majora's Mask, which has a similar game engine.
- 2016 Zelda Ocarina of Time wrong warp glitch:
- www.youtube.com/watch?v=Gso4MuNSuV8 EZScape explains the glitch, 2016
- Zelda Majora's Mask debug menu
It is also amusing to see console verification of emulations, e.g.: Video 1. "Super Mario 64 '120 Stars' in 1:20:41.52 Console Verified by Soul Umbreon (2012)".
| Grade | Name | Notes |
|---|---|---|
| 4 | C / C++ | Cheatsheets: C, C++, POSIX C API |
| 3 | x86 assembly, ELF | Cheatsheet, x86 Paging Tutorial, Bare Metal |
| 4 | Python | Cheatsheet |
| 4 | Bash | Cheatsheets: language, POSIX / GNU utils |
| 4 | HTML, CSS, JavaScript | web technology, Node.js, CoffeScript |
| 4 | Java | Cheatsheet, school projects |
| 3 | Ruby, Rails | GitLab contributions, cheatsheets: Ruby, rails-cheat |
| 3 | GDB | Cheatsheet |
| 2 | MySQL | Tutorial |
| 3 | LaTeX, Markdown | LaTeX cheatsheet, Markdown style guide, Markdown Testsuite contributions, Jekyll cheatsheet |
The term loosely refers to certain layers of the computer abstraction layers hierarchy, usually high level hardware internals like CPU pipeline, caching and the memory system. Basically exactly what gem5 models.
Fundamental theorem on homomorphisms by 
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-11 +Created 1970-01-01
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