User:Polygon/Page for analyses - Revision history

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ added link to discovery

2026-03-30T14:42:33Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: added link to discovery

← Older revision		Revision as of 14:42, 30 March 2026
Line 1,857:		Line 1,857:

	={{TM\|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}=		={{TM\|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}=
	Currently work in progress.		Currently work in progress. Discovered by Pavel Kropitz in May 2023[https://discord.com/channels/960643023006490684/1084047886494470185/1110341613479268442].

	<div class="toccolours mw-collapsible mw-collapsed">'''Analysis'''<div class="mw-collapsible-content">		<div class="toccolours mw-collapsible mw-collapsed">'''Analysis'''<div class="mw-collapsible-content">
	{\| class="wikitable"		{\| class="wikitable"

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ added rule #18

2026-03-24T17:54:01Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: added rule #18

← Older revision		Revision as of 17:54, 24 March 2026
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	--> S 1^a-4 2 1^4k+9 0 (21)^2 <C 0^inf [+14k^2 +100k +176]		--> S 1^a-4 2 1^4k+9 0 (21)^2 <C 0^inf [+14k^2 +100k +176]
	--> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [+14k^2 +100k +180] by rule 5		--> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [+14k^2 +100k +180] by rule 5

			18. S 1^4m+v 2 1^2k+1 0 <C (21)^2 0^inf --> S 1^v 2 1^(2^(m+1)*k+2^(m+3)-7) 0 <C (21)^2 0^inf
			by repetition of rule 17.
			Obtaining the ones count:
			(2k+1)2+7=4k+9 --> Rule 17 applies 2+7
			(2^ak+2^b-7)2+7 = (2^(a+1)k+2^(b+1)-14)+7 = 2^(a+1)k+2^(b+1)-7
			2k+1 is of the form 2^ak+2^b-7 (=2^1k+2^3-7)
			Each reduction of m increases both exponents, there are m reductions of m (until m = 0)
			--> ones: 2^(m+1)*k+2^(m+3)-7
	</pre>		</pre>
	</div></div>		</div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ no #'s in the construction

2026-03-24T17:29:34Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: no #'s in the construction

← Older revision		Revision as of 17:29, 24 March 2026
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	--> S 1^a-4 2 1^4k+9 0 (21)^2 B> 0^inf [+14k^2 +100k +175]		--> S 1^a-4 2 1^4k+9 0 (21)^2 B> 0^inf [+14k^2 +100k +175]
	--> S 1^a-4 2 1^4k+9 0 (21)^2 <C 0^inf [+14k^2 +100k +176]		--> S 1^a-4 2 1^4k+9 0 (21)^2 <C 0^inf [+14k^2 +100k +176]
	--> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [+14k^2 +100k +180] by rule #5		--> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [+14k^2 +100k +180] by rule 5
	</pre>		</pre>
	</div></div>		</div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ completed rule #17

2026-03-24T17:29:12Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: completed rule #17

← Older revision		Revision as of 17:29, 24 March 2026
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	by repetition of rule 15.		by repetition of rule 15.

	17. S 1^a 2 1^2k+1 0 <C (21)^2 0^inf --> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [~~TODO~~ steps]		17. S 1^a 2 1^2k+1 0 <C (21)^2 0^inf --> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [+14k^2 +100k +180 steps]
	by:		by:
	S 1^a 2 1^2k+1 0 <C (21)^2 0^inf		S 1^a 2 1^2k+1 0 <C (21)^2 0^inf
Line 2,030:		Line 2,030:
	--> S 1^a-4 0 <C (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +146] by rule 5		--> S 1^a-4 0 <C (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +146] by rule 5
	--> S 1^a-4 2 A> (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +147]		--> S 1^a-4 2 A> (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +147]
			--> S 1^a-4 2 (11)^2k+4 A> 0 1^2 (21) 0^inf [+14k^2 +100k +155] by rule 4
			--> S 1^a-4 2 1^4k+9 B> 1^2 (21) 0^inf [+14k^2 +100k +156]
			--> S 1^a-4 2 1^4k+9 0 D> (12) 1 0^inf [+14k^2 +100k +157]
			--> S 1^a-4 2 1^4k+9 0 (01) D> 1 0^inf [+14k^2 +100k +161] by rule 10
			--> S 1^a-4 2 1^4k+9 0^2 1^2 D> 0^inf [+14k^2 +100k +162]
			--> S 1^a-4 2 1^4k+9 0^2 1^2 <C 0^inf [+14k^2 +100k +163]
			--> S 1^a-4 2 1^4k+9 0^2 <C (01) 0^inf [+14k^2 +100k +169] by rule 8
			--> S 1^a-4 2 1^4k+9 0 (21) 0 <C 0^inf [+14k^2 +100k +173] by rule 12
			--> S 1^a-4 2 1^4k+9 0 (21) 2 A> 0^inf [+14k^2 +100k +174]
			--> S 1^a-4 2 1^4k+9 0 (21)^2 B> 0^inf [+14k^2 +100k +175]
			--> S 1^a-4 2 1^4k+9 0 (21)^2 <C 0^inf [+14k^2 +100k +176]
			--> S 1^a-4 2 1^4k+9 0 <C (21)^2 0^inf [+14k^2 +100k +180] by rule #5
	</pre>		</pre>
	</div></div>		</div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ added missing rule name

2026-03-24T17:16:00Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: added missing rule name

← Older revision		Revision as of 17:16, 24 March 2026
Line 2,028:		Line 2,028:
	--> S 1^a-4 0 (21)^2k+4 0 <B 1^2 (21) 0^inf [+14k^2 +92k +137]		--> S 1^a-4 0 (21)^2k+4 0 <B 1^2 (21) 0^inf [+14k^2 +92k +137]
	--> S 1^a-4 0 (21)^2k+4 <C 0 1^2 (21) 0^inf [+14k^2 +92k +138]		--> S 1^a-4 0 (21)^2k+4 <C 0 1^2 (21) 0^inf [+14k^2 +92k +138]
	--> S 1^a-4 0 <C (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +146]		--> S 1^a-4 0 <C (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +146] by rule 5
	--> S 1^a-4 2 A> (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +147]		--> S 1^a-4 2 A> (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +147]
	</pre>		</pre>
	</div></div>		</div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ step count fixing and continuation of rule #17

2026-03-24T17:14:14Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: step count fixing and continuation of rule #17

← Older revision		Revision as of 17:14, 24 March 2026
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	--> S 1^a-4 0 (21)^2 0 (01)^2k+2 <C (21)^2 0^inf [+14k^2 +80k +125] by rule 5		--> S 1^a-4 0 (21)^2 0 (01)^2k+2 <C (21)^2 0^inf [+14k^2 +80k +125] by rule 5
	--> S 1^a-4 0 (21)^2 0 <C (01)^2k+2 (21)^2 0^inf [+14k^2 +84k +129] by rule 6		--> S 1^a-4 0 (21)^2 0 <C (01)^2k+2 (21)^2 0^inf [+14k^2 +84k +129] by rule 6
	--> S 1^a-4 0 (21)^2 (21)^2k+1 0 <C (01) (21)^2 0^inf [+14k^2 +~~88k~~ +133] by rule 12		--> S 1^a-4 0 (21)^2 (21)^2k+1 0 <C (01) (21)^2 0^inf [+14k^2 +92k +133] by rule 12
	--> S 1^a-4 0 (21)^2k+3 2 A> (01) (21)^2 0^inf [+14k^2 +~~88k~~ +134]		--> S 1^a-4 0 (21)^2k+3 2 A> (01) (21)^2 0^inf [+14k^2 +92k +134]
	--> S 1^a-4 0 (21)^2k+4 B> 1 (21)^2 0^inf [+14k^2 +~~88k~~ +135]		--> S 1^a-4 0 (21)^2k+4 B> 1 (21)^2 0^inf [+14k^2 +92k +135]
			--> S 1^a-4 0 (21)^2k+4 0 D> (21)^2 0^inf [+14k^2 +92k +136]
			--> S 1^a-4 0 (21)^2k+4 0 <B 1^2 (21) 0^inf [+14k^2 +92k +137]
			--> S 1^a-4 0 (21)^2k+4 <C 0 1^2 (21) 0^inf [+14k^2 +92k +138]
			--> S 1^a-4 0 <C (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +146]
			--> S 1^a-4 2 A> (21)^2k+4 0 1^2 (21) 0^inf [+14k^2 +96k +147]
	</pre>		</pre>
	</div></div>		</div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ continued rule #17

2026-03-24T17:03:56Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: continued rule #17

@@ Line 2,014: / Line 2,014: @@
 --> S 1^a-4 0 (21)^2 0 (01)^2k+3 D> 1 0^inf [+14k^2 +80k +106] by rule 10
 --> S 1^a-4 0 (21)^2 0 (01)^2k+3 1 D> 0^inf [+14k^2 +80k +107]
 </pre>
 </div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ fixed error in the step counts and continued

2026-03-24T16:54:11Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: fixed error in the step counts and continued

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ continued rule #17

2026-03-24T16:47:24Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: continued rule #17

@@ Line 1,997: / Line 1,997: @@
 --> S 1^a-2 0 <C (01) (21)^2k+4 0^inf [+14k^2 +72k +66] by rule 6
 --> S 1^a-2 2 A> (01) (21)^2k+4 0^inf [+14k^2 +72k +67]
 </pre>
 </div></div>

Polygon: /* {{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}} */ continued rule #17

2026-03-24T16:36:05Z

{{TM|1RB1RA1RA_0LC0RD2LC_2RA1LB---_0LC1RD1LB}}: continued rule #17

@@ Line 1,984: / Line 1,984: @@
 --> S 1^a (21)^2 <C (01)^2k+2 0^inf [+14k^2 +60k +19] by rule 8
 --> S 1^a <C (21)^2 (01)^2k+2 0^inf [+14k^2 +60k +23] by rule 5
 </pre>
 </div></div>

← Older revision		Revision as of 16:54, 24 March 2026
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	--> S 1^a-2 (21) 0 <B 1^2 (21)^2k+3 0^inf [+14k^2 +72k +70]		--> S 1^a-2 (21) 0 <B 1^2 (21)^2k+3 0^inf [+14k^2 +72k +70]
	--> S 1^a-2 (21) <C (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +71]		--> S 1^a-2 (21) <C (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +71]
	--> S 1^a-2 <C (21) (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +72] by rule 5		--> S 1^a-2 <C (21) (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +73] by rule 5
	--> S 1^a-3 <B 1 (21) (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +73]		--> S 1^a-3 <B 1 (21) (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +74]
	--> S 1^a-4 0 D> (12) 1 (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +74]		--> S 1^a-4 0 D> (12) 1 (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +75]
	--> S 1^a-4 0 (01) D> 1 (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +78] by rule 10		--> S 1^a-4 0 (01) D> 1 (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +79] by rule 10
	--> S 1^a-4 0^2 1^2 D> (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +79]		--> S 1^a-4 0^2 1^2 D> (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +80]
	--> S 1^a-4 0^2 1^2 <C (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +80]		--> S 1^a-4 0^2 1^2 <C (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +81]
	--> S 1^a-4 0^2 <C (01)^2 1 (21)^2k+3 0^inf [+14k^2 +72k +86] by rule 8		--> S 1^a-4 0^2 <C (01)^2 1 (21)^2k+3 0^inf [+14k^2 +72k +87] by rule 8
	--> S 1^a-4 0 (21) 0 <C (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +90] by rule 12		--> S 1^a-4 0 (21) 0 <C (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +91] by rule 12
	--> S 1^a-4 0 (21) 2 A> (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +91]		--> S 1^a-4 0 (21) 2 A> (01) 1 (21)^2k+3 0^inf [+14k^2 +72k +92]
	--> S 1^a-4 0 (21)^2 B> 1^2 (21)^2k+3 0^inf [+14k^2 +72k +92]		--> S 1^a-4 0 (21)^2 B> 1^2 (21)^2k+3 0^inf [+14k^2 +72k +93]
			--> S 1^a-4 0 (21)^2 0 D> (12)^2k+3 1 0^inf [+14k^2 +72k +94]
			--> S 1^a-4 0 (21)^2 0 (01)^2k+3 D> 1 0^inf [+14k^2 +80k +106] by rule 10
			--> S 1^a-4 0 (21)^2 0 (01)^2k+3 1 D> 0^inf [+14k^2 +80k +107]
	</pre>		</pre>
	</div></div>		</div></div>