User:Polygon/Page for testing: Difference between revisions

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-{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}} is the current [[BB(2,6)]] [[champion]]. It was discovered on the 19th of May 2023 by Pavel Kropitz. It halts with a score > <math>10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}}</math>.
-==Analysis by Shawn Ligocki==
-https://www.sligocki.com/2023/05/20/bb-2-6-p3.html
-<pre>
-Analysis
-Level 1
-These rules can all be verified by direct simulation:
-<A 212 22^n 55 → <A 212 22^n+2
-<A 212 22^n 2 55 → <A 212 55^n+2 2
-^5 <A 212 22^n 52 5555 → <A 212 55 2 55^n+3 52
-<A 212 22^n 2 52 5 → <A 212 55^n+2 52
-Level 2
-Repeating the first rule above we get:
-^∞ <A 212 22^n 55^k → 0^∞ 212 22^n+2k
-which let's us prove Rule 2:
-^∞ <A 212 22^n 2 55 → 0^∞ <A 212 55^n+2 2
-                     → 0^∞ <A 212 22^2n+4 2
-Level 3
-Repeating Rule 2 we get:
-^∞ <A 212 22^n 2 55^k → 0^∞ <A 212 22^(n+4)*((2^k)-4) 2
-which let's us prove Rule 3:
-^∞ <A 212 22^n 52 5^5 → 0^∞ <A 212 55 2 55^n+3 52 5
-                       → 0^∞ <A 212 22^2 2 55^n+3 52 5
-                       → 0^∞ <A 212 22^(6*2^(n+3)-2) 52 5
-                       → 0^∞ <A 212 55^(6*2^(n+3)-2) 52
-                       → 0^∞ <A 212 22^(6*2^(n+4)-4) 52
-</pre>
-∞∞∞∞
-→→→→

Latest revision as of 21:05, 25 October 2025