[{"content":"前言 在复习圆锥曲线时, 笔者遇到了“过曲线外一点 \\(P\\) 作直线 \\(l\\) 与曲线交于 \\(A, B\\) 两点, 求 \\(|PA|\\cdot|PB|\\) 范围”这类问题.这与圆中的圆幂定理颇为相似, 因此笔者试图找到一个统一的表达式, 使圆锥曲线也拥有类似的性质.本篇使用AI帮助进行排版, 检验.\n引理：圆幂定理 设圆 \\(\\Gamma\\) 的半径为 \\(r\\), 点 \\(P\\) 到圆心的距离为 \\(OP\\).则有\n\\[\r\\boxed{\\overline{PA}\\cdot\\overline{PB}=OP^2-r^2}\r\\]其中 \\(\\overline{PA}\\) 表示有向线段 \\(PA\\).有向线段的乘法为：模直接相乘, 但带上符号.\n若取单位方向向量 \\(\\vec v^0\\), 参数化 \\(X=P+t\\vec v^0\\), 并令 \\(\\overline{PA}=t_A, \\ \\overline{PB}=t_B\\), 则上式与广义幂等式一致.\n广义圆幂定理（广义幂等式） 设二次曲线\n\\[\r\\Gamma:\\quad F(x, y)=Ax^2+Bxy+Cy^2+Dx+Ey+F_0=0\r\\]满足二次项系数不全为 \\(0\\) 且非退化.其二次齐次部分为\n\\[\rQ(x, y)=Ax^2+Bxy+Cy^2.\r\\]对单位方向向量\n\\[\r\\vec v^0=(\\cos\\theta, \\sin\\theta), \\]记\n\\[\r\\varphi(\\vec v^0)=Q(\\cos\\theta, \\sin\\theta)\r=A\\cos^2\\theta+B\\cos\\theta\\sin\\theta+C\\sin^2\\theta.\r\\]过不在 \\(\\Gamma\\) 上的点 \\(P(x_0, y_0)\\) 作直线 \\(l\\), 方向向量为 \\(\\vec v^0\\).设 \\(l\\) 与 \\(\\Gamma\\) 交于 \\(A, B\\), 则由韦达定理可得\n\\[\r\\boxed{\\overline{PA}\\cdot\\overline{PB}\r=\\frac{F(P)}{\\varphi(\\vec v^0)}}\r\\]其中\n\\[\rF(P)=F(x_0, y_0).\r\\]该式称为广义圆幂定理或广义幂等式.\n若用非单位方向向量 \\(\\vec u\\), 则\n\\[\r\\boxed{\\overline{PA}\\cdot\\overline{PB}\r=\\frac{|\\vec u|^2F(P)}{\\varphi(\\vec u)}}\r\\]普通长度乘积为\n\\[\r\\boxed{|PA|\\cdot|PB|\r=\\frac{|F(P)|}{\\varphi(\\vec v^0)}\\qquad(\\varphi(\\vec v^0)\u003e0)}\r\\]若 \\(\\varphi(\\vec v^0)=0\\), 直线与曲线至多有一个交点, 不能构成割线, 广义幂等式不适用.\n圆幂不等式 椭圆 设椭圆\n\\[\r\\Gamma:\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1\\qquad(a\u003eb\u003e0).\r\\]其二次齐次部分为\n\\[\rQ(x, y)=\\frac{x^2}{a^2}+\\frac{y^2}{b^2},\r\\]于是\n\\[\r\\varphi(\\vec v^0)\r=\\frac{\\cos^2\\theta}{a^2}+\\frac{\\sin^2\\theta}{b^2}.\r\\]由正定性直接得到\n\\[\r\\boxed{\r\\frac1{a^2}\\le \\varphi(\\vec v^0)\\le \\frac1{b^2}\r}\r\\]设 \\(P\\) 在椭圆外, 即 \\(F(P)\u003e0\\), 有实切线 \\(PT\\), 且割线与椭圆有两个实交点.切线方向为 \\(\\vec v_t^0\\), 割线方向为 \\(\\vec v^0\\).由广义圆幂定理,\n\\[\r|PA|\\cdot|PB|=\\frac{F(P)}{\\varphi(\\vec v^0)},\\qquad\r|PT|^2=\\frac{F(P)}{\\varphi(\\vec v_t^0)}.\r\\]因此\n\\[\r\\boxed{\r\\frac{b^2}{a^2}|PT|^2\r\\le |PA|\\cdot|PB|\r\\le \\frac{a^2}{b^2}|PT|^2\r}\r\\]不论 \\(PT\\) 是哪一支切线, 该不等式都成立.它是利用 \\(\\varphi(\\vec v^0)\\in[1/a^2, 1/b^2]\\) 得到的较宽松全局界; 对给定 \\(P\\), 最优范围应直接用 \\(|F(P)|/\\varphi(\\vec v^0)\\) 在可行方向上的极值确定.\n若 \\(P\\) 在椭圆内, 则无实切线, \\(PT\\) 无几何意义, 上述不等式不适用.\n抛物线 设抛物线\n\\[\r\\Gamma:y^2=2px\\qquad(p\u003e0).\r\\]其二次齐次部分为 \\(Q(x, y)=y^2\\), 于是\n\\[\r\\varphi(\\vec v^0)=\\sin^2\\alpha,\r\\]其中 \\(\\alpha\\) 为直线方向与对称轴的夹角.\n设 \\(PT\\) 为任意一支切线, 方向向量为 \\(\\vec v_t^0\\); \\(PA, PB\\) 为割线, 方向向量为 \\(\\vec v^0\\),且\n\\[\r\\varphi(\\vec v^0)\u003e0.\r\\]由广义圆幂定理,\n\\[\r|PA|\\cdot|PB|=\\frac{|F(P)|}{\\varphi(\\vec v^0)},\\qquad\r|PT|^2=\\frac{|F(P)|}{\\varphi(\\vec v_t^0)}.\r\\]于是\n\\[\r\\boxed{\r|PT|^2\\varphi(\\vec v_t^0)\r\\le |PA|\\cdot|PB|\r}\r\\]该式在 \\(P\\) 在抛物线外、存在实切线且 \\(\\varphi(\\vec v^0)\u003e0\\) 时成立.\n若 \\(l\\) 平行于抛物线的对称轴, 则 \\(\\varphi(\\vec v^0)=0\\).此时直线与抛物线至多有一个交点, 不能构成割线, 故广义幂等式不适用.\n固定 \\(P\\) 的特殊情况 设\n\\[\rP(x_0, y_0),\\qquad\rG(2pt_G^2,2pt_G)\r\\]为切点, 记\n\\[\r\\boxed{F(P)=y_0^2-2px_0}\r\\]切点参数 \\(t_G\\) 满足切线条件\n\\[\r2pt_G^2-2y_0t_G+x_0=0.\r\\]\\(P\\) 在对称轴上且外部 设\n\\[\rP(x_0, 0), \\qquad x_0\u003c0.\r\\]此时\n\\[\rF(P)=-2px_0\u003e0, \\]有两条关于 \\(x\\) 轴对称的实切线, 切点参数满足\n\\[\rt_G^2=-\\frac{x_0}{2p}\u003e0.\r\\]并且\n\\[\r|OG|^2=4p^2t_G^2(t_G^2+1)\r=x_0(x_0-2p)\r=\\bigl|x_0(x_0-2p)\\bigr|.\r\\]于是\n\\[\r\\boxed{\r|OA|\\cdot|OB|\\ge |OG|^2,\r}\r\\]\\[\r\\boxed{\r|PA|\\cdot|PB|\\ge |PG|^2\r}\r\\]等号均在割线退化为切线时取得.\n\\(P\\) 在对称轴上且内部 设\n\\[\rP(x_0, 0),\\qquad x_0\u003e0.\r\\]此时\n\\[\rF(P)=-2px_0\u003c0, \\]无实切线, \\(G\\) 不存在.但有\n\\[\r\\boxed{\r|OA|\\cdot|OB|\\ge |x_0(x_0+2p)|\r}\r\\]这是因为弦 \\(AB\\) 过 \\(P(x_0,0)\\) 时,参数满足 \\[\rt_1t_2=-\\frac{x_0}{2p}\u003c0 \\quad (x_0\u003e0),\r\\] 再令 \\[\rt_1+t_2=0,\r\\] 即竖直割线时取到最小.\n且有: \\[\r\\boxed{\r|PA|\\cdot|PB|\\ge 2px_0=|F(P)|\r}\r\\]等号在竖直割线 \\(x=x_0\\) 时取得.\n\\(P\\) 不在对称轴上 若 \\(F(P)\u003e0\\), 即 \\(P\\) 在抛物线外, 存在实切线 \\(PG\\), 则\n\\[\r\\boxed{\r|PA|\\cdot|PB|\r\\ge\r\\frac{|PG|^2}{4t_G^2+1}\r=F(P)\r}\r\\]这是由 \\(\\varphi(\\vec v^0)=\\sin^2\\alpha\\le1\\) 得到的较宽松下界; 当\\(x\u003e0\\), 竖直直线\\(x=x_0\\)确为割线，此时等号成立; 当\\(x\u003c0\\), 竖直直线与抛物线无实交点, 不能取等号, 只能取下确界.\n若 \\(F(P)\u003c0\\), 即 \\(P\\) 在抛物线内部, 无实切线, \\(G\\) 不存在, 但仍有\n\\[\r\\boxed{\r|PA|\\cdot|PB|\\ge |F(P)|=2px_0-y_0^2\r}\r\\]一般地, 当 \\(P\\) 不在对称轴上时, 没有\n\\[\r|OA|\\cdot|OB|\\ge |OG|^2\r\\]的统一结论; 该结论只在 \\(P\\) 位于对称轴上时有上述特殊形式.\n","permalink":"https://weishi1079.top/life/guangyimidengshi/","summary":"对圆幂定理在圆锥曲线中的延拓的初步探究.","title":"圆锥曲线中的圆幂定理与圆幂不等式"},{"content":"谨以此文，纪念我的童年，那是一段小有遗憾的幸福时光。\n夕阳斜照，孤独地悬于西天，将云层染成火烧般的赭红与暗紫，徒劳地留下这有如终场幕布的晚霞。密密麻麻的老旧大楼间，费劲地挤出一条小路，街旁堆满了电线杆，小贩摊位，或是停下来贩卖水果的皮卡。夏，是那样燥热，街上的汉子们光着膀子，连树上的寒蝉也不免尖声鸣叫，大声控诉这酷暑。 少年所穿的仍是数年前的春衫，走在这无比熟识却又陌生的街道上，眼眸不自觉地黯下。——他继续向前走，缓缓穿过孩提时嬉戏的公园，同奶奶一起买菜的市场，放学时常常拜访的小卖部，和翻新得已经陌生的校园……回到了那栋老屋。跨过摇摇欲坠的铁门，周遭顿时安静下来，原是蓝白相间的瓦早已在时光洗濯之下或脱落或褪色，连窗台上遮雨的蓝色铁棚也难逃生锈命运。——这栋老屋仿佛处于时间的间隙，与一旁拔地而起的崭新大楼格格不入。\n他沉默着伫立片刻，已是晚饭时间，左邻右舍传来翻炒食物的声音和农家小炒的香气。他终于下定决心，推开吱呀作响的单元门，越过经年累月堆砌的小广告，一连上了六层楼——来到了门前。拭去厚重的一层灰，他拧开生锈的锁，步入其中。客厅，卧室，厨房——布置与记忆中几乎完全一样。他看到了奶奶炒菜时萦绕的烟火气，想起自己攥着五角一包的辣条抿着嘴角的模样，也还会记得自己的欢笑与泪……夕阳将最后一抹光辉投射入窗，浮尘在光柱里翻飞，如蓬草般漂游，木地板上洒下片片金黄的光晕。\n他又想起了那些时光。是在斑驳树影下等父母接他回家，还是运动会上同学们的追逐嬉戏？——不过，这一切也终定格在毕业照上的那个黄昏了。 一片恍惚之中，他的眼眶浸润了，清泪缓缓落下，夕阳照耀之下，不禁令他一阵炫目。\n岁月空长，徒留下份份炫目，令人逐渐忘却罢了。\n","permalink":"https://weishi1079.top/gal/guxiangshi/","summary":"有些事物始终如一，有些事物悄然改变。即便如此，依然存在令人想要归去的地方。","title":"故乡识"},{"content":" 你总是告诉我\n你冷若冰霜\n不止用言语\n还有每一次突临的寒芒\n是啊\n因而你垂泪，因为世人疏离\n可你想啊\n你的泪反而是馈赠\n世上少数平等的东西\n万物都爱你，亦或恨你\n构筑喜悦，激动，相思，愁绪\n那点点滴滴，我们一生\n一身雨里风尘\n——星月呓《寄于雨》\n印象音乐·My Soul 初识 见到他的第一眼，我会以为他是不苟言笑、高冷有礼、对尘世提不起兴趣的谦谦君子。 然而接触下来，却是另一幅模样。他会玩王者荣耀、1999，却又对通俗文学深恶痛绝；他会大大咧咧的，也会有感伤寂寞的时候；他是我心目中的大作家，却还是会在感情显得稚嫩……总之，他的形象复杂又立体，和初印象完全不同。\n渐近的灵魂 直到相处久了才会发现，其实他疯疯癫癫的行为，也不过是为了掩藏内心中孤高自洁的灵魂罢了。——也许他有着贾宝玉那样的敏感多情，也有着荒原狼的孤独与不羁。\n正如另一名同学所评：有的人生来就是孤独的。 而他就是这样的人。\n或许他总是表现得大大咧咧，不过在我看来，这都只是为了掩藏那脆弱而敏感的内心。\n一个人总是戴着面具，戴的太久——以至于人们都忘记了他本来的面貌。\n文学交流 星月呓在文学上有着自己独特的见解，他对于诗歌有着近乎偏执的追求，尤其是对现代诗的创作。 他的作品中，既有对自然景物的细腻描写，也有对人生哲理的深刻思考。\n值得一提的是，他在B站发布的作品，都是他自己觉得“不太满意”的。真正满意的作品，他通常会收起来，希望以后能结集成诗集出版。\n因为他独特的创作美学，他也在创作上多次与我发生争执。在他的小说的创作中，我们多次就人物塑造和情节发展产生分歧，他坚持自己的创作理念，而我则提出不同的看法。正是在这种激烈的交流中，我才看到了他对文学的热爱与坚守。\n何以如此？ 从我对他的了解而言，他的文学思考和创作理念受多方面因素影响。\n家庭熏陶 因为家里要求比较严，他从小接触的更多的是《荒野大镖客2：救赎》等需要耐心慢慢体会的作品，而不是快餐式的短视频或者网文。这使得他更加关注作品的深度和内涵，而并非其所带来的快感。\n个人偏好 他看事情偏悲观，所以更喜欢带有“物哀”气质、人文关怀和哲学思考的作品。\n从他喜欢的书里也能看出来：\n长日将尽\n献给阿尔吉侬的花束\n红楼梦\n……\nPride and Prejudice 不过，他也是个很固执且爱表达的人，这方面需要严肃批判。\n比如，他对 “物哀” 的偏爱太深，从阅读到写作，以至于对见到的其他的作品，也会不自觉的进行预先评判。他曾被介绍到一部作品，但只翻了翻目录就 武断地 说：“不喜欢，我对它不感兴趣。” 这个时候，对文学的爱好反而变成了一座囚笼——他很少与其他体裁或形式的作品交流，不论那些作品 优秀与否。\n如果有人谈及他不曾接触过的艺术形式，或者向他介绍其他通俗但亦有一定特色的作品，他也往往以此为理由拒绝。\n我无意在此深入探讨这种偏爱本身，然而还是以为，这种 （可以称之为傲慢的） 态度会令他错失更多优秀的作品。 一个作品是否优秀并不在于它的表现形式，如果一个人只是因为体裁就放弃接触，那他离见证优秀作品的优秀的鉴赏家，可能还有一些距离。\n于雨于梦，溶解与和解； 他的梦想颇为朴素，没什么野心。\n只是想考上一所好大学的文学专业，成为一名作家。\n然后和心爱的人在一起，平静地过完一生。\n他写雨，但真正喜欢的是晨曦与春光；他写孤独，但终究渴望陪伴与爱。\n随着纸页翻动声与父母的严厉管教，那个曾高喊着诗歌美学、与我在争论中碰撞出火花的少年，似乎也在现实的温水中渐渐放缓了激烈的姿态。 那些曾经锋利的寒芒、对通俗与庸俗的不屑一顾，最终没有变成戳破现实的凶器，而是像冰雪落入温热的河流——不可逆转地溶解了。\n但这种“溶解”，并非泯灭，而是一种融入。 他不再需要以狂傲与疯癫作为御寒的铠甲，也不再把所有的脆弱与敏感锁在深夜的文字里。他开始试着与这个曾经让他感到“疏离”的世界和解，将那些藏在暗处的哲思与对“物哀”的独到理解，悄然化作对待生活与身边人的温存。\n他依然会在下雨天独自驻足，任由那“一身雨里风尘”打湿衣襟；也依然会在夜深人静时开一盏小灯，在笔记本上续写他那未竟的诗集梦。 只是，现在的他已经不再介意世人是否能读懂他的孤高，也不再执拗于每一场文学争论的输赢。\n每个雨天，他还是会掏出那本写满诗歌的笔记本，翻阅那些曾经的文字——然而不必再担心 “死亡” 与 “孤独”， 因为经过人生种种，他才明白，正是因为不完美，才能称为明天。\n最纯粹的诗歌梦，或许很难轰轰烈烈地实现——\n可那个曾经在冷霜与朝露间挣扎的灵魂，早已将自己活成了一首无需发表的诗，\n悄然溶解，又历久弥新。\n奔星赶月，不以梦呓止。 追风赶月莫停留，平芜尽处是春山。\n我们仍期待着，能见到他更好的作品；\n也希望，他能活出自己真正钟情的人生。\n未时 作于2026/10/2\n本文未完结，期待修改。\n","permalink":"https://weishi1079.top/gal/xingyueyi/","summary":"星月呓：尚未实现的纯粹的诗歌梦","title":"文学人物志·星月呓"},{"content":"对所有制作者致以最崇高的敬意。\n博客使用了大量开源项目和第三方服务，且 不依赖访客本机安装的字体，字体文件 通过子集化后自托管。\n字体 用途 字体 版权 许可 中文正文与标题 Noto Serif SC / 思源宋体（Source Han Serif） © 2012 Google Inc.；© 2017–2022 Adobe SIL OFL 1.1 代码块（等宽） Cascadia Mono © 2019–Present Microsoft Corporation SIL OFL 1.1 实际上属于 \u0026ldquo;Modified Version\u0026rdquo;。\n建站工具与前端库 组件 用途 版权 许可 Hugo 静态站点生成器 © The Hugo Authors Apache 2.0 PaperMod 主题 © 2020 nanxiaobei and adityatelange；© 2021–2026 adityatelange MIT Fuse.js 搜索的模糊匹配（随主题打包） © 2023 Kiro Risk Apache 2.0 Feather Icons 页面里的箭头图标 © 2013–2023 Cole Bemis MIT Chroma 代码块语法高亮（Hugo 内置） © 2017 Alec Thomas MIT MathJax 数学公式渲染 © The MathJax Consortium Apache 2.0 GoatCounter 访问统计（只用了 count.js） © Martin Tournoij ISC Pillow 图片处理（背景图、图标、字体子集） © 1997–2011 Secret Labs AB；© 1995–2011 Fredrik Lundh 等 MIT-CMU 自托管 count.js 和 MathJax 源网站被墙。\n符合 ISC 许可。\n第三方服务 网站运行所依赖的外部服务。\n服务 用途 说明 Cloudflare DNS 解析、CDN、Tunnel 内网穿透、TLS 证书 商标与品牌使用遵循 Cloudflare Trademark Policy；服务条款见 Website Terms；隐私政策见 Privacy Policy Cloudflare Tunnel 将端口映射到公网 同上 GoatCounter 访问统计的托管服务 无 Cookie、不存 IP GitHub 代码托管、字体与工具的分发源 服务条款 Cloudflare Registrar / DNS 域名注册与解析 同上 本站与上述公司没有任何隶属或赞助关系。使用它们的服务 不代表它们认可本站内容。上面列出的名称与商标归各自所有者。\n其它工具（未随站点分发） 构建过程中还用了这些工具。\n工具 用途 许可 fontTools 字体子集化（把 24MB 压到 365KB） MIT Brotli woff2 压缩 MIT Hugo Pipes 资源打包与压缩 Apache 2.0（属 Hugo） Deepseek Harness 协助部署网站的Agent N/A Netease Music 音乐CDN服务 N/A 背景图与素材 用途 来源 说明 横屏背景(白昼) Summer Pockets REFLECTION BLUE 游戏原画，版权归 Key / Visual Arts 所有 横屏背景(黑夜) 哲风壁纸 壁纸，侵删 竖屏背景 崩坏：星穹铁道 · 风菫 同人作品，版权归米哈游和原作者所有 本站作为个人非商业博客的 装饰性使用，未主张任何权利，也未用于任何商业目的。 若版权方有异议，立即移除。\n许可全文 以下是上面提到的所有许可的完整文本。\nSIL Open Font License 1.1 —— 思源宋体（Source Han Serif / Noto Serif SC） 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 Copyright 2017-2022 Adobe (http://www.adobe.com/), with Reserved Font Name \u0026#39;Source\u0026#39;. Source is a trademark of Adobe in the United States and/or other countries. This Font Software is licensed under the SIL Open Font License, Version 1.1. This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL ----------------------------------------------------------- SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007 ----------------------------------------------------------- PREAMBLE The goals of the Open Font License (OFL) are to stimulate worldwide development of collaborative font projects, to support the font creation efforts of academic and linguistic communities, and to provide a free and open framework in which fonts may be shared and improved in partnership with others. The OFL allows the licensed fonts to be used, studied, modified and redistributed freely as long as they are not sold by themselves. The fonts, including any derivative works, can be bundled, embedded, redistributed and/or sold with any software provided that any reserved names are not used by derivative works. The fonts and derivatives, however, cannot be released under any other type of license. The requirement for fonts to remain under this license does not apply to any document created using the fonts or their derivatives. DEFINITIONS \u0026#34;Font Software\u0026#34; refers to the set of files released by the Copyright Holder(s) under this license and clearly marked as such. This may include source files, build scripts and documentation. \u0026#34;Reserved Font Name\u0026#34; refers to any names specified as such after the copyright statement(s). \u0026#34;Original Version\u0026#34; refers to the collection of Font Software components as distributed by the Copyright Holder(s). \u0026#34;Modified Version\u0026#34; refers to any derivative made by adding to, deleting, or substituting -- in part or in whole -- any of the components of the Original Version, by changing formats or by porting the Font Software to a new environment. \u0026#34;Author\u0026#34; refers to any designer, engineer, programmer, technical writer or other person who contributed to the Font Software. PERMISSION \u0026amp; CONDITIONS Permission is hereby granted, free of charge, to any person obtaining a copy of the Font Software, to use, study, copy, merge, embed, modify, redistribute, and sell modified and unmodified copies of the Font Software, subject to the following conditions: 1) Neither the Font Software nor any of its individual components, in Original or Modified Versions, may be sold by itself. 2) Original or Modified Versions of the Font Software may be bundled, redistributed and/or sold with any software, provided that each copy contains the above copyright notice and this license. These can be included either as stand-alone text files, human-readable headers or in the appropriate machine-readable metadata fields within text or binary files as long as those fields can be easily viewed by the user. 3) No Modified Version of the Font Software may use the Reserved Font Name(s) unless explicit written permission is granted by the corresponding Copyright Holder. This restriction only applies to the primary font name as presented to the users. 4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font Software shall not be used to promote, endorse or advertise any Modified Version, except to acknowledge the contribution(s) of the Copyright Holder(s) and the Author(s) or with their explicit written permission. 5) The Font Software, modified or unmodified, in part or in whole, must be distributed entirely under this license, and must not be distributed under any other license. The requirement for fonts to remain under this license does not apply to any document created using the Font Software. TERMINATION This license becomes null and void if any of the above conditions are not met. DISCLAIMER THE FONT SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE. SIL Open Font License 1.1 —— Cascadia Mono 与上面是同一份标准 OFL 文本，差别只在版权声明部分。\n展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 Copyright (c) 2019 - Present, Microsoft Corporation, with Reserved Font Name Cascadia Code. This Font Software is licensed under the SIL Open Font License, Version 1.1. This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL ----------------------------------------------------------- SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007 ----------------------------------------------------------- PREAMBLE The goals of the Open Font License (OFL) are to stimulate worldwide development of collaborative font projects, to support the font creation efforts of academic and linguistic communities, and to provide a free and open framework in which fonts may be shared and improved in partnership with others. The OFL allows the licensed fonts to be used, studied, modified and redistributed freely as long as they are not sold by themselves. The fonts, including any derivative works, can be bundled, embedded, redistributed and/or sold with any software provided that any reserved names are not used by derivative works. The fonts and derivatives, however, cannot be released under any other type of license. The requirement for fonts to remain under this license does not apply to any document created using the fonts or their derivatives. DEFINITIONS \u0026#34;Font Software\u0026#34; refers to the set of files released by the Copyright Holder(s) under this license and clearly marked as such. This may include source files, build scripts and documentation. \u0026#34;Reserved Font Name\u0026#34; refers to any names specified as such after the copyright statement(s). \u0026#34;Original Version\u0026#34; refers to the collection of Font Software components as distributed by the Copyright Holder(s). \u0026#34;Modified Version\u0026#34; refers to any derivative made by adding to, deleting, or substituting -- in part or in whole -- any of the components of the Original Version, by changing formats or by porting the Font Software to a new environment. \u0026#34;Author\u0026#34; refers to any designer, engineer, programmer, technical writer or other person who contributed to the Font Software. PERMISSION \u0026amp; CONDITIONS Permission is hereby granted, free of charge, to any person obtaining a copy of the Font Software, to use, study, copy, merge, embed, modify, redistribute, and sell modified and unmodified copies of the Font Software, subject to the following conditions: 1) Neither the Font Software nor any of its individual components, in Original or Modified Versions, may be sold by itself. 2) Original or Modified Versions of the Font Software may be bundled, redistributed and/or sold with any software, provided that each copy contains the above copyright notice and this license. These can be included either as stand-alone text files, human-readable headers or in the appropriate machine-readable metadata fields within text or binary files as long as those fields can be easily viewed by the user. 3) No Modified Version of the Font Software may use the Reserved Font Name(s) unless explicit written permission is granted by the corresponding Copyright Holder. This restriction only applies to the primary font name as presented to the users. 4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font Software shall not be used to promote, endorse or advertise any Modified Version, except to acknowledge the contribution(s) of the Copyright Holder(s) and the Author(s) or with their explicit written permission. 5) The Font Software, modified or unmodified, in part or in whole, must be distributed entirely under this license, and must not be distributed under any other license. The requirement for fonts to remain under this license does not apply to any document created using the Font Software. TERMINATION This license becomes null and void if any of the above conditions are not met. DISCLAIMER THE FONT SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE. MIT License —— PaperMod 主题 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 MIT License Copyright (c) 2020 nanxiaobei and adityatelange Copyright (c) 2021-2026 adityatelange Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \u0026#34;Software\u0026#34;), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. MIT License —— Feather Icons 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 The MIT License (MIT) Copyright (c) 2013-2023 Cole Bemis Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \u0026#34;Software\u0026#34;), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. MIT License —— Chroma（语法高亮） 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 Copyright (C) 2017 Alec Thomas Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the \u0026#34;Software\u0026#34;), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. // formatters/svg/font_liberation_mono.go Digitized data copyright (c) 2010 Google Corporation with Reserved Font Arimo, Tinos and Cousine. Copyright (c) 2012 Red Hat, Inc. with Reserved Font Name Liberation. This Font Software is licensed under the SIL Open Font License, Version 1.1. This license is copied below, and is also available with a FAQ at: https://openfontlicense.org ----------------------------------------------------------- SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007 ----------------------------------------------------------- PREAMBLE The goals of the Open Font License (OFL) are to stimulate worldwide development of collaborative font projects, to support the font creation efforts of academic and linguistic communities, and to provide a free and open framework in which fonts may be shared and improved in partnership with others. The OFL allows the licensed fonts to be used, studied, modified and redistributed freely as long as they are not sold by themselves. The fonts, including any derivative works, can be bundled, embedded, redistributed and/or sold with any software provided that any reserved names are not used by derivative works. The fonts and derivatives, however, cannot be released under any other type of license. The requirement for fonts to remain under this license does not apply to any document created using the fonts or their derivatives. DEFINITIONS \u0026#34;Font Software\u0026#34; refers to the set of files released by the Copyright Holder(s) under this license and clearly marked as such. This may include source files, build scripts and documentation. \u0026#34;Reserved Font Name\u0026#34; refers to any names specified as such after the copyright statement(s). \u0026#34;Original Version\u0026#34; refers to the collection of Font Software components as distributed by the Copyright Holder(s). \u0026#34;Modified Version\u0026#34; refers to any derivative made by adding to, deleting, or substituting -- in part or in whole -- any of the components of the Original Version, by changing formats or by porting the Font Software to a new environment. \u0026#34;Author\u0026#34; refers to any designer, engineer, programmer, technical writer or other person who contributed to the Font Software. PERMISSION \u0026amp; CONDITIONS Permission is hereby granted, free of charge, to any person obtaining a copy of the Font Software, to use, study, copy, merge, embed, modify, redistribute, and sell modified and unmodified copies of the Font Software, subject to the following conditions: 1) Neither the Font Software nor any of its individual components, in Original or Modified Versions, may be sold by itself. 2) Original or Modified Versions of the Font Software may be bundled, redistributed and/or sold with any software, provided that each copy contains the above copyright notice and this license. These can be included either as stand-alone text files, human-readable headers or in the appropriate machine-readable metadata fields within text or binary files as long as those fields can be easily viewed by the user. 3) No Modified Version of the Font Software may use the Reserved Font Name(s) unless explicit written permission is granted by the corresponding Copyright Holder. This restriction only applies to the primary font name as presented to the users. 4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font Software shall not be used to promote, endorse or advertise any Modified Version, except to acknowledge the contribution(s) of the Copyright Holder(s) and the Author(s) or with their explicit written permission. 5) The Font Software, modified or unmodified, in part or in whole, must be distributed entirely under this license, and must not be distributed under any other license. The requirement for fonts to remain under this license does not apply to any document created using the Font Software. TERMINATION This license becomes null and void if any of the above conditions are not met. DISCLAIMER THE FONT SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE. MIT-CMU License —— Pillow（图片处理） 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 The Python Imaging Library (PIL) is Copyright © 1997-2011 by Secret Labs AB Copyright © 1995-2011 by Fredrik Lundh and contributors Pillow is the friendly PIL fork. It is Copyright © 2010 by Jeffrey \u0026#39;Alex\u0026#39; Clark and contributors Like PIL, Pillow is licensed under the open source MIT-CMU License: By obtaining, using, and/or copying this software and/or its associated documentation, you agree that you have read, understood, and will comply with the following terms and conditions: Permission to use, copy, modify and distribute this software and its documentation for any purpose and without fee is hereby granted, provided that the above copyright notice appears in all copies, and that both that copyright notice and this permission notice appear in supporting documentation, and that the name of Secret Labs AB or the author not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission. SECRET LABS AB AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL SECRET LABS AB OR THE AUTHOR BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. Apache License 2.0 —— Hugo 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. 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Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form. 3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed. 4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions: (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and (b) You must cause any modified files to carry prominent notices stating that You changed the files; and (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and (d) If the Work includes a \u0026#34;NOTICE\u0026#34; text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License. You may add Your own copyright statement to Your modifications and may provide additional or different license terms and conditions for use, reproduction, or distribution of Your modifications, or for any such Derivative Works as a whole, provided Your use, reproduction, and distribution of the Work otherwise complies with the conditions stated in this License. 5. Submission of Contributions. Unless You explicitly state otherwise, any Contribution intentionally submitted for inclusion in the Work by You to the Licensor shall be under the terms and conditions of this License, without any additional terms or conditions. Notwithstanding the above, nothing herein shall supersede or modify the terms of any separate license agreement you may have executed with Licensor regarding such Contributions. 6. Trademarks. This License does not grant permission to use the trade names, trademarks, service marks, or product names of the Licensor, except as required for reasonable and customary use in describing the origin of the Work and reproducing the content of the NOTICE file. 7. Disclaimer of Warranty. Unless required by applicable law or agreed to in writing, Licensor provides the Work (and each Contributor provides its Contributions) on an \u0026#34;AS IS\u0026#34; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied, including, without limitation, any warranties or conditions of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A PARTICULAR PURPOSE. You are solely responsible for determining the appropriateness of using or redistributing the Work and assume any risks associated with Your exercise of permissions under this License. 8. Limitation of Liability. In no event and under no legal theory, whether in tort (including negligence), contract, or otherwise, unless required by applicable law (such as deliberate and grossly negligent acts) or agreed to in writing, shall any Contributor be liable to You for damages, including any direct, indirect, special, incidental, or consequential damages of any character arising as a result of this License or out of the use or inability to use the Work (including but not limited to damages for loss of goodwill, work stoppage, computer failure or malfunction, or any and all other commercial damages or losses), even if such Contributor has been advised of the possibility of such damages. 9. Accepting Warranty or Additional Liability. While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability. END OF TERMS AND CONDITIONS APPENDIX: How to apply the Apache License to your work. To apply the Apache License to your work, attach the following boilerplate notice, with the fields enclosed by brackets \u0026#34;[]\u0026#34; replaced with your own identifying information. (Don\u0026#39;t include the brackets!) The text should be enclosed in the appropriate comment syntax for the file format. We also recommend that a file or class name and description of purpose be included on the same \u0026#34;printed page\u0026#34; as the copyright notice for easier identification within third-party archives. Copyright [yyyy] [name of copyright owner] Licensed under the Apache License, Version 2.0 (the \u0026#34;License\u0026#34;); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \u0026#34;AS IS\u0026#34; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. Apache License 2.0 —— Fuse.js 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. \u0026#34;License\u0026#34; shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. \u0026#34;Licensor\u0026#34; shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. \u0026#34;Legal Entity\u0026#34; shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, \u0026#34;control\u0026#34; means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. \u0026#34;You\u0026#34; (or \u0026#34;Your\u0026#34;) shall mean an individual or Legal Entity exercising permissions granted by this License. \u0026#34;Source\u0026#34; form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files. \u0026#34;Object\u0026#34; form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types. \u0026#34;Work\u0026#34; shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below). \u0026#34;Derivative Works\u0026#34; shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof. \u0026#34;Contribution\u0026#34; shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, \u0026#34;submitted\u0026#34; means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as \u0026#34;Not a Contribution.\u0026#34; \u0026#34;Contributor\u0026#34; shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work. 2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form. 3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed. 4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions: (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and (b) You must cause any modified files to carry prominent notices stating that You changed the files; and (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and (d) If the Work includes a \u0026#34;NOTICE\u0026#34; text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License. You may add Your own copyright statement to Your modifications and may provide additional or different license terms and conditions for use, reproduction, or distribution of Your modifications, or for any such Derivative Works as a whole, provided Your use, reproduction, and distribution of the Work otherwise complies with the conditions stated in this License. 5. Submission of Contributions. Unless You explicitly state otherwise, any Contribution intentionally submitted for inclusion in the Work by You to the Licensor shall be under the terms and conditions of this License, without any additional terms or conditions. Notwithstanding the above, nothing herein shall supersede or modify the terms of any separate license agreement you may have executed with Licensor regarding such Contributions. 6. Trademarks. This License does not grant permission to use the trade names, trademarks, service marks, or product names of the Licensor, except as required for reasonable and customary use in describing the origin of the Work and reproducing the content of the NOTICE file. 7. Disclaimer of Warranty. Unless required by applicable law or agreed to in writing, Licensor provides the Work (and each Contributor provides its Contributions) on an \u0026#34;AS IS\u0026#34; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied, including, without limitation, any warranties or conditions of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A PARTICULAR PURPOSE. You are solely responsible for determining the appropriateness of using or redistributing the Work and assume any risks associated with Your exercise of permissions under this License. 8. Limitation of Liability. In no event and under no legal theory, whether in tort (including negligence), contract, or otherwise, unless required by applicable law (such as deliberate and grossly negligent acts) or agreed to in writing, shall any Contributor be liable to You for damages, including any direct, indirect, special, incidental, or consequential damages of any character arising as a result of this License or out of the use or inability to use the Work (including but not limited to damages for loss of goodwill, work stoppage, computer failure or malfunction, or any and all other commercial damages or losses), even if such Contributor has been advised of the possibility of such damages. 9. Accepting Warranty or Additional Liability. While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability. END OF TERMS AND CONDITIONS APPENDIX: How to apply the Apache License to your work. To apply the Apache License to your work, attach the following boilerplate notice, with the fields enclosed by brackets \u0026#34;{}\u0026#34; replaced with your own identifying information. (Don\u0026#39;t include the brackets!) The text should be enclosed in the appropriate comment syntax for the file format. We also recommend that a file or class name and description of purpose be included on the same \u0026#34;printed page\u0026#34; as the copyright notice for easier identification within third-party archives. Copyright 2017 Kirollos Risk Licensed under the Apache License, Version 2.0 (the \u0026#34;License\u0026#34;); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \u0026#34;AS IS\u0026#34; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. Apache License 2.0 —— MathJax 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 Apache License Version 2.0, January 2004 http://www.apache.org/licenses/ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 1. Definitions. \u0026#34;License\u0026#34; shall mean the terms and conditions for use, reproduction, and distribution as defined by Sections 1 through 9 of this document. \u0026#34;Licensor\u0026#34; shall mean the copyright owner or entity authorized by the copyright owner that is granting the License. \u0026#34;Legal Entity\u0026#34; shall mean the union of the acting entity and all other entities that control, are controlled by, or are under common control with that entity. For the purposes of this definition, \u0026#34;control\u0026#34; means (i) the power, direct or indirect, to cause the direction or management of such entity, whether by contract or otherwise, or (ii) ownership of fifty percent (50%) or more of the outstanding shares, or (iii) beneficial ownership of such entity. \u0026#34;You\u0026#34; (or \u0026#34;Your\u0026#34;) shall mean an individual or Legal Entity exercising permissions granted by this License. \u0026#34;Source\u0026#34; form shall mean the preferred form for making modifications, including but not limited to software source code, documentation source, and configuration files. \u0026#34;Object\u0026#34; form shall mean any form resulting from mechanical transformation or translation of a Source form, including but not limited to compiled object code, generated documentation, and conversions to other media types. \u0026#34;Work\u0026#34; shall mean the work of authorship, whether in Source or Object form, made available under the License, as indicated by a copyright notice that is included in or attached to the work (an example is provided in the Appendix below). \u0026#34;Derivative Works\u0026#34; shall mean any work, whether in Source or Object form, that is based on (or derived from) the Work and for which the editorial revisions, annotations, elaborations, or other modifications represent, as a whole, an original work of authorship. For the purposes of this License, Derivative Works shall not include works that remain separable from, or merely link (or bind by name) to the interfaces of, the Work and Derivative Works thereof. \u0026#34;Contribution\u0026#34; shall mean any work of authorship, including the original version of the Work and any modifications or additions to that Work or Derivative Works thereof, that is intentionally submitted to Licensor for inclusion in the Work by the copyright owner or by an individual or Legal Entity authorized to submit on behalf of the copyright owner. For the purposes of this definition, \u0026#34;submitted\u0026#34; means any form of electronic, verbal, or written communication sent to the Licensor or its representatives, including but not limited to communication on electronic mailing lists, source code control systems, and issue tracking systems that are managed by, or on behalf of, the Licensor for the purpose of discussing and improving the Work, but excluding communication that is conspicuously marked or otherwise designated in writing by the copyright owner as \u0026#34;Not a Contribution.\u0026#34; \u0026#34;Contributor\u0026#34; shall mean Licensor and any individual or Legal Entity on behalf of whom a Contribution has been received by Licensor and subsequently incorporated within the Work. 2. Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form. 3. Grant of Patent License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed. 4. Redistribution. You may reproduce and distribute copies of the Work or Derivative Works thereof in any medium, with or without modifications, and in Source or Object form, provided that You meet the following conditions: (a) You must give any other recipients of the Work or Derivative Works a copy of this License; and (b) You must cause any modified files to carry prominent notices stating that You changed the files; and (c) You must retain, in the Source form of any Derivative Works that You distribute, all copyright, patent, trademark, and attribution notices from the Source form of the Work, excluding those notices that do not pertain to any part of the Derivative Works; and (d) If the Work includes a \u0026#34;NOTICE\u0026#34; text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file, excluding those notices that do not pertain to any part of the Derivative Works, in at least one of the following places: within a NOTICE text file distributed as part of the Derivative Works; within the Source form or documentation, if provided along with the Derivative Works; or, within a display generated by the Derivative Works, if and wherever such third-party notices normally appear. The contents of the NOTICE file are for informational purposes only and do not modify the License. You may add Your own attribution notices within Derivative Works that You distribute, alongside or as an addendum to the NOTICE text from the Work, provided that such additional attribution notices cannot be construed as modifying the License. You may add Your own copyright statement to Your modifications and may provide additional or different license terms and conditions for use, reproduction, or distribution of Your modifications, or for any such Derivative Works as a whole, provided Your use, reproduction, and distribution of the Work otherwise complies with the conditions stated in this License. 5. Submission of Contributions. Unless You explicitly state otherwise, any Contribution intentionally submitted for inclusion in the Work by You to the Licensor shall be under the terms and conditions of this License, without any additional terms or conditions. Notwithstanding the above, nothing herein shall supersede or modify the terms of any separate license agreement you may have executed with Licensor regarding such Contributions. 6. Trademarks. This License does not grant permission to use the trade names, trademarks, service marks, or product names of the Licensor, except as required for reasonable and customary use in describing the origin of the Work and reproducing the content of the NOTICE file. 7. Disclaimer of Warranty. Unless required by applicable law or agreed to in writing, Licensor provides the Work (and each Contributor provides its Contributions) on an \u0026#34;AS IS\u0026#34; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied, including, without limitation, any warranties or conditions of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A PARTICULAR PURPOSE. You are solely responsible for determining the appropriateness of using or redistributing the Work and assume any risks associated with Your exercise of permissions under this License. 8. Limitation of Liability. In no event and under no legal theory, whether in tort (including negligence), contract, or otherwise, unless required by applicable law (such as deliberate and grossly negligent acts) or agreed to in writing, shall any Contributor be liable to You for damages, including any direct, indirect, special, incidental, or consequential damages of any character arising as a result of this License or out of the use or inability to use the Work (including but not limited to damages for loss of goodwill, work stoppage, computer failure or malfunction, or any and all other commercial damages or losses), even if such Contributor has been advised of the possibility of such damages. 9. Accepting Warranty or Additional Liability. While redistributing the Work or Derivative Works thereof, You may choose to offer, and charge a fee for, acceptance of support, warranty, indemnity, or other liability obligations and/or rights consistent with this License. However, in accepting such obligations, You may act only on Your own behalf and on Your sole responsibility, not on behalf of any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against, such Contributor by reason of your accepting any such warranty or additional liability. END OF TERMS AND CONDITIONS APPENDIX: How to apply the Apache License to your work. To apply the Apache License to your work, attach the following boilerplate notice, with the fields enclosed by brackets \u0026#34;[]\u0026#34; replaced with your own identifying information. (Don\u0026#39;t include the brackets!) The text should be enclosed in the appropriate comment syntax for the file format. We also recommend that a file or class name and description of purpose be included on the same \u0026#34;printed page\u0026#34; as the copyright notice for easier identification within third-party archives. Copyright [yyyy] [name of copyright owner] Licensed under the Apache License, Version 2.0 (the \u0026#34;License\u0026#34;); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \u0026#34;AS IS\u0026#34; BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. ISC License —— GoatCounter 的 count.js 展开完整许可文本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Copyright © Martin Tournoij \u0026lt;martin@arp242.net\u0026gt; ––– public/count.js; ISC license –––––––––––––––––––––––––––––––––––––––––––––– Permission to use, copy, modify, and/or distribute this software for any purpose with or without fee is hereby granted, provided that the above copyright notice and this permission notice appear in all copies. THE SOFTWARE IS PROVIDED \u0026#34;AS IS\u0026#34; AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 说明 本站是个人博客，不含商业目的。\n如果本站有任何署名遗漏或许可错误， 请通过关于页里的联系方式告知笔者，将立即修复。\n","permalink":"https://weishi1079.top/acknowledgments/","summary":"本站用到的字体、工具、库、服务与素材的完整出处与许可声明。","title":"致谢"},{"content":"文章框架由ai生成，由笔者重写。包含一部分从社区获得的经验与笔者的实战经历。\n起因 从二手市场淘了一台魔百盒 CM311-1，2GB 内存 + 16GB 闪存，四核 Cortex-A53、百兆网口、两个 USB 2.0。\n前任机主已经刷好了Android 9.0，ADB 默认开着。刚好可以满足小型服务器的需求。\n准备 ai提到的工具很多，但是我只用上了一部分。\n用上的 没用上的 网线 TTL U盘 双公头 USB 线 免拆神器 万用表 镊子 烙铁 12V3A 电源 Type-C 充电线 第一步：确认芯片 。CM311-1 和 CM311-1a 只差一个字母，但芯片完全不同：\n型号 SoC 平台家族 CPU 核心 CM311-1 S905L3 / L3B meson-gxl Cortex-A53 CM311-1a S905L3A meson-g12a Cortex-A55 两者镜像、设备树、引导文件不通用。\n交叉验证 Agent老是要求确认。下面是交叉验证方法（适用于已打开ADB）：\n1 2 3 4 5 # 系统属性 adb shell getprop ro.board.platform # → p291_iptv # CPU 核心型号（内核报告，难以伪造） adb shell cat /proc/cpuinfo | grep \u0026#34;CPU part\u0026#34; # → 0xd03 CPU part 核心 对应芯片 0xd03 Cortex-A53 S905L3 / L3B 0xd05 Cortex-A55 S905L3A 0xd03 一行排除 L3A。\n刷完之后看 Armbian 的开机横幅：\n1 Amlogic Meson GXL (S905L2) X7 5G Tv Box GXL 确认了平台家族，X7 5G 对应设备树 meson-gxl-s905l2-x7-5g.dtb。\n第二步：刷机 用 ADB 触发，不用双公头线 如果盒子还能进安卓、ADB 还开着，有条捷径：\n1 2 adb connect \u0026lt;盒子IP\u0026gt;:5555 adb shell reboot update 盒子会重启并尝试从 U 盘引导。全程不需要拆机。\n写盘工具的选择 工具 结果 balenaEtcher 2.1.7 安装成功但进程起不来 Rufus 4.15 便携版 直接可用 写入时必须选「DD 映像模式」，ISO 模式会写错。\n最大的坑：首次启动网络不通 U 盘启动 Armbian 后，HDMI 显示进入了Amrbian的终端，但路由器上找不到这台设备。\n当时排查了很久：网段扫描、端口探测、ARP 表。\n断电重启即可\n重启后 SSH 立即可用，HDMI显示变为满屏幕的命令。\n第三步：写入 eMMC 先备份原厂系统 1 armbian-ddbr # 交互式，选 b（backup） L3 的安卓底包不好找，这个备份是唯一的退路。\n14.6 GiB 的 eMMC 压缩后 3.2 GB。\n安装 1 armbian-install 机型菜单里选 ID 122：\n1 122 s905l3 CM311-1,HG680-LC,M401A,UNT402A,CM201-1-6-YS meson-gxl-s905l2-x7-5g.dtb 文件系统选 ext4（2GB 内存跑 btrfs 太吃力）。\n权限污染 装完之后 sudo 报错：\n1 sudo: /etc/sudo.conf is owned by uid 1023, should be 0 检查发现：\n1 2 find / -uid 1023 2\u0026gt;/dev/null | wc -l # → 58448 属主错误\n原因是：在安卓运行时插着 U 盘，然后从 U 盘引导，文件属主继承了错误的 uid。\n修复：\n1 chown -R root:root /etc /usr /var /opt /srv /root 改完重启，systemctl --failed 显示 0 个失败单元。\n第四步：SSD 与存储(需要加Nofail) 一块 120GB 的 SATA SSD 装在 JMicron JMS578 芯片的硬盘盒（联想Thinkplus）里。\nUAS 不兼容 JMS578 支持 UAS（USB Attached SCSI），但在这个内核上会掉盘。要禁用：\n编辑 /boot/uEnv.txt，在 APPEND= 行末尾追加：\n1 usb-storage.quirks=0x152d:0xa578:u 重启后验证：\n1 2 3 4 $ lsusb -t |__ Port 001: Dev 003, If 0, Class=Mass Storage, Driver=usb-storage, 480M ↑ 不是 uas，正确 拓展坞逆供电 本来买的是拓展坞（独立供电），但是插上之后发现拔了盒子电源线盒子还能工作，说明拓展坞在给盒子逆供电，这是廉价拓展坞的通病。\n所以拔掉了拓展坞的电源线，改用盒子自带的 12V1A 电源，勉强能跑满USB 2.00的10MBps带宽。\n第五步：目录隔离 SSD 上跑两类东西，必须隔离：\n1 2 3 /mnt/ssd/ ├── nas/ drwx------ root:root ← Samba 共享 └── tuwunel/ drwx------ tuwunel:tuwunel ← Matrix 数据 方向 结果 Samba → Matrix 数据 看不见（共享路径只指向 nas/） Matrix 进程 → NAS 数据 进不去（权限 700，属主不是它） 再加一层 systemd 加固：\n1 2 3 4 5 6 [Service] ProtectSystem=strict ReadWritePaths=/var/lib/tuwunel /etc/tuwunel /run/tuwunel ProtectHome=yes NoNewPrivileges=yes RestrictAddressFamilies=AF_INET AF_INET6 AF_UNIX InaccessiblePaths 会启动失败 本来还想加一条 InaccessiblePaths=/mnt/ssd/nas，结果服务起不来：\n1 2 tuwunel.service: Failed to set up mount namespacing: /mnt/ssd/nas: No such file or directory 原因是 /mnt/ssd 本身是 USB 设备的挂载点，在它的子路径上做命名空间覆盖挂载会失败。\n去掉这条，改用目录权限（chmod 700）实现隔离，效果一样。\n第六步：私有 Matrix 服务器 选 Tuwunel —— Conduwuit 的官方继任者，Rust 写的，1–5 个用户只占 100–200MB 内存。\n对比 Synapse 要 800MB–1.5GB 还得外加 PostgreSQL，2GB 盒子上只有这条路。\n安装 1 2 3 4 5 6 7 8 9 10 11 12 curl -fsSL -o /usr/share/keyrings/tuwunel-archive-keyring.gpg \\ https://apt.f.dog/tuwunel-archive-keyring.gpg tee /etc/apt/sources.list.d/tuwunel.sources \u0026gt;/dev/null \u0026lt;\u0026lt;\u0026#39;EOF\u0026#39; Types: deb URIs: https://apt.f.dog Suites: stable Components: main Signed-By: /usr/share/keyrings/tuwunel-archive-keyring.gpg EOF apt update \u0026amp;\u0026amp; apt install tuwunel 配置要点 1 2 3 4 5 6 7 8 9 10 11 12 13 [global] server_name = \u0026#34;weishi1079.top\u0026#34; # 永不可改 database_path = \u0026#34;/var/lib/tuwunel\u0026#34; address = \u0026#34;127.0.0.1\u0026#34; port = 6167 allow_registration = true registration_token = \u0026#34;\u0026lt;随机令牌\u0026gt;\u0026#34; allow_federation = false # 关闭联邦 ip_source = \u0026#34;cf_connecting_ip\u0026#34; # 走 Cloudflare [global.well_known] client = \u0026#34;\u0026lt;个人Server URL\u0026gt;\u0026#34; server = \u0026#34;\u0026lt;个人Server URL\u0026gt;:443\u0026#34; server_name 一旦启动就烧进数据库，永久不可改。 所以官方建议用根域而不是子域 —— 以后换部署位置不用动身份。\n数据库放在 SSD 上，用 bind mount 绕开 AppArmor 的路径限制：\n1 /mnt/ssd/tuwunel /var/lib/tuwunel none bind 0 0 systemd Type=notify 不兼容 cloudflared service install 生成的服务单元用了 Type=notify，但手工运行 cloudflared tunnel run 不会发就绪信号，systemd 一直等到超时：\n1 Job for cloudflared.service failed because a timeout was exceeded. 修复（drop-in 覆盖）：\n1 2 3 4 5 mkdir -p /etc/systemd/system/cloudflared.service.d cat \u0026gt; /etc/systemd/system/cloudflared.service.d/type-fix.conf \u0026lt;\u0026lt;\u0026#39;EOF\u0026#39; [Service] Type=simple EOF Token 账号不匹配 这个最难查。服务启动后日志报：\n1 ERR Register tunnel error from server side error=\u0026#34;Failed to get tunnel\u0026#34; Token 结构完全合法 —— base64 能解码、a/t/s 三个字段齐全、Tunnel ID 也对得上 DNS 记录。\n但服务端说这条 Tunnel 不存在。\n最后把 token 解码对比才发现：\n1 2 {\u0026#34;a\u0026#34;:\u0026#34;3302164450cbae93e3b693cc1b38d\u0026#34;, ...} ← 旧 token 的账号 ID {\u0026#34;a\u0026#34;:\u0026#34;b2cc745c2e169f50bb6ac0c9cabe2850\u0026#34;, ...} ← 后台实际账号 ID 两个完全不同的账号。 换成后台重新生成的 token 后立刻正常。\n最终架构 1 2 3 4 5 6 7 8 9 10 11 12 Cloudflare Tunnel ├── weishi1079.top → Caddy:80 → 博客静态文件 │ └─ /.well-known/matrix/* → JSON（委托） ├── matrix.weishi1079.top → Tuwunel:6167 └── www.weishi1079.top → Caddy:80 盒子内部： eMMC 14G → 系统 SSD 110G → /mnt/ssd ├── nas/ → Samba 共享 ├── tuwunel/ → Matrix 数据库 └── www/blog/ → 博客 资源占用 进程 内存 Tuwunel 88 MB cloudflared 39 MB Caddy 35 MB 合计 ~163 MB / 1.7 GB CPU 温度稳定在 52–58°C。\n复盘 整件事没用上：双公头 USB 线、短接、免拆神器、TTL 串口。\n但踩了七个坑：\n首次 U 盘启动网络不通 → 断电重启 权限污染 58448 个文件 → chown JMS578 的 UAS 不兼容 → usb-storage.quirks SSD 供电不足掉盘 → 修 fsck InaccessiblePaths 跨挂载点失败 → 改用目录权限 Type=notify 不兼容 → drop-in 改 Type=simple Tunnel token 账号 ID 不匹配 → 换后台新 token 排查时用过一个诊断脚本，把配置层、服务层、链路层、证据层一次性收集起来 —— 包括用 openssl s_client 抓 TLS 证书来判断有没有中间人。证书 issuer 显示是 Cloudflare 的正规证书，才排除了 MITM，把方向转到 Connector 归属上。\n","permalink":"https://weishi1079.top/tech/first-post/","summary":"将电视盒子刷成小型服务器。","title":"把CM311-1改造成家用服务器"},{"content":"关于笔者 一个喜欢 gal，书和电脑的普通中学生。\n关于站点 分享软硬件的研究过程，以及读书和 Gal 相关的一些想法。\n不追求更新频率，想到什么写什么。\n联系 GitHub\nBilibili\n小黑盒\n若您想联系到我，通过平台私信即可。\nCC BY-NC-SA 4.0 协议 文章以CC BY-NC-SA 4.0协议发布，若您转载文章，需满足署名（BY）、非商业性使用（NC）、相同方式共享（SA）三个条件。\n然而您可以演绎和共享。\n","permalink":"https://weishi1079.top/about/","summary":"\u003ch2 id=\"关于笔者\"\u003e关于笔者\u003c/h2\u003e\n\u003cp\u003e一个喜欢 gal，书和电脑的普通中学生。\u003c/p\u003e\n\u003ch2 id=\"关于站点\"\u003e关于站点\u003c/h2\u003e\n\u003cp\u003e分享软硬件的研究过程，以及读书和 Gal 相关的一些想法。\u003c/p\u003e\n\u003cp\u003e不追求更新频率，想到什么写什么。\u003c/p\u003e\n\u003ch2 id=\"联系\"\u003e联系\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cp\u003e\u003ca href=\"https://github.com/Liushiweiying\"\u003eGitHub\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003ca href=\"https://space.bilibili.com/1564081548\"\u003eBilibili\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e\u003ca href=\"https://www.xiaoheihe.cn/app/user/profile/85429453\"\u003e小黑盒\u003c/a\u003e\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003e若您想联系到我，通过平台私信即可。\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ul\u003e","title":"关于"}]