Seventh row template problem - Revision history

Bobson8: updating verification status

2023-12-01T14:25:51Z

updating verification status

Selinger: Link to KataHex

2023-11-18T14:55:55Z

Link to KataHex

Selinger: Fixed links

2023-11-18T13:49:01Z

Fixed links

Selinger: Added carrier sizes

2023-11-18T13:32:36Z

Added carrier sizes

Selinger: /* Validity */ All templates are checked using Mohex.

2023-11-18T13:27:31Z

‎Validity: All templates are checked using Mohex.

Selinger: Fixed line break

2023-11-18T13:25:57Z

Fixed line break

Selinger: Fixed the chronological order

2023-11-18T13:24:33Z

Fixed the chronological order

Bobson8 at 10:04, 18 November 2023

2023-11-18T10:04:42Z

Bobson8 at 09:42, 18 November 2023

2023-11-18T09:42:11Z

Bobson8: Added descriptions to VII1c

2023-11-18T08:34:10Z

Added descriptions to VII1c

@@ Line 51: / Line 51: @@
 For Blue playing a,b,c,d, Red can respond with X,Y,Y,Z respectively. For the rest Red can respond with b.
-Bobson continued to reduce the size of this pre-template. He first considered the following width 19 carrier (contained in the width 23 pre-template):
+Bobson continued to reduce the size of this pre-template. He first considered the following width 19 carrier (the gray area):
 <hexboard size="7x23"
@@ Line 57: / Line 57: @@
    edges="bottom"
 visible="area(a7,w7,w5,u3,r3,p1,n1,j3,g3,c5)"
-   contents="R o1 E *:m4 *:n4 S gray:area(c7,u7,u5,s3,r3,p1,n1,j3,i3,e5)"
+   contents="R o1 E *:m4 *:n4 +:(a7 b6 c5 e4 g3 w7 w6 w5 v4 u3) S gray:area(c7,u7,u5,s3,r3,p1,n1,j3,i3,e5)"
    />
-MoHex shows that every intrusions other than * are solvable within this carrier. On the other hand, Bobson found that intrusions at * can be solved within width 21, so the pre-template was then reduced to width 21 on October 27. The minimality was checked by a collaborative effort using [[MoHex]] (patched version made by Comonoid and Quasar so that it can be run on a 23×23 board), and was finally verified on November 8.
+MoHex shows that every intrusions other than * are solvable within this carrier. On the other hand, Bobson found that intrusions at * can be solved within width 21 (removing + cells), so the pre-template was then reduced to width 21 on October 27. The minimality was checked by a collaborative effort using [[MoHex]] (patched version made by Comonoid and Quasar so that it can be run on a 23×23 board), and was finally verified on November 8.
 === Edge template VII-1b ===
@@ Line 73: / Line 73: @@
 This template has width 19, and its [[carrier]] has size 90, including the red stone.
-While checking the minimality of [[edge template VII1c]], Comonoid first proposed that there might be a width-19 template if the carrier is wide enough. Comonoid, Quasar, and Mason came up with different carriers, and Mason described what turned out to be the final shape of the template on November 4 and proved its validity. Minimality was subsequently verified by a collaboration among several users, and the final case was finished by Quasar on November 17.
+While checking the minimality of [[edge template VII1c]], Comonoid first proposed that there might be a width-19 template if the carrier has more vertical space. Comonoid, Quasar, and Mason came up with different carriers, and Mason described what turned out to be the final shape of the template on November 4 and proved its validity. Minimality was subsequently verified by a collaboration among several users, and the final case was finished by Quasar on November 17.
 == Methodology ==
@@ Line 79: / Line 79: @@
 === Validity ===
-The validity of all templates was checked by Mason and Quasar using [[MoHex]], in some cases manually supplying the winning move to Mohex. Bobson also checked the validity of VII1c and VII1b using the interactive [[HexProver]] software.
+The validity of all templates was checked by Mason and Quasar using [[MoHex]], in some cases manually supplying the winning move to Mohex. Bobson also checked the validity of the three templates using the interactive [[HexProver]] software.
 === Minimality ===

@@ Line 16: / Line 16: @@
 This template has width 17, and its [[carrier]] has size 84, including the red stone.
-While checking the minimality of [[edge template VII1c]], Comonoid first noticed on November 4 that [[Strategic advice from KataHex|KataHex]] seemed to indicate that the red stone was connected within this carrier. The validity and minimality of the template was subsequently verified using [[MoHex]], and the minimality proof was finished on November 6.
+While checking the minimality of [[edge template VII1c]], Comonoid first noticed on November 4 that [[KataHex]] seemed to indicate that the red stone was connected within this carrier. The validity and minimality of the template was subsequently verified using [[MoHex]], and the minimality proof was finished on November 6.
 === Edge template VII-1c ===

@@ Line 16: / Line 16: @@
 This template has width 17, and its [[carrier]] has size 84, including the red stone.
-While checking the minimality of [[edge template VII-1c]], Comonoid first noticed on November 4 that [[Strategic advice from KataHex|KataHex]] seemed to indicate that the red stone was connected within this carrier. The validity and minimality of the template was subsequently verified using [[MoHex]], and the minimality proof was finished on November 6.
+While checking the minimality of [[edge template VII1c]], Comonoid first noticed on November 4 that [[Strategic advice from KataHex|KataHex]] seemed to indicate that the red stone was connected within this carrier. The validity and minimality of the template was subsequently verified using [[MoHex]], and the minimality proof was finished on November 6.
 === Edge template VII-1c ===
@@ Line 73: / Line 73: @@
 This template has width 19, and its [[carrier]] has size 90, including the red stone.
-While checking the minimality of [[edge template VII-1c]], Comonoid first proposed that there might be a width-19 template if the carrier is wide enough. Comonoid, Quasar, and Mason came up with different carriers, and Mason described what turned out to be the final shape of the template on November 4 and proved its validity. Minimality was subsequently verified by a collaboration among several users, and the final case was finished by Quasar on November 17.
+While checking the minimality of [[edge template VII1c]], Comonoid first proposed that there might be a width-19 template if the carrier is wide enough. Comonoid, Quasar, and Mason came up with different carriers, and Mason described what turned out to be the final shape of the template on November 4 and proved its validity. Minimality was subsequently verified by a collaboration among several users, and the final case was finished by Quasar on November 17.
 == Methodology ==
@@ Line 85: / Line 85: @@
 Checking minimality is far more work than checking validity. In principle, one must sequentially remove each cell from the carrier (by placing a blue stone in it) and check that the resulting pattern is not connected, i.e., i.e., is a first-player win for Blue. However, due to symmetries and [[domination]], not all cells need to be checked. Specifically, if x dominates y from Blue's point of view, then if removing x from the carrier kept the template connected for Red, then removing y from the carrier would also keep the template connected. Therefore, if minimality has been confirmed with respect to y, then minimality does not need to be checked with respect to x.
-For example, to verify the minimality of [[edge template VII-1a]], only the shaded cells needed to be checked:
+For example, to verify the minimality of [[edge template VII1a]], only the shaded cells needed to be checked:
 <hexboard size="7x17"

@@ Line 14: / Line 14: @@
    />
-This template has width 17.
+This template has width 17, and its [[carrier]] has size 84, including the red stone.
 While checking the minimality of [[edge template VII-1c]], Comonoid first noticed on November 4 that [[Strategic advice from KataHex|KataHex]] seemed to indicate that the red stone was connected within this carrier. The validity and minimality of the template was subsequently verified using [[MoHex]], and the minimality proof was finished on November 6.
@@ Line 27: / Line 27: @@
    />
-This template has width 21.
+This template has width 21, and its [[carrier]] has size 98, including the red stone.
 After Eric Demer's discovery of [[edge template VI1b]] on October 6, Bobson noticed that this could likely be turned into a single-stone 7th row template. He found the first such pre-template of arbitrary width using HexProver on October 13. The pre-template was soon reduced to width 23 on October 14, as he realized that using edge template VI1b was not necessary.
@@ Line 71: / Line 71: @@
    />
-This template has width 19.
+This template has width 19, and its [[carrier]] has size 90, including the red stone.
 While checking the minimality of [[edge template VII-1c]], Comonoid first proposed that there might be a width-19 template if the carrier is wide enough. Comonoid, Quasar, and Mason came up with different carriers, and Mason described what turned out to be the final shape of the template on November 4 and proved its validity. Minimality was subsequently verified by a collaboration among several users, and the final case was finished by Quasar on November 17.

@@ Line 79: / Line 79: @@
 === Validity ===
-The validity of VII1b and VII1a was checked by Mason using [[MoHex]], in some cases manually supplying the winning move to Mohex. Bobson also checked the validity of VII1c and VII1b using the interactive [[HexProver]] software.
+The validity of all templates was checked by Mason and Quasar using [[MoHex]], in some cases manually supplying the winning move to Mohex. Bobson also checked the validity of VII1c and VII1b using the interactive [[HexProver]] software.
 === Minimality ===

@@ Line 5: / Line 5: @@
 In chronological order:
-=== Edge template VII-1c ===
+=== Edge template VII-1a ===
 <hexboard size="7x21"
@@ Line 48: / Line 59: @@
 MoHex shows that every intrusions other than * are solvable within this carrier. On the other hand, Bobson found that intrusions at * can be solved within width 21, so the pre-template was then reduced to width 21 on October 27. The minimality was checked by a collaborative effort using [[MoHex]] (patched version made by Comonoid and Quasar so that it can be run on a 23×23 board), and was finally verified on November 8.
 === Edge template VII-1b ===

@@ Line 13: / Line 13: @@
    contents="R n1"
    />
 After Eric Demer's discovery of [[edge template VI1b]] on October 6, Bobson noticed that this could likely be turned into a single-stone 7th row template. He found the first such pre-template of arbitrary width using HexProver on October 13. The pre-template was soon reduced to width 23 on October 14, as he realized that using edge template VI1b was not necessary.
@@ Line 55: / Line 57: @@
    contents="R l1"
    />
 While checking the minimality of [[edge template VII-1c]], Comonoid first noticed on November 4 that [[Strategic advice from KataHex|KataHex]] seemed to indicate that the red stone was connected within this carrier. The validity and minimality of the template was subsequently verified using [[MoHex]], and the minimality proof was finished on November 6.
@@ Line 66: / Line 70: @@
    contents="R m1"
    />
 While checking the minimality of [[edge template VII-1c]], Comonoid first proposed that there might be a width-19 template if the carrier is wide enough. Comonoid, Quasar, and Mason came up with different carriers, and Mason described what turned out to be the final shape of the template on November 4 and proved its validity. Minimality was subsequently verified by a collaboration among several users, and the final case was finished by Quasar on November 17.