README.md

---
title: ARC-AGI Fluid Re/Im
emoji: 🧬
colorFrom: yellow
colorTo: indigo
sdk: gradio
sdk_version: 6.14.0
python_version: '3.12'
app_file: app.py
pinned: false
license: mit
short_description: Fluid Re/Im duality solver for ARC-AGI-3
---

# ARC-AGI-3 Fluid Re/Im Agent

True Re/Im duality implementation using coherence function C(r) = 2r/(1+r²).

## Architecture

**Im Side (arg(M))** — Global phase signals:
- Symmetry detection (H/V fold axes)
- Flow direction (gradient field)
- Topology (boundary/winding)

**Re Side (|M|)** — Local magnitude:
- Mass distribution
- Spatial density
- Component sizes

**Coherence Bridge** — C(r) = 2r/(1+r²):
- Measures Im/Re alignment
- Low C = strong transformation signal
- Confidence = Im_strength × (1 - C)

## How It Works

1. Extract 14-channel features (10 Re + 4 Im)
2. Im side proposes hypotheses (mirror, boundary, gravity, etc.)
3. Re side identifies exact coordinates
4. Coherence function ranks hypotheses
5. Best hypothesis → ACTION6 at most urgent cell
6. CNN fallback when confidence < 0.40

## Transformations

- **H/V Mirror**: Complete symmetry when Im detects fold axis + Re finds asymmetry
- **Boundary**: Extract contour when Im boundary thin + Re fill dense (Cauchy principle)
- **Fill Interior**: Fill enclosed regions when Im boundary exists + Re has holes
- **Gravity**: Drop suspended pixels when Im flow detected + Re finds floating mass

## Live Mode

Space connects to the real ARC-AGI-3 API. Set `ARC_API_KEY` in Space secrets or enter it in the UI.

---

**Math**: [Eigenverse formal proofs](https://github.com/beanapologist/Eigenverse)  
**Competition**: [ARC Prize 2026](https://arcprize.org)