GOs - 希尔伯特空间高维围棋 (Hilbert Space Go)

English | 中文

GOs 是一款运行在 VS Code 中的硬核策略小游戏插件。它将传统的二维围棋（Weiqi/Go）在数学和物理概念上进行了极致的拓展，将对局舞台延伸到了从零维到十一维的希尔伯特空间 (Hilbert Space)。

准备好燃烧你的大脑，在多维空间中进行布局与绞杀了吗？

GitHub: github.com/23J1633

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核心特性

• 多维自由度：支持从 0维 到 11维 的空间维度配置。
• 自定义棋盘：支持多种棋盘尺寸（3, 5, 7, 9, 13, 15, 17, 19）。
• 现代化界面：基于 VS Code 主题变量的原生风格 UI，支持中英文切换。
• 原生侧边栏交互：专属的侧边栏视图，提供创建对局、坐标输入、落子记录、提子计数等功能。
• 三维棋盘渲染：
  • 鼠标拖拽旋转、滚轮缩放。
  • 三维坐标轴指示器（X/Y/Z），实时跟随旋转方向。
  • 深度排序渲染，支持透明度渐变。
  • 底部缩放控制栏（缩放按钮、百分比输入、Fit 适配、1:1 原始比例）。
• 高维棋盘支持：
  • 维度 >= 3 时可用 3D 视图，通过切片导航器控制更高维度坐标。
  • 切片导航器统一显示在视图顶部。
  • 2D 视图支持在当前切片直接点击落子，自动映射到完整 N 维坐标。
  • 矩阵视图展示原始数据。
• 二维棋盘交互增强：
  • Ctrl + 鼠标滚轮缩放，支持 17 级缩放档位（25% ~ 500%）。
  • 底部缩放控制栏，可手动输入缩放比例，支持 Fit 适配和 1:1 原始比例。
  • 棋盘默认居中显示，支持鼠标拖拽平移。
• 键盘快捷键：
  • 双击单键循环切换视图（默认 q：2D → 3D → Matrix → 2D）。
  • 双击单键反向循环切换视图（默认 w：2D → Matrix → 3D → 2D）。
  • 快捷键可在设置中自定义为任意单字符。
• 严谨的围棋算法：根据空间维度动态计算"气"（Liberties），完美支持多维空间的提子规则。
• AI 对战模式：
  • 支持 PVP（人人对战）和 PVE（人机对战）两种模式。
  • 集成 AI Core 扩展，支持 OpenAI、Claude、Gemini 等多种 AI 提供商。
  • 4 个难度等级：简单（初学者）、普通（业余爱好者）、高手（业余5段）、大师（职业九段）。
  • AI 可执黑（先手）或执白（后手），灵活配置。
  • AI 思考时显示状态提示，落子后自动更新棋盘。
• 劫规则（Ko Rule）：完整实现围棋劫争规则，禁止立即回提同一劫。
• 实时文件持久化：所有对局状态以 JSON 格式实时保存在本地文件夹中。
• 最近对局记录：自动保存最近打开的对局，一键继续。
• 默认保存路径：在设置中配置默认保存路径，创建对局时自动填入，游戏名自动递增（Game1, Game2, ...）。
• 设置页面：
  • 语言切换（中文/English）。
  • 默认保存路径配置（支持浏览选择）。
  • 视图切换快捷键自定义。
  • 对局模式切换（PVP/PVE）。
  • AI 难度设置。
  • AI 模型选择与配置。

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玩法指引

1. 创建对局

1. 在 VS Code 左侧活动栏点击 GOs 图标，打开插件侧边栏。
2. 点击右上角齿轮图标进入设置页面，可切换语言、配置默认保存路径和自定义快捷键。
3. 点击 "创建新对局"。
4. 在配置页面中输入：
   • 对局名称：默认自动生成（Game1, Game2, ...），可自定义。
   • 保存位置：自动填入默认路径，可修改。
   • 维度：输入 0 到 11 之间的整数。
   • 棋盘大小：从下拉列表选择（3x3 到 19x19）。
   • AI 设置（PVE 模式）：选择 AI 执棋颜色和 AI 模型。
5. 点击 "开始对局" 进入对局。

提示：如需 AI 对战，请先在设置页面切换到 PVE 模式，并配置 AI 难度和模型。首次使用需安装 AI Core 扩展并配置 API 密钥。

2. 进行对弈

• 右侧自动弹出棋盘面板，左侧边栏显示操作面板。
• 黑棋先手（记为 1），白棋后手（记为 -1），空位为 0。
• 落子方式：
  • 在侧边栏输入坐标（逗号分隔，位数与维度一致，如三维输入 2,5,8）。
  • 在 2D 棋盘上直接点击落子（高维棋盘会映射到当前切片坐标）。
  • 在 3D 棋盘上点击最近的空位落子。
• 每次落子后，侧边栏实时更新提子数和落子记录。

3. 视图切换

• 2D 视图：经典棋盘网格，支持点击落子。高维棋盘通过切片导航器选择显示哪个二维切片。
• 3D 视图（维度 >= 3）：三维层级渲染，鼠标拖拽旋转、滚轮缩放。右下角显示坐标轴指示器。
• Matrix 视图：原始矩阵数据展示。
• 快捷键切换：双击 q 正向循环（2D → 3D → Matrix），双击 w 反向循环。可在设置中自定义按键。

4. 棋盘操作

• 缩放：Ctrl + 鼠标滚轮缩放，或使用底部缩放控制栏。
• 平移：缩放后棋盘超出视口时，鼠标拖拽平移查看。
• 适配：点击 Fit 按钮自动适配视口大小，点击 1:1 恢复原始比例。

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高维围棋规则

传统围棋的规则被严格类推到 N 维空间：

• 气的计算：一颗棋子的相邻正交点称为"气"。
  • 1维：2 口气
  • 2维：4 口气（上下左右）
  • 3维：6 口气（上下左右前后）
  • N维：2N 口气
• 吃子：当一块相连的同色棋子的所有"气"都被对手占据时，这块棋子将被提掉并计入俘虏。
• 禁着点：禁止自杀，除非该步落子能同时提掉对方的棋子。
• 劫规则：禁止立即回提同一劫（Ko），防止无限循环。当一方提子后，对方不能立即提回同一位置。
• 贴目：白方获得贴目补偿（大棋盘 6.5 目，小棋盘 3.5 目），确保公平性。

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数据存储说明

创建对局后，会在指定目录下生成以对局名称命名的文件夹，包含：

1. config.json：对局元数据（名称、维度、棋盘大小、创建时间）。
2. GOs.json：N 维嵌套数组，黑子为 1，白子为 -1，空位为 0。
3. history.json：逐手记录（步数、落子方、坐标、提子列表）。

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棋盘内存与存储分析

数据结构

type Tensor = number | Tensor[];

棋盘是一个递归嵌套的数组结构：

• 0维：一个数字 0
• 1维：[0, 0, ..., 0]（s 个元素）
• d维：s 个 (d-1)维 Tensor 的数组

总交叉点数 = size^dimension

内存计算（JavaScript/V8 引擎）

在 V8 引擎中：

• 数字 0、1、-1 是 SMI（Small Integer），内联存储在数组槽中，不额外占堆内存
• 每个数组对象开销：56 字节（对象头）+ 8 字节 × 元素数（指针槽位）
• 数组总数（维度 d，大小 s）：A = (s^d - 1) / (s - 1)（s > 1 时）

内存(d, s) = A(d, s) × (56 + 8 × s)
其中 A(d, s) = (s^d - 1) / (s - 1)   (s > 1)
          A(d, 1) = d

以下所有数值为空棋盘（全部为 0）的内存占用。放置棋子后内存不变（SMI 0/1/-1 大小相同）。

size = 1

维度	交叉点数	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	1	1	64	64 B
2	1	2	128	128 B
3	1	3	192	192 B
4	1	4	256	256 B
5	1	5	320	320 B
6	1	6	384	384 B
7	1	7	448	448 B
8	1	8	512	512 B
9	1	9	576	576 B
10	1	10	640	640 B
11	1	11	704	704 B

size = 3

维度	交叉点数 (3^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	3	1	80	80 B
2	9	4	320	320 B
3	27	13	1,040	~1.0 KB
4	81	40	3,200	~3.1 KB
5	243	121	9,680	~9.5 KB
6	729	364	29,120	~28.4 KB
7	2,187	1,093	87,440	~85.4 KB
8	6,561	3,280	262,400	~256.3 KB
9	19,683	9,841	787,280	~768.8 KB
10	59,049	29,524	2,361,920	~2.25 MB
11	177,147	88,573	7,085,840	~6.76 MB

size = 5

维度	交叉点数 (5^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	5	1	96	96 B
2	25	6	576	576 B
3	125	31	2,976	~2.9 KB
4	625	156	14,976	~14.6 KB
5	3,125	781	74,976	~73.2 KB
6	15,625	3,906	374,976	~366.2 KB
7	78,125	19,531	1,874,976	~1.79 MB
8	390,625	97,656	9,374,976	~8.94 MB
9	1,953,125	488,281	46,874,976	~44.7 MB
10	9,765,625	2,441,406	234,374,976	~223.5 MB
11	48,828,125	12,207,031	1,171,874,976	~1.09 GB

size = 7

维度	交叉点数 (7^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	7	1	112	112 B
2	49	8	896	896 B
3	343	57	6,384	~6.2 KB
4	2,401	400	44,800	~43.8 KB
5	16,807	2,801	313,712	~306.4 KB
6	117,649	19,608	2,196,096	~2.09 MB
7	823,543	137,257	15,372,784	~14.66 MB
8	5,764,801	960,800	107,609,600	~102.6 MB
9	40,353,607	6,725,601	753,267,312	~718.4 MB
10	282,475,249	47,079,208	5,272,871,296	~4.91 GB
11	1,977,326,743	329,554,457	36,910,099,184	~34.38 GB

size = 9

维度	交叉点数 (9^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	9	1	128	128 B
2	81	10	1,280	~1.3 KB
3	729	91	11,648	~11.4 KB
4	6,561	820	104,960	~102.5 KB
5	59,049	7,381	944,768	~922.6 KB
6	531,441	66,430	8,503,040	~8.11 MB
7	4,782,969	597,871	76,527,488	~73.0 MB
8	43,046,721	5,380,840	688,747,520	~656.9 MB
9	387,420,489	48,427,561	6,198,727,808	~5.77 GB
10	3,486,784,401	435,848,050	55,788,550,400	~51.96 GB
11	31,381,059,609	3,922,632,451	502,096,953,728	~467.6 GB

size = 13

维度	交叉点数 (13^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	13	1	160	160 B
2	169	14	2,240	~2.2 KB
3	2,197	183	29,280	~28.6 KB
4	28,561	2,380	380,800	~371.9 KB
5	371,293	30,941	4,950,560	~4.72 MB
6	4,826,809	402,234	64,357,440	~61.4 MB
7	62,748,517	5,229,043	836,646,880	~798.0 MB
8	815,730,721	67,977,560	10,876,409,600	~10.13 GB
9	10,604,499,373	883,708,282	141,393,325,120	~131.7 GB
10	137,858,491,849	11,488,207,658	~1.84 TB	~1.84 TB
11	1,792,160,394,037	149,346,699,507	~23.9 TB	~23.9 TB

size = 15

维度	交叉点数 (15^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	15	1	176	176 B
2	225	16	2,816	~2.7 KB
3	3,375	241	42,416	~41.4 KB
4	50,625	3,616	636,416	~621.5 KB
5	759,375	54,241	9,546,416	~9.10 MB
6	11,390,625	813,616	143,196,416	~136.6 MB
7	170,859,375	12,204,241	2,147,946,416	~2.00 GB
8	2,562,890,625	183,063,616	32,219,328,416	~30.0 GB
9	38,443,359,375	2,745,954,241	~483.3 GB	~483.3 GB
10	576,650,390,625	41,189,313,616	~7.25 TB	~7.25 TB
11	8,649,755,859,375	617,839,704,241	~108.7 TB	~108.7 TB

size = 17

维度	交叉点数 (17^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	17	1	192	192 B
2	289	18	3,456	~3.4 KB
3	4,913	307	58,944	~57.6 KB
4	83,521	5,220	997,920	~974.5 KB
5	1,419,857	88,741	16,964,640	~16.2 MB
6	24,137,569	1,508,598	288,649,248	~275.3 MB
7	410,338,673	25,646,167	4,907,041,104	~4.57 GB
8	6,975,757,441	435,984,840	~83.4 GB	~83.4 GB
9	118,587,876,497	7,411,742,281	~1.42 TB	~1.42 TB
10	2,015,993,900,449	~1.26×10^11	~24.1 TB	~24.1 TB
11	34,271,896,307,633	~2.14×10^12	~410 TB	~410 TB

size = 19（标准围棋棋盘大小）

维度	交叉点数 (19^d)	数组数	内存 (bytes)	内存 (可读)
0	1	0	0	0 B
1	19	1	208	208 B
2	361	20	4,160	~4.1 KB
3	6,859	381	79,248	~77.4 KB
4	130,321	7,240	1,505,920	~1.44 MB
5	2,476,099	137,561	28,612,688	~27.3 MB
6	47,045,881	2,613,660	543,641,280	~518.5 MB
7	893,871,739	49,659,541	10,329,184,528	~9.62 GB
8	16,983,563,041	943,531,280	~196.3 GB	~196.3 GB
9	322,687,697,779	~1.79×10^10	~3.73 TB	~3.73 TB
10	6,131,066,257,801	~3.41×10^11	~70.8 TB	~70.8 TB
11	116,490,258,898,219	~6.47×10^12	~1.35 PB	~1.35 PB

存储计算（JSON 文件）

棋盘存储在 GOs.json 中，使用紧凑 JSON（无缩进）。

f(0) = 1 字节                           // "0"
f(d) = s × f(d-1) + s + 1 字节          // d >= 1

推导：一个 s 元素数组的 JSON 表示为 [elem1,elem2,...,elemN]， 即 1（[）+ s 个子元素 + (s-1) 个逗号 + 1（]）= s×f(d-1) + s + 1

size = 1

维度	存储 (bytes)
0~11	1~23（极小）

size = 3

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	3	7	7 B
2	9	25	25 B
3	27	79	79 B
4	81	241	241 B
5	243	727	727 B
6	729	2,185	~2.1 KB
7	2,187	6,559	~6.4 KB
8	6,561	19,681	~19.2 KB
9	19,683	59,047	~57.7 KB
10	59,049	177,145	~173.0 KB
11	177,147	531,439	~519.0 KB

size = 5

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	5	11	11 B
2	25	61	61 B
3	125	311	311 B
4	625	1,561	~1.5 KB
5	3,125	7,811	~7.6 KB
6	15,625	39,061	~38.1 KB
7	78,125	195,311	~190.7 KB
8	390,625	976,561	~953.7 KB
9	1,953,125	4,882,811	~4.66 MB
10	9,765,625	24,414,061	~23.3 MB
11	48,828,125	122,070,311	~116.4 MB

size = 7

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	7	15	15 B
2	49	113	113 B
3	343	799	799 B
4	2,401	5,601	~5.5 KB
5	16,807	39,215	~38.3 KB
6	117,649	274,513	~268.1 KB
7	823,543	1,921,599	~1.83 MB
8	5,764,801	13,451,201	~12.8 MB
9	40,353,607	94,158,415	~89.8 MB
10	282,475,249	659,108,913	~628.6 MB
11	1,977,326,743	4,613,762,399	~4.30 GB

size = 9

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	9	19	19 B
2	81	181	181 B
3	729	1,639	~1.6 KB
4	6,561	14,761	~14.4 KB
5	59,049	132,859	~129.7 KB
6	531,441	1,195,741	~1.14 MB
7	4,782,969	10,761,679	~10.26 MB
8	43,046,721	96,855,121	~92.4 MB
9	387,420,489	871,696,099	~831.3 MB
10	3,486,784,401	7,845,264,901	~7.31 GB
11	31,381,059,609	70,607,384,119	~65.8 GB

size = 13

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	13	27	27 B
2	169	361	361 B
3	2,197	4,699	~4.6 KB
4	28,561	61,093	~59.7 KB
5	371,293	794,215	~775.6 KB
6	4,826,809	10,324,801	~9.85 MB
7	62,748,517	134,222,419	~128.0 MB
8	815,730,721	1,744,891,453	~1.62 GB
9	10,604,499,373	22,683,588,893	~21.1 GB
10	137,858,491,849	~295 GB	~295 GB
11	1,792,160,394,037	~3.8 TB	~3.8 TB

size = 15

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	15	31	31 B
2	225	481	481 B
3	3,375	7,231	~7.1 KB
4	50,625	108,481	~106.0 KB
5	759,375	1,627,231	~1.55 MB
6	11,390,625	24,408,481	~23.3 MB
7	170,859,375	366,127,231	~349.2 MB
8	2,562,890,625	5,491,908,481	~5.11 GB
9	38,443,359,375	~82.4 GB	~82.4 GB
10	576,650,390,625	~1.2 TB	~1.2 TB
11	8,649,755,859,375	~18 TB	~18 TB

size = 17

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	17	35	35 B
2	289	611	611 B
3	4,913	10,411	~10.2 KB
4	83,521	176,993	~172.8 KB
5	1,419,857	3,008,899	~2.87 MB
6	24,137,569	51,151,297	~48.8 MB
7	410,338,673	869,572,063	~829.3 MB
8	6,975,757,441	~14.8 GB	~14.8 GB
9	118,587,876,497	~251 GB	~251 GB
10	2,015,993,900,449	~4.3 TB	~4.3 TB
11	34,271,896,307,633	~73 TB	~73 TB

size = 19（标准围棋棋盘大小）

维度	交叉点数	JSON 大小 (bytes)	可读
0	1	1	1 B
1	19	39	39 B
2	361	761	761 B
3	6,859	14,479	~14.1 KB
4	130,321	275,121	~268.7 KB
5	2,476,099	5,227,319	~4.99 MB
6	47,045,881	99,319,081	~94.7 MB
7	893,871,739	1,887,062,559	~1.76 GB
8	16,983,563,041	~33.4 GB	~33.4 GB
9	322,687,697,779	~635 GB	~635 GB
10	6,131,066,257,801	~12 TB	~12 TB
11	116,490,258,898,219	~228 TB	~228 TB

综合速查表（推荐配置）

以下列出每个维度下推荐的最大棋盘大小（内存 < 1 GB，存储 < 1 GB 的范围）：

维度	推荐最大 size	交叉点数	内存	存储
0	任意	1	~0 B	1 B
1	任意	≤19	≤208 B	≤39 B
2	任意	≤361	≤4.1 KB	≤761 B
3	19	6,859	~77 KB	~14 KB
4	19	130,321	~1.4 MB	~269 KB
5	19	2,476,099	~27 MB	~5.0 MB
6	19	47,045,881	~519 MB	~95 MB
7	9~13	4.7M~62.7M	73~798 MB	10~128 MB
8	5~9	390K~43M	9~657 MB	1~92 MB
9	5~7	59K~40M	45~718 MB	5~90 MB
10	3~5	59K~9.8M	2.2~224 MB	173 KB~23 MB
11	3~5	177K~48.8M	6.8 MB~1.1 GB	519 KB~116 MB

其他开销

除棋盘外，游戏运行时还有以下额外开销（相比棋盘可忽略不计）：

数据	说明
config.json	游戏配置，~200 bytes
history.json	落子历史，每步 ~80 bytes，最多 s^d 步
GameHistoryItem[] 内存	每个对象 ~120 bytes + 坐标数组
其他游戏状态	captures、currentPlayer 等，~100 bytes

注意：history.json 的最大理论大小 = s^d × 80 bytes。在高维大棋盘下，历史记录也可能成为显著的存储负担。

结论

• 低维（0-4维）：所有 size 均可正常使用，内存和存储开销极小
• 中维（5-6维）：使用 size ≤ 19 仍可接受（~500 MB 内存上限）
• 高维（7-9维）：需要缩小 size 至 5~9 才能在普通电脑上运行
• 超高维（10-11维）：仅 size = 3~5 可行，且 11维 + size=5 需要约 1 GB 内存

---

系统要求

• Visual Studio Code 1.80.0 或更高版本。
• 高维度大棋盘可能消耗较多内存，建议从低维度开始体验。

---

发行说明

2.0.0

• 新增 AI 对战模式（PVE），支持与 AI 进行围棋对弈。
• 集成 AI Core 扩展，支持 OpenAI、Claude、Gemini 等多种 AI 提供商。
• 新增 4 个 AI 难度等级：简单（初学者）、普通（业余爱好者）、高手（业余5段）、大师（职业九段）。
• 新增 AI 执棋颜色选择（黑棋/白棋）。
• 新增 AI 思考状态显示和落子提示。
• 新增劫规则（Ko Rule），禁止立即回提同一劫。
• 新增贴目系统，白方获得贴目补偿。
• 优化对局模式选择界面，支持 PVP/PVE 切换。
• 新增 AI 模型配置界面，可从设置页面直接打开 AI Core 配置。

0.0.2

• 新增设置页面：语言切换、默认保存路径、视图切换快捷键自定义。
• 新增默认保存路径配置，创建对局时自动填入，游戏名自动递增（Game1, Game2, ...）。
• 新增三维坐标轴指示器（X/Y/Z），实时跟随旋转方向。
• 新增 2D 棋盘缩放（Ctrl+滚轮、17 级档位）、平移（拖拽）、底部缩放控制栏。
• 新增 3D 视图底部缩放控制栏。
• 新增双击单键循环切换视图功能（默认 q 正向、w 反向，可自定义）。
• 优化 3D 旋转操作逻辑，鼠标拖拽方向与视角旋转方向一致。
• 优化切片导航器位置，统一显示在视图顶部。
• 优化 2D 棋盘默认居中显示。
• 优化 3D 棋子大小一致性，不随深度缩放。
• 修复游戏结束图标在切换对局后残留的问题。
• 修复高维棋盘 3D 视图可用性（维度 >= 3 即可使用）。

0.0.1

• 初始版本发布。
• 实现 0-11 维矩阵状态系统与文件存取。
• 实装高维空间的"气"与提子算法。
• 实现 Webview 棋盘渲染与侧边栏交互。
• 支持中英文语言切换。
• 支持三维棋盘旋转/缩放及坐标轴指示器。
• 支持高维 3D 视图与切片导航。
• 支持默认保存路径与自动递增游戏名。

---

Enjoy conquering the Hilbert Space!

---

---

---

GOs - Hilbert Space Go

English | 中文

GOs is a hardcore strategy game extension for VS Code. It extends the traditional 2D game of Go (Weiqi) into the mathematical realm of Hilbert Spaces, supporting gameplay across 0 to 11 dimensions.

Ready to challenge your brain with multi-dimensional territory battles?

GitHub: github.com/23J1633

---

Features

• Multi-Dimensional Freedom: Configure game spaces from 0D to 11D.
• Custom Board Sizes: Choose from 3x3 to 19x19.
• Modern UI: Native VS Code theme-integrated interface with Chinese/English language support.
• Sidebar Interaction: Dedicated sidebar for game creation, coordinate input, move history, and capture counts.
• 3D Board Rendering:
  • Mouse drag rotation and scroll zoom.
  • Real-time XYZ axis indicator that follows rotation.
  • Depth-sorted rendering with transparency gradients.
  • Bottom zoom control bar (zoom buttons, percentage input, Fit, 1:1 reset).
• High-Dimensional Board Support:
  • 3D view available for dimensions >= 3, with a slice navigator for higher dimensions.
  • Slice navigator displayed at the top of the view.
  • 2D view supports click-to-place on the current slice, automatically mapping to full N-dimensional coordinates.
  • Matrix view for raw data visualization.
• Enhanced 2D Board Interaction:
  • Ctrl + mouse wheel zoom with 17 zoom levels (25% ~ 500%).
  • Bottom zoom control bar with manual percentage input, Fit and 1:1 buttons.
  • Board centered by default, supports mouse drag panning.
• Keyboard Shortcuts:
  • Double-press single key to cycle views (default q: 2D → 3D → Matrix → 2D).
  • Double-press single key to reverse-cycle views (default w: 2D → Matrix → 3D → 2D).
  • Keys are fully customizable in settings.
• Rigorous Go Algorithm: Dynamically calculates liberties based on spatial dimension, with full capture rule support.
• AI Battle Mode:
  • Supports PVP (Player vs Player) and PVE (Player vs AI) modes.
  • Integrates AI Core extension with support for OpenAI, Claude, Gemini and other AI providers.
  • 4 difficulty levels: Easy (Beginner), Normal (Club Player), Hard (5-dan Amateur), Master (Professional 9-dan).
  • AI can play as Black (first) or White (second), with flexible configuration.
  • AI thinking status display and automatic board update after moves.
• Ko Rule: Full implementation of Go ko rule, preventing immediate recapture.
• Real-time File Persistence: All game states saved as JSON in local folders.
• Recent Games: Automatically tracks recently opened games for quick access.
• Default Save Path: Configure a default save directory in settings. Game names auto-increment (Game1, Game2, ...).
• Settings Page:
  • Language switching (Chinese/English).
  • Default save path configuration (with browse support).
  • View switch shortcut customization.
  • Game mode switching (PVP/PVE).
  • AI difficulty settings.
  • AI model selection and configuration.

---

How to Play

1. Create a Game

1. Click the GOs icon in the VS Code activity bar to open the sidebar.
2. Click the gear icon (top-right) to access Settings for language, default save path, and shortcut configuration.
3. Click "Create New Game".
4. Configure:
   • Game Name: Auto-generated (Game1, Game2, ...), customizable.
   • Save Location: Pre-filled from default path, editable.
   • Dimension: Enter a number between 0 and 11.
   • Board Size: Select from the dropdown (3x3 to 19x19).
   • AI Settings (PVE mode): Select AI color and AI model.
5. Click "Start Game".

Tip: For AI battles, first switch to PVE mode in settings and configure AI difficulty and model. First-time use requires installing the AI Core extension and configuring API keys.

2. Play

• The board panel opens on the right; the sidebar shows the control panel.
• Black plays first (encoded as 1), White second (-1), empty as 0.
• Place stones by:
  • Entering coordinates in the sidebar (comma-separated, matching dimension count, e.g. 2,5,8 for 3D).
  • Clicking directly on the 2D board (maps to the current slice in high-dimensional games).
  • Clicking the nearest empty cell on the 3D board.
• The sidebar updates capture counts and move history in real-time after each move.

3. View Modes

• 2D View: Classic board grid with click-to-place. High-dimensional boards use a slice navigator to select the displayed 2D slice.
• 3D View (dimensions >= 3): Layered 3D rendering with mouse rotation and zoom. Axis indicator in the bottom-right corner.
• Matrix View: Raw matrix data display.
• Shortcut Switching: Double-press q to cycle forward (2D → 3D → Matrix), double-press w to cycle backward. Keys are customizable in settings.

4. Board Interaction

• Zoom: Ctrl + mouse wheel, or use the bottom zoom control bar.
• Pan: After zooming, drag the board to pan around.
• Fit: Click the Fit button to auto-fit the board to the viewport, or 1:1 to reset to original size.

---

Rules of N-Dimensional Go

Traditional Go rules are strictly generalized to N dimensions:

• Liberties: Adjacent orthogonal points of a stone.
  • 1D: 2 liberties
  • 2D: 4 liberties (up, down, left, right)
  • 3D: 6 liberties (up, down, left, right, front, back)
  • N-dimensional: 2N liberties
• Capture: When all liberties of a connected group of same-color stones are occupied by the opponent, the entire group is removed and counted as captured.
• Suicide Rule: Self-capture is forbidden unless the move simultaneously captures opponent stones.
• Ko Rule: Prevents immediate recapture of the same ko, avoiding infinite loops. After one player captures, the opponent cannot immediately recapture at the same position.
• Komi: White receives compensation points (6.5 for large boards, 3.5 for small boards) to ensure fairness.

---

Data Storage

Each game creates a folder containing:

1. config.json: Game metadata (name, dimension, board size, creation time).
2. GOs.json: N-dimensional nested array. Black = 1, White = -1, Empty = 0.
3. history.json: Per-move log (step number, player, coordinates, captured stones).

---

Board Memory & Storage Analysis

Data Structure

type Tensor = number | Tensor[];

The board is a recursively nested array:

• 0D: A single number 0
• 1D: [0, 0, ..., 0] (s elements)
• dD: An array of s (d-1)-dimensional Tensors

Total intersection points = size^dimension

Memory Calculation (JavaScript/V8 Engine)

In the V8 engine:

• Numbers 0, 1, -1 are SMI (Small Integers), stored inline in array slots with no extra heap allocation
• Per-array overhead: 56 bytes (object header) + 8 bytes x element count (pointer slots)
• Total arrays (dimension d, size s): A = (s^d - 1) / (s - 1) (for s > 1)

Memory(d, s) = A(d, s) x (56 + 8 x s)
where A(d, s) = (s^d - 1) / (s - 1)   (s > 1)
          A(d, 1) = d

All values below are for an empty board (all zeros). Memory does not change after placing stones (SMI 0/1/-1 are the same size).

size = 1

Dimension	Intersections	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	1	1	64	64 B
2	1	2	128	128 B
3	1	3	192	192 B
4	1	4	256	256 B
5	1	5	320	320 B
6	1	6	384	384 B
7	1	7	448	448 B
8	1	8	512	512 B
9	1	9	576	576 B
10	1	10	640	640 B
11	1	11	704	704 B

size = 3

Dimension	Intersections (3^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	3	1	80	80 B
2	9	4	320	320 B
3	27	13	1,040	~1.0 KB
4	81	40	3,200	~3.1 KB
5	243	121	9,680	~9.5 KB
6	729	364	29,120	~28.4 KB
7	2,187	1,093	87,440	~85.4 KB
8	6,561	3,280	262,400	~256.3 KB
9	19,683	9,841	787,280	~768.8 KB
10	59,049	29,524	2,361,920	~2.25 MB
11	177,147	88,573	7,085,840	~6.76 MB

size = 5

Dimension	Intersections (5^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	5	1	96	96 B
2	25	6	576	576 B
3	125	31	2,976	~2.9 KB
4	625	156	14,976	~14.6 KB
5	3,125	781	74,976	~73.2 KB
6	15,625	3,906	374,976	~366.2 KB
7	78,125	19,531	1,874,976	~1.79 MB
8	390,625	97,656	9,374,976	~8.94 MB
9	1,953,125	488,281	46,874,976	~44.7 MB
10	9,765,625	2,441,406	234,374,976	~223.5 MB
11	48,828,125	12,207,031	1,171,874,976	~1.09 GB

size = 7

Dimension	Intersections (7^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	7	1	112	112 B
2	49	8	896	896 B
3	343	57	6,384	~6.2 KB
4	2,401	400	44,800	~43.8 KB
5	16,807	2,801	313,712	~306.4 KB
6	117,649	19,608	2,196,096	~2.09 MB
7	823,543	137,257	15,372,784	~14.66 MB
8	5,764,801	960,800	107,609,600	~102.6 MB
9	40,353,607	6,725,601	753,267,312	~718.4 MB
10	282,475,249	47,079,208	5,272,871,296	~4.91 GB
11	1,977,326,743	329,554,457	36,910,099,184	~34.38 GB

size = 9

Dimension	Intersections (9^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	9	1	128	128 B
2	81	10	1,280	~1.3 KB
3	729	91	11,648	~11.4 KB
4	6,561	820	104,960	~102.5 KB
5	59,049	7,381	944,768	~922.6 KB
6	531,441	66,430	8,503,040	~8.11 MB
7	4,782,969	597,871	76,527,488	~73.0 MB
8	43,046,721	5,380,840	688,747,520	~656.9 MB
9	387,420,489	48,427,561	6,198,727,808	~5.77 GB
10	3,486,784,401	435,848,050	55,788,550,400	~51.96 GB
11	31,381,059,609	3,922,632,451	502,096,953,728	~467.6 GB

size = 13

Dimension	Intersections (13^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	13	1	160	160 B
2	169	14	2,240	~2.2 KB
3	2,197	183	29,280	~28.6 KB
4	28,561	2,380	380,800	~371.9 KB
5	371,293	30,941	4,950,560	~4.72 MB
6	4,826,809	402,234	64,357,440	~61.4 MB
7	62,748,517	5,229,043	836,646,880	~798.0 MB
8	815,730,721	67,977,560	10,876,409,600	~10.13 GB
9	10,604,499,373	883,708,282	141,393,325,120	~131.7 GB
10	137,858,491,849	11,488,207,658	~1.84 TB	~1.84 TB
11	1,792,160,394,037	149,346,699,507	~23.9 TB	~23.9 TB

size = 15

Dimension	Intersections (15^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	15	1	176	176 B
2	225	16	2,816	~2.7 KB
3	3,375	241	42,416	~41.4 KB
4	50,625	3,616	636,416	~621.5 KB
5	759,375	54,241	9,546,416	~9.10 MB
6	11,390,625	813,616	143,196,416	~136.6 MB
7	170,859,375	12,204,241	2,147,946,416	~2.00 GB
8	2,562,890,625	183,063,616	32,219,328,416	~30.0 GB
9	38,443,359,375	2,745,954,241	~483.3 GB	~483.3 GB
10	576,650,390,625	41,189,313,616	~7.25 TB	~7.25 TB
11	8,649,755,859,375	617,839,704,241	~108.7 TB	~108.7 TB

size = 17

Dimension	Intersections (17^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	17	1	192	192 B
2	289	18	3,456	~3.4 KB
3	4,913	307	58,944	~57.6 KB
4	83,521	5,220	997,920	~974.5 KB
5	1,419,857	88,741	16,964,640	~16.2 MB
6	24,137,569	1,508,598	288,649,248	~275.3 MB
7	410,338,673	25,646,167	4,907,041,104	~4.57 GB
8	6,975,757,441	435,984,840	~83.4 GB	~83.4 GB
9	118,587,876,497	7,411,742,281	~1.42 TB	~1.42 TB
10	2,015,993,900,449	~1.26x10^11	~24.1 TB	~24.1 TB
11	34,271,896,307,633	~2.14x10^12	~410 TB	~410 TB

size = 19 (Standard Go board size)

Dimension	Intersections (19^d)	Arrays	Memory (bytes)	Memory (readable)
0	1	0	0	0 B
1	19	1	208	208 B
2	361	20	4,160	~4.1 KB
3	6,859	381	79,248	~77.4 KB
4	130,321	7,240	1,505,920	~1.44 MB
5	2,476,099	137,561	28,612,688	~27.3 MB
6	47,045,881	2,613,660	543,641,280	~518.5 MB
7	893,871,739	49,659,541	10,329,184,528	~9.62 GB
8	16,983,563,041	943,531,280	~196.3 GB	~196.3 GB
9	322,687,697,779	~1.79x10^10	~3.73 TB	~3.73 TB
10	6,131,066,257,801	~3.41x10^11	~70.8 TB	~70.8 TB
11	116,490,258,898,219	~6.47x10^12	~1.35 PB	~1.35 PB

Storage Calculation (JSON File)

The board is stored in GOs.json using compact JSON (no indentation).

f(0) = 1 byte                           // "0"
f(d) = s x f(d-1) + s + 1 bytes         // d >= 1

Derivation: A s-element array in JSON is [elem1,elem2,...,elemN], i.e. 1 ([) + s sub-elements + (s-1) commas + 1 (]) = sxf(d-1) + s + 1

size = 1

Dimension	Storage (bytes)
0~11	1~23 (negligible)

size = 3

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	3	7	7 B
2	9	25	25 B
3	27	79	79 B
4	81	241	241 B
5	243	727	727 B
6	729	2,185	~2.1 KB
7	2,187	6,559	~6.4 KB
8	6,561	19,681	~19.2 KB
9	19,683	59,047	~57.7 KB
10	59,049	177,145	~173.0 KB
11	177,147	531,439	~519.0 KB

size = 5

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	5	11	11 B
2	25	61	61 B
3	125	311	311 B
4	625	1,561	~1.5 KB
5	3,125	7,811	~7.6 KB
6	15,625	39,061	~38.1 KB
7	78,125	195,311	~190.7 KB
8	390,625	976,561	~953.7 KB
9	1,953,125	4,882,811	~4.66 MB
10	9,765,625	24,414,061	~23.3 MB
11	48,828,125	122,070,311	~116.4 MB

size = 7

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	7	15	15 B
2	49	113	113 B
3	343	799	799 B
4	2,401	5,601	~5.5 KB
5	16,807	39,215	~38.3 KB
6	117,649	274,513	~268.1 KB
7	823,543	1,921,599	~1.83 MB
8	5,764,801	13,451,201	~12.8 MB
9	40,353,607	94,158,415	~89.8 MB
10	282,475,249	659,108,913	~628.6 MB
11	1,977,326,743	4,613,762,399	~4.30 GB

size = 9

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	9	19	19 B
2	81	181	181 B
3	729	1,639	~1.6 KB
4	6,561	14,761	~14.4 KB
5	59,049	132,859	~129.7 KB
6	531,441	1,195,741	~1.14 MB
7	4,782,969	10,761,679	~10.26 MB
8	43,046,721	96,855,121	~92.4 MB
9	387,420,489	871,696,099	~831.3 MB
10	3,486,784,401	7,845,264,901	~7.31 GB
11	31,381,059,609	70,607,384,119	~65.8 GB

size = 13

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	13	27	27 B
2	169	361	361 B
3	2,197	4,699	~4.6 KB
4	28,561	61,093	~59.7 KB
5	371,293	794,215	~775.6 KB
6	4,826,809	10,324,801	~9.85 MB
7	62,748,517	134,222,419	~128.0 MB
8	815,730,721	1,744,891,453	~1.62 GB
9	10,604,499,373	22,683,588,893	~21.1 GB
10	137,858,491,849	~295 GB	~295 GB
11	1,792,160,394,037	~3.8 TB	~3.8 TB

size = 15

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	15	31	31 B
2	225	481	481 B
3	3,375	7,231	~7.1 KB
4	50,625	108,481	~106.0 KB
5	759,375	1,627,231	~1.55 MB
6	11,390,625	24,408,481	~23.3 MB
7	170,859,375	366,127,231	~349.2 MB
8	2,562,890,625	5,491,908,481	~5.11 GB
9	38,443,359,375	~82.4 GB	~82.4 GB
10	576,650,390,625	~1.2 TB	~1.2 TB
11	8,649,755,859,375	~18 TB	~18 TB

size = 17

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	17	35	35 B
2	289	611	611 B
3	4,913	10,411	~10.2 KB
4	83,521	176,993	~172.8 KB
5	1,419,857	3,008,899	~2.87 MB
6	24,137,569	51,151,297	~48.8 MB
7	410,338,673	869,572,063	~829.3 MB
8	6,975,757,441	~14.8 GB	~14.8 GB
9	118,587,876,497	~251 GB	~251 GB
10	2,015,993,900,449	~4.3 TB	~4.3 TB
11	34,271,896,307,633	~73 TB	~73 TB

size = 19 (Standard Go board size)

Dimension	Intersections	JSON Size (bytes)	Readable
0	1	1	1 B
1	19	39	39 B
2	361	761	761 B
3	6,859	14,479	~14.1 KB
4	130,321	275,121	~268.7 KB
5	2,476,099	5,227,319	~4.99 MB
6	47,045,881	99,319,081	~94.7 MB
7	893,871,739	1,887,062,559	~1.76 GB
8	16,983,563,041	~33.4 GB	~33.4 GB
9	322,687,697,779	~635 GB	~635 GB
10	6,131,066,257,801	~12 TB	~12 TB
11	116,490,258,898,219	~228 TB	~228 TB

Quick Reference (Recommended Configurations)

Recommended maximum board sizes per dimension (Memory < 1 GB, Storage < 1 GB):

Dimension	Max Recommended Size	Intersections	Memory	Storage
0	Any	1	~0 B	1 B
1	Any	<=19	<=208 B	<=39 B
2	Any	<=361	<=4.1 KB	<=761 B
3	19	6,859	~77 KB	~14 KB
4	19	130,321	~1.4 MB	~269 KB
5	19	2,476,099	~27 MB	~5.0 MB
6	19	47,045,881	~519 MB	~95 MB
7	9~13	4.7M~62.7M	73~798 MB	10~128 MB
8	5~9	390K~43M	9~657 MB	1~92 MB
9	5~7	59K~40M	45~718 MB	5~90 MB
10	3~5	59K~9.8M	2.2~224 MB	173 KB~23 MB
11	3~5	177K~48.8M	6.8 MB~1.1 GB	519 KB~116 MB

Additional Overhead

Besides the board, the game has these additional costs (negligible compared to the board):

Data	Description
config.json	Game config, ~200 bytes
history.json	Move history, ~80 bytes per move, up to s^d moves
GameHistoryItem[] memory	~120 bytes per object + coordinate array
Other game state	captures, currentPlayer, etc., ~100 bytes

Note: history.json max theoretical size = s^d x 80 bytes. On high-dimensional large boards, history can also become a significant storage burden.

Summary

• Low dimensions (0-4D): All sizes work fine, minimal memory and storage overhead
• Mid dimensions (5-6D): Size <= 19 is still acceptable (~500 MB memory ceiling)
• High dimensions (7-9D): Need to reduce size to 5~9 for typical computers
• Ultra-high dimensions (10-11D): Only size = 3~5 is feasible; 11D + size=5 needs ~1 GB memory

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Requirements

• Visual Studio Code 1.80.0 or higher.
• High-dimensional large boards may consume significant memory. Start with lower dimensions.

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Release Notes

2.0.0

• Added AI battle mode (PVE) for playing against AI.
• Integrated AI Core extension with support for OpenAI, Claude, Gemini and other AI providers.
• Added 4 AI difficulty levels: Easy (Beginner), Normal (Club Player), Hard (5-dan Amateur), Master (Professional 9-dan).
• Added AI color selection (Black/White).
• Added AI thinking status display and move notifications.
• Added Ko Rule to prevent immediate recapture.
• Added komi system for White compensation.
• Improved game mode selection interface with PVP/PVE switching.
• Added AI model configuration interface accessible from settings.

0.0.2

• Added settings page: language switching, default save path, view switch shortcut customization.
• Added default save path configuration with auto-incrementing game names (Game1, Game2, ...).
• Added 3D axis indicator (XYZ) that follows rotation in real-time.
• Added 2D board zoom (Ctrl+wheel, 17 levels), panning (drag), and bottom zoom control bar.
• Added 3D view bottom zoom control bar.
• Added double-press single key to cycle views (default q forward, w backward, customizable).
• Improved 3D rotation logic — drag direction matches view rotation direction.
• Improved slice navigator position — displayed consistently at the top of the view.
• Improved 2D board centered by default.
• Improved 3D stone size consistency across depth layers.
• Fixed game over overlay persisting after switching to a new game.
• Fixed 3D view availability for high-dimensional boards (available for dimension >= 3).

0.0.1

• Initial release.
• 0-11 dimensional matrix state system with file persistence.
• N-dimensional liberty calculation and capture algorithm.
• Webview board rendering and sidebar interaction.
• Chinese/English language switching.
• 3D board rotation/zoom with axis indicator.
• High-dimensional 3D view with slice navigator.
• Default save path with auto-incrementing game names.

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Enjoy conquering the Hilbert Space!