THEOREM

## Full description

Every action produces N, the game's mathematical resource. Begin by counting manually, then unlock the successor and let the system produce N automatically. As your machine grows, the expression itself becomes the progression: repeated addition becomes multiplication, multiplication opens additive composition, and additive composition culminates in the common-factor form.

Numbers in the canonical formula are not decoration. Click any interactive value to inspect its meaning, see the next value, preview its cost and upgrade it directly. The Horizon panel always states the exact next objective, so progression remains readable instead of cryptic.

THEOREM v0.1 is the complete public Layer 0 sample: a focused 8–12 minute playable arc designed to show the foundation of a larger mathematical incremental game.

## Main progression

1. **Counting** — click manually to create N.

2. **Successor** — spend N to automate production with `N ← N + a`.

3. **Repeated addition** — develop the base, multiplicity and frequency of the canonical sum.

4. **Multiplication** — prove that repeated addition can be rewritten as `a × b`.

5. **Additive composition** — extend the product into `ab + ac`.

6. **Common factor** — extract the shared base into `a(b + c)`.

## Features

- Complete Layer 0 progression.

- Exact objectives shown in the persistent Horizon panel.

- Interactive formula numbers linked to their corresponding controls.

- Upgrade previews with concrete production impact and costs.

- Smooth animated number updates.

- Persistent saves, import/export and offline progress.

- Responsive HTML5 build with no server required.

- English and Spanish localization.

- Automatic language detection from the browser, with a manual switch in Settings.

- Sound, animation and notation preferences.

## Controls

- **Main screen:** click `+1` to produce N manually.

- **Operations:** upgrade `a` (base), `b` (multiplicity), `c` (extension) and `f` (frequency).

- **Formula:** click any highlighted number to open its meaning and destination.

- **Horizon:** follow the exact target shown in the sidebar.

- **Settings:** change language, notation, sound, animation and save options.

## Language support

On first launch, THEOREM selects English when the browser language starts with `en`; otherwise it starts in Spanish. The language can always be changed manually from **Settings → Language**. The choice is stored with the save.

## Technical information

This is an HTML5/Vite build. Extract the ZIP and open `index.html` in a modern browser. Chrome, Firefox and Edge are recommended.

## Credits

Created by Feli. THEOREM v0.1 public playable release.