feat: image core — format math, sharp pipeline, sticker contour, prompts, pg-boss queue+worker

- format.ts: exact px (cm/2.54*dpi), catalog incl. The Frame/portrait, aspect ratio
- pipeline.ts: finalizeToFormat (cover/attention crop, dpi metadata), stickerContour
  (alpha dilation -> white border), heic->png, german filename slug
- prompts.ts: task prompts (clean/cutout/format) — reproduce, don't reinterpret
- process.ts: per-item chain (load -> model /v1/images -> finalize -> contour -> store)
- queue.ts + worker.ts: pg-boss (concurrency, retry, counters, 402 pause, completion)
- verified locally: 30x40@300dpi = exact 3543x4724 + dpi meta; sticker white border + alpha

src/lib/format.ts

@@ -0,0 +1,67 @@
+// Zielformate & exakte Pixelberechnung (siehe 01 §5, 06 §3).
+// px = round(cm / 2.54 * dpi)
+
+export type Orientation = 'portrait' | 'landscape';
+
+export interface Dimensions { w: number; h: number; cm?: [number, number]; label: string; }
+
+// cm-Formate: [Breite, Höhe] in Hochformat-Konvention (kurze Seite × lange Seite)
+const CM: Record<string, [number, number]> = {
+  '9x13': [9, 13], '10x15': [10, 15], '13x18': [13, 18], '15x20': [15, 20],
+  '20x30': [20, 30], '30x40': [30, 40], '30x45': [30, 45], '40x50': [40, 50],
+  '40x60': [40, 60], '50x70': [50, 70], '60x90': [60, 90],
+  A4: [21, 29.7], A3: [29.7, 42], A2: [42, 59.4],
+  '20x20': [20, 20], '30x30': [30, 30],
+};
+
+// Reine Bildschirmformate (feste Pixel, kein cm/dpi)
+const SCREEN: Record<string, [number, number]> = {
+  theframe: [3840, 2160],   // 16:9 quer
+  hochformat: [2160, 3840], // 9:16 hoch
+};
+
+export const cmToPx = (cm: number, dpi: number) => Math.round((cm / 2.54) * dpi);
+
+export interface ResolveInput {
+  format: string;             // Schlüssel oben, 'sticker', 'custom' oder 'keep'
+  orientation?: Orientation;
+  dpi?: number;
+  customCm?: [number, number]; // für 'sticker'/'custom'
+}
+
+/** Liefert exakte Zielpixel + Label. `keep` → null (Original behalten). */
+export function resolveDimensions(input: ResolveInput): Dimensions | null {
+  const { format } = input;
+  const dpi = input.dpi ?? 300;
+  const orient = input.orientation ?? 'portrait';
+
+  if (format === 'keep') return null;
+
+  if (format in SCREEN) {
+    const [w, h] = SCREEN[format];
+    return { w, h, label: format === 'theframe' ? 'The Frame' : 'Hochformat' };
+  }
+
+  let cm: [number, number] | undefined;
+  if (format in CM) cm = CM[format];
+  else if (format === 'sticker' || format === 'custom') cm = input.customCm ?? [5, 5];
+  if (!cm) throw new Error(`Unbekanntes Format: ${format}`);
+
+  // Hochformat-Konvention → gewünschte Orientierung anwenden
+  let [wCm, hCm] = cm;
+  if (orient === 'landscape') [wCm, hCm] = [hCm, wCm];
+  return { w: cmToPx(wCm, dpi), h: cmToPx(hCm, dpi), cm: [wCm, hCm],
+           label: `${cm[0]}×${cm[1]} cm` };
+}
+
+/** Vereinfachtes Seitenverhältnis als "b:h" für die Bild-API. */
+export function aspectRatio(w: number, h: number): string {
+  const g = gcd(w, h);
+  return `${Math.round(w / g)}:${Math.round(h / g)}`;
+}
+function gcd(a: number, b: number): number { return b === 0 ? a : gcd(b, a % b); }
+
+/** Reicht die native Auflösung für echte 300 dpi? (Hinweis in der UI.) */
+export function upscaleWarning(srcW: number, srcH: number, target: Dimensions): boolean {
+  return srcW < target.w * 0.95 || srcH < target.h * 0.95;
+}