/* ==========================================================
   SimpleAIHub — Lesson 28
   Vector Representation
========================================================== */

.lesson28-page,.lesson28-page *{box-sizing:border-box}
.lesson28-page{min-width:0;overflow-x:clip}
.lesson28-content{width:100%;min-width:0;padding:0 0 60px;color:#172033}
.lesson28-breadcrumb{margin-bottom:18px;color:#667085;font-size:14px}
.lesson28-breadcrumb a{color:#5b21b6;text-decoration:none}
.lesson28-breadcrumb span{padding:0 7px}
.lesson28-hero{padding-bottom:28px;border-bottom:1px solid #e7eaf0}
.lesson28-label,.lesson28-practice-label,.lesson28-quiz-label,.lesson28-recap-label{color:#5b21b6;font-size:14px;font-weight:800;letter-spacing:.07em}
.lesson28-hero h1{margin:7px 0 12px;color:#172033;font-size:46px;line-height:1.08}
.lesson28-hero p{max-width:820px;margin:0;color:#475467;font-size:18px;line-height:1.7}
.lesson28-meta{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px;color:#667085;font-size:14px}
.lesson28-objectives{margin:24px 0;padding:20px;border:1px solid #e4e7ec;border-radius:12px;background:#f8fafc}
.lesson28-objectives h2{margin:0 0 10px;font-size:21px}
.lesson28-objectives ul{margin:0;padding-left:20px}
.lesson28-objectives li{margin:7px 0;color:#475467;font-size:15px;line-height:1.6}
.lesson28-section{display:grid;grid-template-columns:36px minmax(0,1fr);gap:14px;width:100%;margin:38px 0}
.lesson28-number{width:34px;height:34px;display:flex;align-items:center;justify-content:center;border-radius:50%;background:#eee8ff;color:#5b21b6;font-size:14px;font-weight:800}
.lesson28-body{min-width:0}
.lesson28-body h2{margin:0 0 10px;font-size:28px;line-height:1.25}
.lesson28-body h3{margin:8px 0;font-size:18px}
.lesson28-body p{margin:9px 0;color:#475467;font-size:16px;line-height:1.75}
.lesson28-body code{padding:2px 5px;border-radius:4px;background:#f2f4f7;font-size:.9em}

.lesson28-vector-card{margin:20px 0;padding:24px;border:1px solid #d8c7f7;border-radius:12px;background:#faf8ff;text-align:center}
.lesson28-vector-title{color:#667085;font-size:11px;font-weight:800;letter-spacing:.08em}
.lesson28-vector{margin:13px 0;color:#5b21b6;font:700 22px/1.6 ui-monospace,SFMono-Regular,Menlo,monospace;overflow-wrap:anywhere}
.lesson28-vector-caption{color:#667085;font-size:13px}

.lesson28-callout{display:grid;grid-template-columns:max-content minmax(0,1fr);gap:10px;align-items:start;min-width:0;margin:17px 0;padding:15px 16px;border-left:3px solid #7c3aed;border-radius:0 9px 9px 0;background:#faf8ff}
.lesson28-callout strong{color:#5b21b6;font-size:15px;line-height:1.6}
.lesson28-callout span{min-width:0;color:#475467;font-size:15px;line-height:1.6;overflow-wrap:anywhere}
.lesson28-callout--green{border-left-color:#147a55;background:#f5fbf8}
.lesson28-callout--green strong{color:#147a55}

.lesson28-map{position:relative;height:300px;margin:22px 0;border:1px solid #e4e7ec;border-radius:12px;background:#fff;overflow:hidden}
.lesson28-map-axis-x,.lesson28-map-axis-y{position:absolute;background:#d9dee5}
.lesson28-map-axis-x{left:9%;right:9%;bottom:24%;height:1px}
.lesson28-map-axis-y{top:12%;bottom:12%;left:50%;width:1px}
.lesson28-point{position:absolute;width:74px;height:74px;display:flex;align-items:center;justify-content:center;border:1px solid #d8c7f7;border-radius:50%;background:#faf8ff;color:#5b21b6;font-size:14px;font-weight:800}
.lesson28-point-a{left:39%;bottom:39%}
.lesson28-point-b{left:48%;bottom:47%}
.lesson28-point-c{right:17%;top:25%}
.lesson28-point-d{left:17%;top:17%}
.lesson28-map-caption{position:absolute;left:0;right:0;bottom:8px;text-align:center;color:#667085;font-size:12px}

.lesson28-dimensions{display:grid;grid-template-columns:repeat(3,1fr);gap:9px;margin:20px 0}
.lesson28-dimension{padding:15px;border:1px solid #e4e7ec;border-radius:9px;background:#fff}
.lesson28-dimension span,.lesson28-dimension b{display:block}
.lesson28-dimension span{color:#667085;font-size:11px;font-weight:800}
.lesson28-dimension b{margin-top:7px;color:#5b21b6;font:700 17px/1.4 ui-monospace,SFMono-Regular,Menlo,monospace}

.lesson28-geometry{position:relative;height:260px;margin:20px 0;border:1px solid #e4e7ec;border-radius:12px;background:#fff;overflow:hidden}
.lesson28-origin{position:absolute;width:8px;height:8px;left:28%;bottom:25%;border-radius:50%;background:#344054}
.lesson28-line{position:absolute;left:28%;bottom:25%;height:3px;transform-origin:left center;border-radius:3px;background:#7c3aed}
.lesson28-line-one{width:230px;transform:rotate(-27deg)}
.lesson28-line-two{width:180px;transform:rotate(-8deg)}
.lesson28-arrow-label{position:absolute;color:#5b21b6;font-size:13px;font-weight:800}
.label-one{left:64%;top:18%}
.label-two{left:64%;top:39%}
.lesson28-geometry-origin{position:absolute;left:25%;bottom:17%;color:#667085;font-size:12px}

.lesson28-neighborhood{position:relative;min-height:360px;margin:22px 0;border:1px solid #e4e7ec;border-radius:12px;background:#fff}
.lesson28-neighborhood-center{position:absolute;left:50%;top:50%;width:210px;transform:translate(-50%,-50%);padding:18px;border:2px solid #7c3aed;border-radius:12px;background:#faf8ff;color:#24163e;text-align:center;font-size:15px;font-weight:800;line-height:1.5}
.lesson28-neighbor{position:absolute;width:190px;padding:12px;border:1px solid #b9dfcf;border-radius:10px;background:#f5fbf8;color:#3e5c51;text-align:center;font-size:13px;line-height:1.45}
.n1{left:7%;top:20%}.n2{right:7%;top:18%}.n3{left:10%;bottom:17%}.n4{right:8%;bottom:17%;border-color:#e4e7ec;background:#f8fafc;color:#667085}

.lesson28-compare{display:grid;grid-template-columns:1fr auto 1fr;gap:12px;align-items:center;margin:20px 0}
.lesson28-compare-card{min-width:0;padding:18px;border:1px solid #e4e7ec;border-radius:11px;background:#fff}
.lesson28-compare-card--purple{border-color:#d8c7f7;background:#faf8ff}
.lesson28-compare-card>span{color:#667085;font-size:11px;font-weight:800;letter-spacing:.07em}
.lesson28-compare-card--purple>span{color:#5b21b6}
.lesson28-compare-card h3{font-size:18px}
.lesson28-compare-card p{font-size:14px}
.lesson28-compare-arrow{color:#7c3aed;font-weight:800}

.lesson28-formula{margin:20px 0;padding:20px;text-align:center;border:1px solid #d8ccef;border-radius:11px;background:#faf8ff}
.lesson28-formula span,.lesson28-formula strong,.lesson28-formula small{display:block}
.lesson28-formula span{color:#667085;font-size:11px;font-weight:800;letter-spacing:.07em}
.lesson28-formula strong{margin:9px 0 6px;color:#24163e;font-size:22px;line-height:1.5}
.lesson28-formula small{color:#667085;font-size:13px}

.lesson28-similarity-bars{display:grid;gap:10px;margin:20px 0}
.lesson28-similarity-bars>div{display:grid;grid-template-columns:150px minmax(0,1fr) 120px;gap:10px;align-items:center}
.lesson28-similarity-bars span,.lesson28-similarity-bars b{font-size:13px}
.lesson28-similarity-bars b{color:#667085;text-align:right}
.lesson28-similarity-bars>div>div{height:12px;border-radius:20px;background:#edf0f2;overflow:hidden}
.lesson28-similarity-bars i{display:block;height:100%;border-radius:20px;background:#7c3aed}

.lesson28-code{width:100%;max-width:100%;min-width:0;margin:18px 0;overflow:hidden;border:1px solid #dfe3e8;border-radius:10px;background:#f8fafc}
.lesson28-codebar{display:flex;justify-content:space-between;gap:12px;padding:10px 12px;border-bottom:1px solid #dfe3e8;background:#f1f3f5;color:#344054;font-size:14px;font-weight:700}
.lesson28-code pre{max-width:100%;margin:0;padding:17px;overflow-x:auto;white-space:pre-wrap;overflow-wrap:anywhere;word-break:break-word;background:#f8fafc;color:#344054;font:14px/1.7 ui-monospace,SFMono-Regular,Menlo,monospace}

.lesson28-metric-grid{display:grid;grid-template-columns:repeat(2,1fr);gap:10px;margin:20px 0}
.lesson28-metric-grid>div{padding:17px;border:1px solid #e4e7ec;border-radius:10px;background:#fff}
.lesson28-metric-grid b,.lesson28-metric-grid span{display:block}
.lesson28-metric-grid b{font-size:16px}
.lesson28-metric-grid span{margin-top:6px;color:#667085;font-size:14px;line-height:1.5}

.lesson28-rag-flow{display:grid;grid-template-columns:1fr auto 1fr auto 1fr auto 1fr;gap:7px;align-items:center;margin:20px 0}
.lesson28-rag-flow>div{min-width:0;padding:15px;border:1px solid #e4e7ec;border-radius:9px;background:#fff}
.lesson28-rag-flow span,.lesson28-rag-flow b,.lesson28-rag-flow small{display:block}
.lesson28-rag-flow span{color:#667085;font-size:10px;font-weight:800}
.lesson28-rag-flow b{margin-top:5px;font-size:14px}
.lesson28-rag-flow small{margin-top:5px;color:#667085;font-size:11px;line-height:1.4}
.lesson28-rag-flow i{color:#7c3aed;font-size:17px;font-style:normal}

.lesson28-usecases{display:grid;grid-template-columns:repeat(3,1fr);gap:10px;margin-top:18px}
.lesson28-usecases>div{min-width:0;padding:17px;border:1px solid #e4e7ec;border-radius:10px;background:#fff}
.lesson28-usecases span{color:#5b21b6;font-size:11px;font-weight:800}
.lesson28-usecases b{display:block;margin-top:6px;font-size:16px}
.lesson28-usecases p{margin-bottom:0;font-size:14px}

.lesson28-misconceptions{display:grid;grid-template-columns:repeat(2,1fr);gap:10px;margin-top:18px}
.lesson28-misconceptions>div{min-width:0;padding:17px;border:1px solid #e4e7ec;border-radius:10px;background:#fff}
.lesson28-misconceptions b{font-size:15px;line-height:1.5}
.lesson28-misconceptions p{margin-bottom:0;font-size:14px}

.lesson28-practice{margin:46px 0 24px;padding:28px;border-radius:12px;background:#17112f;color:#fff}
.lesson28-practice-label{color:#c7b4ff}
.lesson28-practice h2{margin:8px 0 10px;color:#fff;font-size:31px}
.lesson28-practice>p,.lesson28-practice li{color:#d5d0e1;font-size:16px;line-height:1.7}
.lesson28-practice ol{margin:18px 0;padding-left:22px}
.lesson28-practice-box{margin-top:20px;padding:15px 17px;border:1px solid rgba(255,255,255,.13);border-radius:9px;background:rgba(255,255,255,.05);color:#ddd8e7;font-size:15px;line-height:1.6}

.lesson28-quiz{margin:38px 0;padding:22px 20px;border:1px solid #e4e7ec;border-radius:12px;background:#fff}
.lesson28-quiz h2{margin:7px 0 16px;font-size:28px}
.lesson28-question{padding:16px 0;border-top:1px solid #e4e7ec}
.lesson28-question strong{font-size:16px;line-height:1.5}
.lesson28-question p{margin:7px 0 0;color:#667085;font-size:15px;line-height:1.6}

.lesson28-recap{margin:38px 0;padding:24px 25px;border:1px solid #d9cff0;border-radius:12px;background:#faf8ff}
.lesson28-recap h2{margin:7px 0 20px;color:#24163e;font-size:27px}
.lesson28-recap-flow{display:grid;grid-template-columns:1fr auto 1fr auto 1fr auto 1fr;gap:8px;align-items:center}
.lesson28-recap-flow>div{min-width:0;padding:14px;border:1px solid #e4def0;border-radius:9px;background:#fff}
.lesson28-recap-flow b,.lesson28-recap-flow span{display:block}
.lesson28-recap-flow b{color:#5b21b6;font-size:14px}
.lesson28-recap-flow span{margin-top:5px;color:#667085;font-size:13px}
.lesson28-recap-flow i{color:#7c3aed;font-size:18px;font-style:normal}

.lesson28-takeaways{margin:38px 0;padding:24px 25px;border:1px solid #cce8db;border-radius:12px;background:#f5fbf8}
.lesson28-takeaways h2{margin:0 0 13px;color:#147a55;font-size:27px}
.lesson28-takeaways ul{margin:0;padding-left:21px}
.lesson28-takeaways li{margin:7px 0;color:#3e5c51;font-size:15px;line-height:1.6}

.lesson28-bottom-nav{display:grid;grid-template-columns:1fr 1fr;gap:12px;margin-top:35px;padding-top:24px;border-top:1px solid #e4e7ec}
.lesson28-bottom-nav a{min-width:0;padding:17px;border:1px solid #e4e7ec;border-radius:10px;background:#fff;color:#5b21b6;text-decoration:none;font-size:15px;font-weight:700;line-height:1.5;overflow-wrap:anywhere}
.lesson28-bottom-nav a:last-child{text-align:right}
.lesson28-bottom-nav a:hover{border-color:#7c3aed;background:#faf8ff}

@media(max-width:1050px){
.lesson28-rag-flow{grid-template-columns:repeat(4,1fr)}
.lesson28-rag-flow i{display:none}
.lesson28-usecases{grid-template-columns:repeat(2,1fr)}
}
@media(max-width:760px){
.lesson28-hero h1{font-size:36px}
.lesson28-hero p,.lesson28-body p{font-size:16px}
.lesson28-section{grid-template-columns:34px minmax(0,1fr);gap:11px;margin:32px 0}
.lesson28-body h2{font-size:25px}
.lesson28-dimensions,.lesson28-metric-grid,.lesson28-usecases,.lesson28-misconceptions{grid-template-columns:1fr}
.lesson28-compare{grid-template-columns:1fr}
.lesson28-compare-arrow{text-align:center}
.lesson28-similarity-bars>div{grid-template-columns:1fr}
.lesson28-similarity-bars b{text-align:left}
.lesson28-rag-flow{grid-template-columns:repeat(2,1fr)}
.lesson28-callout{grid-template-columns:1fr;gap:3px}
.lesson28-map{height:270px}
.lesson28-neighborhood{min-height:500px}
.lesson28-neighborhood-center{width:180px}
.lesson28-neighbor{width:150px}
.n1{left:5%;top:10%}.n2{right:5%;top:10%}.n3{left:5%;bottom:9%}.n4{right:5%;bottom:9%}
.lesson28-practice{padding:22px 18px}
.lesson28-recap-flow{grid-template-columns:1fr}
.lesson28-recap-flow i{display:none}
.lesson28-bottom-nav{grid-template-columns:1fr}
.lesson28-bottom-nav a:last-child{text-align:left}
}
@media(max-width:480px){
.lesson28-hero h1{font-size:32px}
.lesson28-objectives{padding:16px}
.lesson28-body h2{font-size:24px}
.lesson28-vector{font-size:17px}
.lesson28-geometry{height:220px}
.lesson28-line-one{width:150px}
.lesson28-line-two{width:125px}
.lesson28-map{height:250px}
.lesson28-point{width:58px;height:58px;font-size:12px}
.lesson28-neighborhood{min-height:530px}
.lesson28-neighborhood-center{width:160px;font-size:13px}
.lesson28-neighbor{width:135px;font-size:12px}
.lesson28-code pre{font-size:13px}
}


/* Shared code-block toolbar fix — Lessons 24–29 */
.lesson28-code.sah-code { overflow: hidden; }
.lesson28-code .sah-codebar { display:flex; align-items:center; justify-content:space-between; gap:12px; min-height:58px; padding:10px 12px; box-sizing:border-box; background:#f1f3f5; border-bottom:1px solid #dfe3e8; color:#344054; }
.lesson28-code .sah-codebar__language { display:flex; align-items:center; gap:7px; font-size:15px; font-weight:800; line-height:1; white-space:nowrap; flex-shrink:0; }
.lesson28-code .sah-codebar__icon { font-size:13px; font-weight:900; letter-spacing:-.05em; }
.lesson28-code .sah-codebar__title { display:none; }
.lesson28-code .sah-codebar__actions { display:flex; align-items:center; gap:8px; margin-left:auto; flex-shrink:0; }
.lesson28-code .sah-codebar__button { appearance:none; border:1px solid #cbd3dc; border-radius:8px; background:#fff; color:#344054; min-height:36px; padding:0 12px; font:700 13px/1 system-ui,-apple-system,BlinkMacSystemFont,"Segoe UI",sans-serif; cursor:pointer; box-shadow:0 1px 1px rgba(16,24,40,.03); transition:background .15s,border-color .15s,transform .05s; white-space:nowrap; text-decoration:none; }
.lesson28-code .sah-codebar__button:hover { background:#f8fafc; border-color:#98a2b3; }
.lesson28-code .sah-codebar__button:active { transform:translateY(1px); }
.lesson28-code .sah-codebar__button.is-copied { background:#f0fdf4; border-color:#86efac; color:#166534; }
.lesson28-code pre { margin:0; background:#f8fafc; color:#344054; border:0; border-radius:0; overflow:auto; -webkit-overflow-scrolling:touch; white-space:pre; tab-size:4; font:14px/1.65 ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier New",monospace; }
@media (max-width:600px) { .lesson28-code .sah-codebar { min-height:54px; padding:8px 9px; gap:8px; } .lesson28-code .sah-codebar__language { font-size:14px; } .lesson28-code .sah-codebar__button { min-height:34px; padding:0 9px; font-size:12px; } .lesson28-code .sah-codebar__actions { gap:6px; } .lesson28-code pre { padding:14px; font-size:13px; line-height:1.6; } }
@media (max-width:400px) { .lesson28-code .sah-codebar__button { padding:0 8px; font-size:11px; } }