Role: Principal Engineer and Product Designer. Build a polished, production-ready Multiplication Tables app that covers tables 1–50, optimized for Android, iOS, and Web (PWA). Deliver complete source code, CI/CD, tests, analytics, and documentation. Assume full freedom to choose best-in-class technologies, paid services, and premium assets. Prioritize quality, performance, accessibility, and delightful UX. 1. Product scope • Content coverage: Tables 1–50, with two ranges selectable per table: up to ×20 (default) and advanced up to ×50. Include a global mixed-practice mode spanning 1–50. • Learning modes: • Learn: Explore any table with pattern tips, examples, and audio. • Practice: Type-in and multiple-choice drills, instant feedback, error review. • Speed Run: Timed 30/60/120-second challenges with leaderboards. • Flashcards (SR): Spaced-repetition decks for all facts, adaptive scheduling. • Extras: Printable charts (PDF) for 1–50 and 1–100, dark mode, offline mode, parent/teacher dashboard, and classroom rostering. 2. Learning design • Commutativity: Track a×b and b×a with a shared mastery record to cut duplicates. • Patterns: Teach 5s, 10s, 11s basics, 9s digit-sum and descending-tens pattern, and tens families (20/30/40/50 mirror 2/3/4/5 with zero). • Progression: Phase A (1–12×12), Phase B (13–20×20), Phase C (21–50×20), with optional extension to ×50. • Mastery: Define mastery as fast, correct recall across spaced sessions; discourage counting strategies. 3. Platforms and architecture • Platforms: Native iOS, native Android, and PWA with full installability and offline support. • Architecture: Modular monorepo with shared domain logic in Kotlin Multiplatform or Rust/TypeScript core; native UI layers per platform; PWA via React/Next.js with service workers and manifest for install prompts. • Offline-first: Local database (SQLite/Room/Core Data/IndexedDB) with background sync. • Performance: Target 60fps animations, sub-100ms input latency, <2s cold start on mid-range Android. 4. Data and scheduling • Fact model: {id, a, b, product, commKey, familyTag, difficulty} with commKey = “min(a,b)|max(a,b)”. • SR engine: Implement SM-2/FSRS with kid-friendly constraints (cap intervals, add “quick retry” loops for errors). Offer editable difficulty, lapses, and “re-learn” steps. • Content store: Seed JSON/SQLite for 1–50 up to ×50; include derivable sets like 30s family, 40s family. 5. UX and accessibility • Visual style: Friendly, minimal, high-contrast, large tap targets, dynamic type, and voice-over labels. • Audio: Tap-to-hear facts; subtle positive/negative cues; toggleable. • Cohesive flows: Home → Learn/Practice/Speed/Flashcards; global quick-start “Today’s Review.” • Motivators: Streaks, badges, unlockable themes, and seasonal events; avoid manipulative timers. • Charts: Mastery per table, accuracy trends, average response time, and due reviews. 6. Social and community • Leaderboards: Global and classroom boards with anti-cheat (server validation and device integrity checks). • Shareable achievements and printables (1–50, 1–100 PDFs) with school-friendly branding. 7. Integrations and services • Authentication: Sign-in with Apple/Google; optional guest mode. • Payments: Freemium with premium themes, advanced analytics for parents, and school dashboards. • Analytics: Event schemas for learning behaviors, funnels for onboarding and retention. • Notifications: Smart reminders for due reviews and gentle nudges; PWA push on iOS 16.4+ and Android. 8. PWA excellence • Manifest, icons, install prompts tailored per OS, and add-to-home-screen UX. • Service worker caching strategies (stale-while-revalidate for content, cache-first for assets) and background sync. • iOS PWA caveats and workarounds tested on current Safari/WebKit. 9. Security and privacy • COPPA- and GDPR-K compliant defaults, minimal data collection, kid-safe names/avatars. • Local-first encryption of progress; secure transport (TLS), and privacy-by-design. 10. Testing and quality • Automated unit tests for scheduling, scoring, and state; UI tests; load and offline tests. • Beta distribution via TestFlight/Play Console/internal web channels; staged rollouts and crash monitoring. 11. Deliverables • Source code: iOS, Android, PWA, shared core, and infrastructure-as-code for cloud. • Design system: Figma library, components, and redlines. • Content: Seed databases for facts, PDFs for 1–50 and 1–100 charts, image/audio assets. • Documentation: README, setup, run scripts, deployment guides, and SRS/MRD. • CI/CD: Automated builds, tests, signing, store metadata, and release notes per platform. 12. Stretch features • AI tutor: On-device hints that explain patterns for current fact; explain-why mode. • Classroom: Roster import, teacher dashboards, assignments, CSV export. • Accessibility+: Dyslexia-friendly fonts, colorblind-safe palettes, full keyboard navigation for web. Build and hand over all assets with production readiness. Provide a 30/60/90-day roadmap for growth (content packs, events, partnerships). Ensure meticulous comments, clean architecture, and maintainability.