assets/posts.js

/* The post index. Adding an article = add one entry at the top of POSTS,
   plus the matching file in posts/<slug>.html. Nothing else to touch. */

const CATEGORIES = {
  sequences: { label: "Sequences & Recurrences",
               blurb: "Closed forms, recursions, and the structures hiding behind them." },
  dynamics:  { label: "Dynamics & Iteration",
               blurb: "What happens when you apply the same map over and over." },
  linalg:    { label: "Linear Algebra",
               blurb: "Eigenvalues, matrices, and the geometry they encode." },
  analysis:  { label: "Analysis",
               blurb: "Limits, convergence, approximation." }
};

const POSTS = [
  {
    slug: "fixed-points-and-closed-forms",
    title: "Fixed Points, and Why They Solve Recurrences",
    subtitle: "From a high-school trick to the geometry of a Möbius map",
    category: "sequences",
    tags: ["fixed points", "Möbius maps", "eigenvalues", "conjugation"],
    date: "2026-09-21",
    minutes: 20,
    summary: "Everyone learns to solve aₙ₊₁ = paₙ + q by \"finding the fixed point and subtracting it.\" " +
             "That step looks like luck. It is not: the fixed point is the origin of the coordinate system in which " +
             "the map becomes a pure multiplication, and the multiplier is exactly f′ at that point."
  }
];

/* Not written yet — shown on the home page as what's coming. */
const PLANNED = [
  {
    title: "Characteristic Roots, and Why Fibonacci Has a Closed Form",
    category: "sequences",
    note: "The same eigenvalue story one dimension up: aₙ₊₂ = paₙ₊₁ + qaₙ as a matrix power, " +
          "Binet's formula, and what the repeated-root case really means."
  }
];

/* Expose explicitly so the other scripts never depend on cross-script scoping. */
window.CATEGORIES = CATEGORIES;
window.POSTS = POSTS;
window.PLANNED = PLANNED;