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 <title>Math Notebook</title>
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">
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">
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jj/+OHlv3Ua8jtoieZjhyafbeGUwNwa2EO8RVn6wSbKyD+LbImxOdHAbt9y3PaTjn/ZCFyVrkasW49uiusfVlGaNj0cgqtg4eaY7rzT6qpu2Gf3GyhL/WcCAlMBpJjlemb/14WZ5C+NdDh2UJQsnysWDesjiF9bIgsdexwtJtEzbZnLl0J5OgOZsiSQMndGXdpECzB2u5U2bxpBWWWEDUVYqPtyIbeFyWOOb2JEEfoNAWxw38zBkWiA0zIVQqZSd79lKYYA+EXI5Q4AennaTDBvUXfhxRc8uZ1U4CabAaF6/RKrSeauElptkfbBH+WxcjYNzEZ0ybidINjA5CUqIinIBpWu54ea54O97nG30kCvoYgFIC+XBw3knltbVyuNxuGPPjTO62llm4w4+v9Me4BvOru/X/bKNigP9FCPNyMJ416XURZVWmaBq5EHEAP0U+ZUFx2kgjWtflv0X6bEYYoPkswRANdTVqmMwJ7MbJs6RdR9vxqMqhhSf2mCZhsLuL/AWRG4eM0RGDO/zM4Lg2etaLD4CqPOZ0TsUdRRqjvMr7BEUhMuJZivxre1hHGPxtXRVrUb8ho3fyOKX3pc7cHZQKz3NdDanjvJBg/NwyTir9c9wnqY7X+LLzh3rBYZ07OMwDXAR0xBYh7GcpfCrC1yJ/GIUadHilTLxnqckF9vcQX07yiP/uEHS0/GtQSXpsSVv4RPW1jJ+9EWVUBlUdXpUlULKIaD1rhGJNk8oCiKYrYDM+Ei8CM7Zh1/QUb5cca/8a81D0qdHhrbO+d06yLz7bsT6lCTPPPe2PLH07ZghQVa2usu5ZX75jY/kj8N6K4y3XJwoubRvf66+DKHjlTlPmRVdlMXnjwT9bsn5Y31yimJy3QeQ0PeYFKyH8Fo1U6UeHj6iUF4DvYAGElYfMK4G/EB5m3uvR3YkGsm3Owk4S2BahY0UJfbrZT6w+PsDT8vCJ9+QBbPHy8ZNW2TWQ8vkkVnjpGfXDhUGgPxf7zgqe3KLzbdZqPvBSkJjZO/5UbL2I7DcmakLcb6hysWQKLsKoKRVgAiNC0YER2Lzl70nL63CBwr5R2TB9JukX+9OMnLcdHlx5XrwRCTluFQZ2KcjmTXRqGewUZo2/TmZMuFqGYyXqgvxDpBvk4/DBxbE9+jcTg7gRPmaGx+QM/BB87LF/yXNK3mWQDwlK6dY3vryMPihhg80ai8zbLqSasiBnB9l7owHZffeXAzX5ABvzSqTMUY6B9CgME4q3RBTKxKPxfbk5uOjmkM4GT+qrTrjv6+XU1s1kez9h+SyIT2kS6cz1DG2fD6+I1ix6mOpjyfEaXOX4RitpXz4z0yZ/PilRh5oOoP+EI7ZZ8x7UVYtnYqPmBsrzm9RBQQ3HHgW0bZSzEMWqDFAPTEJzmfLvJnTZPt3O0TSzAObRkDdCb0jpwmgkRE7CVq5ZUMHARquBHQ9Lh4iJzdpIHdP/lPIoVIpHJ+po9csfniC7MHL0Ix+N8sNf31IP3TIaH+q0vOrkiy8GZo641lJwZebP2Ttk+937ZFO55wmycHXqoHomIKq8dqILb9//x6ZO/0++Y7Op6YHcw8KnisMAhm9hI1Q1OyQYiPkkZgi0GxZDg/rpzpKZ90Vz0M4j8yGDewqK5a8LVfiiw+dL0B4210LpOfAW+VPl/WVG/44QIaPuAu/T3gbMTbBjZfl6sYC4wZ3t2z5nP175eEZ98P5nWj5dNNQymCprd1GhpPAmgkGP/rQInOTvPDSWxXgyF0gHG3V+eir+unX2RcN6KLEDMyfrxkkVw/ro0PjMIbBAEyM57Q/JeadQcWSYRP+E7Xl98rcmXB+K7u9a3nrSeiQEUW3NKHJgTPVYBWgUFwx0SJ1KIUlMnHcVjfR2eZNG8kLi25XFtaZWnnjvSZOm8/DGyUmh9dKuTfDn4jZni0/dya7/U6JsOWd7bbB1B/KcHV1wPCraMLxkMffkLhweCqd48R5TFjuXnvnM8vvaDy2cop0yl0O7dddmXlViRQJttvPmTFNx3wkFZ/tOeedgBhRruJyG2joi+J5OFpaiLe2Lkq2Yzg5Qe54Mbm9hKXviedWKYrzwv/VRYWpeIu0f1+WzJk+TbZxzGPCC2131sJYv21oe3nBBSy1Bna2HTueIeu/2S2l2LBESKjMygVOVkJp/HVYIX6ANfJvc2Ud3vIO7vtbqVMbLQA+ciilBpM1JJuFRgZUBh/cK4IHBCpiV/YRdPtHZcf2XWXHPElpQBlnnS2KDARys9i+TVOJLHl5bd6lf56eyh9LmI6gbgSEQYFICqezeEeIn5ZBIaZid9TlFBshhk0PIigPVwViA/lhCA1I9RnW0CkIScDhCk6hKJA/0DJOWynUof5apxXsKyac9pdKbTy3zPzb5ZMSu/22jZx4Yl3dPWGHU7GhTiYNw8ZI0u1mwwbF6PKVURcCZBCQ63AQpAeVVqDCiTPGhXHw6D0Zbjk2cu3dYzcQB4ih0oq2E47o2rU6SYYP7SrRhg1qp4wYjCUKOzw1wbVkwEthuJjpjTtp/GE4mAtDh8OHVwAjjjAEChfzEE848AGPV8fwUlryBhdghFO2tjhbXY0JLNSCD2I5CCyxNrhKiBvOHK67rJdgCkijtKNjR14ozZo1NGd+jsjPKdA2WACOqfvaAwoUTLAUEkMPcX6dZb+ugfbleGW/xxEcw2fpyshzdEDg53Odzj0VGzQ0ejQxPwp5JQ0b1JX5d18nackYX/zVZUzEwBRjrVXCLEa5ht0iKwqIx0t25TcTaIwon6x6oowtngkqVRWghFz/cIR/Qr1aMu/uUXh44gNFtCTYe/bu3kEW3Tda0pOwNcCHkSb5ztNEd1n0MWew0HZNs3xaAc5QrTodzJFsxt5UZQpoUdB/3gjEhZZvUCdNlswZJ+3atghEBQFglC5Ft1i+aIK0O6WxlOJtDr8SD1+sGGEUF1plhQeB0bhbvMFp5J0RxirFG7ghDV0z/EYHcJ7cSssx8sGNunnihzyMd7ydlc7ntJY3n56ij+H+pou/HS5GawSBoNp89IAFi1fJwmXvyqYtP0g+X4xy4qJJah3303FmB1YDHqIoztiOjCwBmRGkaGUgT4AksUXF01kwM2XBTUmtXYSrgzjtSMXhTfvWTTDh9cazx/mm85EgTFMiOLVZiLr5Sski8FSGABYl5xzIz3/tzU/kueXr5L31X0tOLtZ+Z6XzRq2Adneqi9lak8NbmQbmVWIcI1wFGQJOQ9ypOBDWbX2NQ6yTb9wGoGzU6tVNk95d28nF/TpJfxzCpKYlpkhptABiA2L4SEOf/V+9+2xV0nxBgQAAAABJRU5ErkJggg==">
 <!-- MATHNOTE_BUILD_CSS -->
 <style>
 *, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }
diff --git a/public/icons/icon-192.png b/public/icons/icon-192.png
deleted file mode 100644
index 5da2f4d..0000000
Binary files a/public/icons/icon-192.png and /dev/null differ
diff --git a/public/icons/icon-512.png b/public/icons/icon-512.png
deleted file mode 100644
index 6400118..0000000
Binary files a/public/icons/icon-512.png and /dev/null differ
diff --git a/scripts/build.mjs b/scripts/build.mjs
index cd422b2..d115b0b 100644
--- a/scripts/build.mjs
+++ b/scripts/build.mjs
@@ -3,6 +3,7 @@ import { createHash } from 'node:crypto';
 import { cp, mkdir, readFile, readdir, rm, writeFile } from 'node:fs/promises';
 import { relative } from 'node:path';
 import { fileURLToPath } from 'node:url';
+import { deflateSync } from 'node:zlib';
 
 const outdir = new URL('../dist/', import.meta.url);
 const assetsDir = new URL('../dist/assets/', import.meta.url);
@@ -11,6 +12,105 @@ const publicDir = new URL('../public/', import.meta.url);
 const serviceWorkerTemplateUrl = new URL('../src/sw.js', import.meta.url);
 const entryPoint = fileURLToPath(new URL('../src/app.js', import.meta.url));
 
+const PNG_SIGNATURE = Buffer.from([137, 80, 78, 71, 13, 10, 26, 10]);
+let crcTable = null;
+
+function crc32(buffer) {
+  if (!crcTable) {
+    crcTable = new Uint32Array(256);
+    for (let n = 0; n < 256; n++) {
+      let value = n;
+      for (let k = 0; k < 8; k++) {
+        value = (value & 1) ? (0xedb88320 ^ (value >>> 1)) : (value >>> 1);
+      }
+      crcTable[n] = value >>> 0;
+    }
+  }
+
+  let crc = 0xffffffff;
+  for (const byte of buffer) {
+    crc = crcTable[(crc ^ byte) & 0xff] ^ (crc >>> 8);
+  }
+  return (crc ^ 0xffffffff) >>> 0;
+}
+
+function pngChunk(type, data) {
+  const typeBytes = Buffer.from(type, 'ascii');
+  const length = Buffer.alloc(4);
+  length.writeUInt32BE(data.length);
+
+  const crc = Buffer.alloc(4);
+  crc.writeUInt32BE(crc32(Buffer.concat([typeBytes, data])));
+
+  return Buffer.concat([length, typeBytes, data, crc]);
+}
+
+function createAppIcon(size) {
+  const rowSize = 1 + size * 4;
+  const pixels = Buffer.alloc(rowSize * size);
+  const pad = Math.floor(size / 8);
+  const stroke = Math.max(4, Math.floor(size / 24));
+
+  const isSigmaPixel = (x, y) => {
+    const top = Math.floor(size * 0.29);
+    const bottom = Math.floor(size * 0.71);
+    const left = Math.floor(size * 0.31);
+    const right = Math.floor(size * 0.69);
+    const mid = Math.floor(size * 0.50);
+
+    if (Math.abs(y - top) <= stroke && x >= left && x <= right) return true;
+    if (Math.abs(y - bottom) <= stroke && x >= left && x <= right) return true;
+
+    const upperProgress = (y - top) / Math.max(1, mid - top);
+    const lowerProgress = (bottom - y) / Math.max(1, bottom - mid);
+
+    if (y >= top && y <= mid) {
+      const lineX = Math.round(left + upperProgress * (mid - left));
+      if (Math.abs(x - lineX) <= stroke) return true;
+    }
+    if (y > mid && y <= bottom) {
+      const lineX = Math.round(left + lowerProgress * (mid - left));
+      if (Math.abs(x - lineX) <= stroke) return true;
+    }
+    return false;
+  };
+
+  for (let y = 0; y < size; y++) {
+    const rowOffset = y * rowSize;
+    pixels[rowOffset] = 0;
+
+    for (let x = 0; x < size; x++) {
+      const offset = rowOffset + 1 + x * 4;
+      const insideCard = x >= pad && x < size - pad && y >= pad && y < size - pad;
+      const sigma = insideCard && isSigmaPixel(x, y);
+      const color = sigma || !insideCard
+        ? [25, 113, 194, 255]
+        : [255, 255, 255, 255];
+
+      pixels[offset] = color[0];
+      pixels[offset + 1] = color[1];
+      pixels[offset + 2] = color[2];
+      pixels[offset + 3] = color[3];
+    }
+  }
+
+  const ihdr = Buffer.alloc(13);
+  ihdr.writeUInt32BE(size, 0);
+  ihdr.writeUInt32BE(size, 4);
+  ihdr[8] = 8;
+  ihdr[9] = 6;
+  ihdr[10] = 0;
+  ihdr[11] = 0;
+  ihdr[12] = 0;
+
+  return Buffer.concat([
+    PNG_SIGNATURE,
+    pngChunk('IHDR', ihdr),
+    pngChunk('IDAT', deflateSync(pixels, { level: 9 })),
+    pngChunk('IEND', Buffer.alloc(0))
+  ]);
+}
+
 await rm(outdir, { recursive: true, force: true });
 await mkdir(outdir, { recursive: true });
 
@@ -48,6 +148,11 @@ const appCssPath = `./assets/${cssBundles[0]}`;
 
 await cp(publicDir, outdir, { recursive: true });
 
+const iconsDir = new URL('../dist/icons/', import.meta.url);
+await mkdir(iconsDir, { recursive: true });
+await writeFile(new URL('icon-192.png', iconsDir), createAppIcon(192));
+await writeFile(new URL('icon-512.png', iconsDir), createAppIcon(512));
+
 let html = await readFile(templateUrl, 'utf8');
 html = html.replace(
   '<!-- MATHNOTE_BUILD_CSS -->',
diff --git a/scripts/verify-offline.mjs b/scripts/verify-offline.mjs
index fdfa8fc..c616d91 100644
--- a/scripts/verify-offline.mjs
+++ b/scripts/verify-offline.mjs
@@ -18,6 +18,72 @@ const textExtensions = new Set(['.html', '.js', '.css', '.json', '.webmanifest',
 const violations = [];
 let fontCount = 0;
 
+const PNG_SIGNATURE = Buffer.from([137, 80, 78, 71, 13, 10, 26, 10]);
+let crcTable = null;
+
+function getCrcTable() {
+  if (crcTable) return crcTable;
+  crcTable = new Uint32Array(256);
+  for (let n = 0; n < 256; n++) {
+    let value = n;
+    for (let k = 0; k < 8; k++) {
+      value = (value & 1) ? (0xedb88320 ^ (value >>> 1)) : (value >>> 1);
+    }
+    crcTable[n] = value >>> 0;
+  }
+  return crcTable;
+}
+
+function crc32(buffer) {
+  const table = getCrcTable();
+  let crc = 0xffffffff;
+  for (const byte of buffer) {
+    crc = table[(crc ^ byte) & 0xff] ^ (crc >>> 8);
+  }
+  return (crc ^ 0xffffffff) >>> 0;
+}
+
+async function verifyPng(path, expectedWidth, expectedHeight) {
+  const bytes = await readFile(new URL(path, root));
+  if (bytes.length < 33 || !bytes.subarray(0, 8).equals(PNG_SIGNATURE)) {
+    throw new Error('invalid PNG signature');
+  }
+
+  let offset = 8;
+  let width = null;
+  let height = null;
+  let sawIend = false;
+
+  while (offset + 12 <= bytes.length) {
+    const length = bytes.readUInt32BE(offset);
+    const typeStart = offset + 4;
+    const dataStart = offset + 8;
+    const crcOffset = dataStart + length;
+    const nextOffset = crcOffset + 4;
+    if (nextOffset > bytes.length) throw new Error('truncated PNG chunk');
+
+    const type = bytes.toString('ascii', typeStart, typeStart + 4);
+    const expectedCrc = bytes.readUInt32BE(crcOffset);
+    const actualCrc = crc32(bytes.subarray(typeStart, crcOffset));
+    if (actualCrc !== expectedCrc) throw new Error(`bad CRC in ${type} chunk`);
+
+    if (type === 'IHDR') {
+      width = bytes.readUInt32BE(dataStart);
+      height = bytes.readUInt32BE(dataStart + 4);
+    } else if (type === 'IEND') {
+      sawIend = true;
+      break;
+    }
+
+    offset = nextOffset;
+  }
+
+  if (!sawIend) throw new Error('missing IEND chunk');
+  if (width !== expectedWidth || height !== expectedHeight) {
+    throw new Error(`unexpected dimensions ${width}x${height}`);
+  }
+}
+
 async function walk(dirUrl) {
   const entries = await readdir(dirUrl, { withFileTypes: true });
   for (const entry of entries) {
@@ -57,6 +123,16 @@ for (const forbidden of ['cdn.jsdelivr.net', 'esm.sh', 'type="module"', 'type="i
 if (!html.includes('rel="manifest" href="./manifest.webmanifest"')) {
   violations.push('index.html: manifest link missing or not relative');
 }
+
+if (!html.includes('<meta name="mobile-web-app-capable" content="yes">')) {
+  violations.push('index.html: mobile-web-app-capable meta tag missing');
+}
+if (!html.includes('<link rel="icon" type="image/png" sizes="192x192" href="./icons/icon-192.png">')) {
+  violations.push('index.html: local PNG favicon missing');
+}
+if (html.includes('data:image/png;base64')) {
+  violations.push('index.html: embedded base64 favicon must not be used');
+}
 if (!html.includes('id="examples-btn"')) {
   violations.push('index.html: examples button missing');
 }
@@ -142,6 +218,17 @@ const iconSizes = new Set((manifest.icons || []).map(icon => icon.sizes));
 if (!iconSizes.has('192x192')) violations.push('manifest: 192x192 icon missing');
 if (!iconSizes.has('512x512')) violations.push('manifest: 512x512 icon missing');
 
+for (const [path, width, height] of [
+  ['icons/icon-192.png', 192, 192],
+  ['icons/icon-512.png', 512, 512]
+]) {
+  try {
+    await verifyPng(path, width, height);
+  } catch (error) {
+    violations.push(`${path}: ${error.message}`);
+  }
+}
+
 const sw = await readFile(new URL('sw.js', root), 'utf8');
 if (sw.includes('__CACHE_NAME__') || sw.includes('__PRECACHE_ASSETS__')) {
   violations.push('sw.js: build placeholders were not replaced');