diff --git a/content/blog/hello-world.md b/content/blog/hello-world.md new file mode 100644 index 0000000..ea5417a --- /dev/null +++ b/content/blog/hello-world.md @@ -0,0 +1,148 @@ +--- +title: "Topology, Code, and Everything Between" +description: "A test post exploring the rendering capabilities of our blog — LaTeX, code blocks, tables, and more." +date: "2025-03-22" +tags: ["mathematics", "engineering", "topology"] +--- + +Every good system begins with a clear abstraction. In mathematics, we build towers of definitions — each layer precise, composable, and minimal. Software should aspire to the same discipline. + +This post is a tour of our blog's rendering capabilities. If you're reading this, everything below should look right. + +## Inline math and display equations + +The fundamental group $\pi_1(X, x_0)$ captures the algebraic structure of loops in a topological space. For a simply connected space, $\pi_1(X) = 0$. + +A key result in algebraic topology is the **Euler characteristic**: + +$$ +\chi(M) = \sum_{k=0}^{n} (-1)^k \, b_k +$$ + +where $b_k = \text{rank}(H_k(M; \mathbb{Z}))$ are the Betti numbers. For a closed, orientable surface of genus $g$: + +$$ +\chi(\Sigma_g) = 2 - 2g +$$ + +The de Rham cohomology connects differential forms to topology via Stokes' theorem: + +$$ +\int_{\partial \Omega} \omega = \int_{\Omega} d\omega +$$ + +## Code blocks + +Here's a Rust implementation of a simplicial complex: + +```rust +use std::collections::BTreeSet; + +/// A simplex is an ordered set of vertex indices. +type Simplex = BTreeSet; + +/// A simplicial complex is a collection of simplices +/// closed under taking faces. +struct SimplicialComplex { + simplices: Vec, +} + +impl SimplicialComplex { + fn new() -> Self { + Self { simplices: Vec::new() } + } + + /// Insert a simplex and all of its faces. + fn insert(&mut self, simplex: Simplex) { + // Add all faces (subsets) of the simplex + let vertices: Vec = simplex.iter().copied().collect(); + for mask in 1..=((1 << vertices.len()) - 1) { + let face: Simplex = vertices + .iter() + .enumerate() + .filter(|(i, _)| mask & (1 << i) != 0) + .map(|(_, &v)| v) + .collect(); + if !self.simplices.contains(&face) { + self.simplices.push(face); + } + } + } + + /// Compute the Euler characteristic. + fn euler_characteristic(&self) -> i64 { + let max_dim = self.simplices.iter().map(|s| s.len()).max().unwrap_or(0); + (0..max_dim) + .map(|k| { + let count = self.simplices.iter().filter(|s| s.len() == k + 1).count() as i64; + if k % 2 == 0 { count } else { -count } + }) + .sum() + } +} +``` + +And a TypeScript example computing persistent homology intervals: + +```typescript +interface Interval { + birth: number; + death: number | null; // null means the feature persists + dimension: number; +} + +function computePersistenceDiagram(filtration: Map>): Interval[] { + const intervals: Interval[] = []; + + for (const [threshold, simplices] of filtration) { + for (const simplex of simplices) { + const dim = simplex.split(",").length - 1; + intervals.push({ + birth: threshold, + death: null, + dimension: dim, + }); + } + } + + return intervals; +} +``` + +## Blockquotes + +> The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such steps. +> +> — Alexander Grothendieck + +## Lists + +Key properties of a **topological space** $(X, \tau)$: + +1. The empty set $\emptyset$ and the whole space $X$ are in $\tau$ +2. Arbitrary unions of elements of $\tau$ are in $\tau$ +3. Finite intersections of elements of $\tau$ are in $\tau$ + +Tools we use daily: + +- **Rust** — systems programming with algebraic type systems +- **TypeScript** — web interfaces and tooling +- **Python** — numerical experiments and prototyping +- **C++** — high-performance simulation (FEM, rad-hydro) + +## Tables + +| Manifold | $\chi$ | $\pi_1$ | Orientable | +| --------------- | ------ | ------------------------------- | ---------- | +| $S^2$ | $2$ | $0$ | Yes | +| $T^2$ | $0$ | $\mathbb{Z}^2$ | Yes | +| $\mathbb{R}P^2$ | $1$ | $\mathbb{Z}/2\mathbb{Z}$ | No | +| Klein bottle | $0$ | $\mathbb{Z} \rtimes \mathbb{Z}$ | No | + +## Horizontal rules and emphasis + +--- + +We believe that _mathematical rigor_ and **engineering pragmatism** are not at odds — they are complementary. The best abstractions emerge when you understand the structure of your problem deeply enough to see what's essential and what's accidental. + +Build on solid foundations. 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"sha512-KzIbH/9tXat2u30jf+smMwFCsno4wHVdNmzFyL+T/L3UGqqk6JKfVqOFOZEpZSHADH1k40ab6NUIXZq422ov3Q==", + "license": "MIT", + "dependencies": { + "@types/unist": "^3.0.0", + "vfile-message": "^4.0.0" + }, + "funding": { + "type": "opencollective", + "url": "https://opencollective.com/unified" + } + }, + "node_modules/vfile-location": { + "version": "5.0.3", + "resolved": "https://registry.npmjs.org/vfile-location/-/vfile-location-5.0.3.tgz", + "integrity": "sha512-5yXvWDEgqeiYiBe1lbxYF7UMAIm/IcopxMHrMQDq3nvKcjPKIhZklUKL+AE7J7uApI4kwe2snsK+eI6UTj9EHg==", + "license": "MIT", + "dependencies": { + "@types/unist": "^3.0.0", + "vfile": "^6.0.0" + }, + "funding": { + "type": "opencollective", + "url": "https://opencollective.com/unified" + } + }, + "node_modules/vfile-message": { + "version": "4.0.3", + "resolved": "https://registry.npmjs.org/vfile-message/-/vfile-message-4.0.3.tgz", + "integrity": "sha512-QTHzsGd1EhbZs4AsQ20JX1rC3cOlt/IWJruk893DfLRr57lcnOeMaWG4K0JrRta4mIJZKth2Au3mM3u03/JWKw==", + "license": "MIT", + "dependencies": { + "@types/unist": "^3.0.0", + "unist-util-stringify-position": "^4.0.0" + }, + "funding": { + "type": "opencollective", + "url": "https://opencollective.com/unified" + } + }, + "node_modules/web-namespaces": { + "version": "2.0.1", + "resolved": "https://registry.npmjs.org/web-namespaces/-/web-namespaces-2.0.1.tgz", + "integrity": "sha512-bKr1DkiNa2krS7qxNtdrtHAmzuYGFQLiQ13TsorsdT6ULTkPLKuu5+GsFpDlg6JFjUTwX2DyhMPG2be8uPrqsQ==", + "license": "MIT", + "funding": { + "type": "github", + "url": "https://github.com/sponsors/wooorm" + } + }, "node_modules/which": { "version": "2.0.2", "resolved": "https://registry.npmjs.org/which/-/which-2.0.2.tgz", @@ -6317,6 +8253,16 @@ "funding": { "url": "https://github.com/sponsors/sindresorhus" } + }, + "node_modules/zwitch": { + "version": "2.0.4", + "resolved": "https://registry.npmjs.org/zwitch/-/zwitch-2.0.4.tgz", + "integrity": "sha512-bXE4cR/kVZhKZX/RjPEflHaKVhUVl85noU3v6b8apfQEc1x4A+zBxjZ4lN8LqGd6WZ3dl98pY4o717VFmoPp+A==", + "license": "MIT", + "funding": { + "type": "github", + "url": "https://github.com/sponsors/wooorm" + } } } } diff --git a/package.json b/package.json index ee0b623..33cce7a 100644 --- a/package.json +++ b/package.json @@ -14,15 +14,27 @@ }, "dependencies": { "@radix-ui/react-slot": "^1.2.3", + "@shikijs/rehype": "^4.0.2", + "@tailwindcss/typography": "^0.5.19", "class-variance-authority": "^0.7.1", "clsx": "^2.1.1", + "gray-matter": "^4.0.3", "lucide-react": "^0.511.0", "next": "15.3.8", "next-themes": "^0.4.6", "react": "^19.0.0", "react-dom": "^19.0.0", + "rehype-katex": "^7.0.1", + "rehype-slug": "^6.0.0", + "rehype-stringify": "^10.0.1", + "remark-gfm": "^4.0.1", + "remark-math": "^6.0.0", + "remark-parse": "^11.0.0", + "remark-rehype": "^11.1.2", + "shiki": "^4.0.2", "tailwind-merge": "^3.3.0", - "tailwindcss-animate": "^1.0.7" + "tailwindcss-animate": "^1.0.7", + "unified": "^11.0.5" }, "devDependencies": { "@eslint/eslintrc": "^3", diff --git a/src/app/(container)/blog/[slug]/page.tsx b/src/app/(container)/blog/[slug]/page.tsx new file mode 100644 index 0000000..0b7a56d --- /dev/null +++ b/src/app/(container)/blog/[slug]/page.tsx @@ -0,0 +1,71 @@ +import { notFound } from "next/navigation"; +import Link from "next/link"; +import { getAllPostsMeta, getPostBySlug } from "@/lib/blog"; +import type { Metadata } from "next"; + +interface PageProps { + params: Promise<{ slug: string }>; +} + +export async function generateStaticParams() { + const posts = getAllPostsMeta(); + return posts.map((post) => ({ slug: post.slug })); +} + +export async function generateMetadata({ params }: PageProps): Promise { + const { slug } = await params; + const post = await getPostBySlug(slug); + if (!post) return {}; + return { + title: `${post.title} | Harness Labs`, + description: post.description, + }; +} + +export default async function BlogPostPage({ params }: PageProps) { + const { slug } = await params; + const post = await getPostBySlug(slug); + if (!post) notFound(); + + return ( +
+
+
+ + ← Back to blog + +

{post.title}

+
+ + {post.tags.length > 0 && ( +
+ {post.tags.map((tag) => ( + + {tag} + + ))} +
+ )} +
+
+ +
+
+
+ ); +} diff --git a/src/app/(container)/blog/page.tsx b/src/app/(container)/blog/page.tsx new file mode 100644 index 0000000..823f669 --- /dev/null +++ b/src/app/(container)/blog/page.tsx @@ -0,0 +1,74 @@ +import Link from "next/link"; +import { getAllPostsMeta } from "@/lib/blog"; +import type { Metadata } from "next"; + +export const metadata: Metadata = { + title: "Harness Labs | Blog", + description: + "Thoughts on mathematics, software engineering, and the intersection of theory and practice.", +}; + +export default function BlogPage() { + const posts = getAllPostsMeta(); + + return ( +
+
+
+

+ Harness Labs +

+

Blog

+

+ Thoughts on mathematics, software engineering, and the intersection of theory and + practice. +

+
+ +
+ {posts.length === 0 ? ( +

No posts yet. Check back soon.

+ ) : ( +
+ {posts.map((post) => ( + +
+
+

+ {post.title} +

+

{post.description}

+ {post.tags.length > 0 && ( +
+ {post.tags.map((tag) => ( + + {tag} + + ))} +
+ )} +
+ +
+ + ))} +
+ )} +
+
+
+ ); +} diff --git a/src/app/globals.css b/src/app/globals.css index 6e6984c..dc68193 100644 --- a/src/app/globals.css +++ b/src/app/globals.css @@ -115,3 +115,79 @@ @apply bg-background text-foreground; } } + +/* Blog prose customizations */ +.prose { + --tw-prose-body: hsl(var(--foreground)); + --tw-prose-headings: hsl(var(--foreground)); + --tw-prose-links: hsl(var(--foreground)); + --tw-prose-bold: hsl(var(--foreground)); + --tw-prose-counters: hsl(var(--muted-foreground)); + --tw-prose-bullets: hsl(var(--muted-foreground)); + --tw-prose-hr: hsl(var(--border)); + --tw-prose-quotes: hsl(var(--foreground)); + --tw-prose-quote-borders: hsl(var(--border)); + --tw-prose-captions: hsl(var(--muted-foreground)); + --tw-prose-code: hsl(var(--foreground)); + --tw-prose-th-borders: hsl(var(--border)); + --tw-prose-td-borders: hsl(var(--border)); +} + +.prose code:not(pre code) { + @apply bg-muted px-1.5 py-0.5 rounded text-sm font-mono; +} + +.prose code:not(pre code)::before, +.prose code:not(pre code)::after { + content: none; +} + +/* Code blocks */ +.prose pre { + @apply border border-border rounded-lg overflow-x-auto; +} + +.prose pre > code { + @apply font-mono text-sm leading-relaxed; + font-family: var(--font-red-hat-mono), ui-monospace, monospace; +} + +/* Shiki dual-theme: show the correct theme based on light/dark mode */ +.prose pre code { + background: transparent; +} + +html:not(.dark) .shiki, +html:not(.dark) .shiki span { + color: var(--shiki-light) !important; + background-color: var(--shiki-light-bg) !important; +} + +html.dark .shiki, +html.dark .shiki span { + color: var(--shiki-dark) !important; + background-color: var(--shiki-dark-bg) !important; +} + +.prose .shiki { + @apply rounded-lg; +} + +/* KaTeX display math */ +.prose .katex-display { + @apply overflow-x-auto py-4; +} + +/* Tables */ +.prose table { + @apply border-collapse w-full; +} + +.prose th { + @apply bg-muted font-semibold; +} + +.prose th, +.prose td { + @apply border border-border px-4 py-2 text-left; +} diff --git a/src/app/layout.tsx b/src/app/layout.tsx index 9926b3a..1cf623b 100644 --- a/src/app/layout.tsx +++ b/src/app/layout.tsx @@ -47,7 +47,13 @@ export default function RootLayout({ }>) { return ( - + + + (); + Object.defineProperty(globalThis, "localStorage", { + value: { + getItem: (key: string) => storage.get(key) ?? null, + setItem: (key: string, value: string) => storage.set(key, value), + removeItem: (key: string) => storage.delete(key), + clear: () => storage.clear(), + get length() { + return storage.size; + }, + key: (index: number) => [...storage.keys()][index] ?? null, + }, + writable: true, + configurable: true, + }); + } +} diff --git a/src/lib/blog.ts b/src/lib/blog.ts new file mode 100644 index 0000000..db1a61c --- /dev/null +++ b/src/lib/blog.ts @@ -0,0 +1,91 @@ +import fs from "fs"; +import path from "path"; +import matter from "gray-matter"; +import { unified } from "unified"; +import remarkParse from "remark-parse"; +import remarkMath from "remark-math"; +import remarkGfm from "remark-gfm"; +import remarkRehype from "remark-rehype"; +import rehypeKatex from "rehype-katex"; +import rehypeSlug from "rehype-slug"; +import rehypeShiki from "@shikijs/rehype"; +import rehypeStringify from "rehype-stringify"; + +const BLOG_DIR = path.join(process.cwd(), "content/blog"); + +export interface BlogPost { + slug: string; + title: string; + description: string; + date: string; + tags: string[]; + content: string; +} + +export interface BlogPostMeta { + slug: string; + title: string; + description: string; + date: string; + tags: string[]; +} + +function getMarkdownFiles(): string[] { + if (!fs.existsSync(BLOG_DIR)) return []; + return fs.readdirSync(BLOG_DIR).filter((file) => file.endsWith(".md")); +} + +function parseFrontmatter(slug: string): { data: Record; content: string } { + const filePath = path.join(BLOG_DIR, `${slug}.md`); + const raw = fs.readFileSync(filePath, "utf-8"); + return matter(raw); +} + +export function getAllPostsMeta(): BlogPostMeta[] { + const files = getMarkdownFiles(); + const posts = files.map((file) => { + const slug = file.replace(/\.md$/, ""); + const { data } = parseFrontmatter(slug); + return { + slug, + title: (data.title as string) ?? slug, + description: (data.description as string) ?? "", + date: (data.date as string) ?? "", + tags: (data.tags as string[]) ?? [], + }; + }); + + return posts.sort((a, b) => new Date(b.date).getTime() - new Date(a.date).getTime()); +} + +export async function getPostBySlug(slug: string): Promise { + const filePath = path.join(BLOG_DIR, `${slug}.md`); + if (!fs.existsSync(filePath)) return null; + + const { data, content: rawContent } = parseFrontmatter(slug); + + const result = await unified() + .use(remarkParse) + .use(remarkGfm) + .use(remarkMath) + .use(remarkRehype, { allowDangerousHtml: true }) + .use(rehypeKatex) + .use(rehypeSlug) + .use(rehypeShiki, { + themes: { + light: "github-light", + dark: "tokyo-night", + }, + }) + .use(rehypeStringify, { allowDangerousHtml: true }) + .process(rawContent); + + return { + slug, + title: (data.title as string) ?? slug, + description: (data.description as string) ?? "", + date: (data.date as string) ?? "", + tags: (data.tags as string[]) ?? [], + content: String(result), + }; +} diff --git a/tailwind.config.ts b/tailwind.config.ts index 298696b..c2427cb 100644 --- a/tailwind.config.ts +++ b/tailwind.config.ts @@ -76,5 +76,5 @@ export default { }, }, }, - plugins: [require("tailwindcss-animate")], + plugins: [require("tailwindcss-animate"), require("@tailwindcss/typography")], } satisfies Config;