feat(python): implement python bindings for all components and solvers

docs/TUTORIAL.md

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+# Tutorial: Getting Started with Entropyk
+
+This guide will walk you through setting up your environment, running your first simulation, using the visual UI, and building your own thermodynamic models.
+
+## 1. Environment Setup
+
+### Prerequisites
+Ensure you have the latest stable version of [Rust](https://www.rust-lang.org/) installed:
+```bash
+rustup update stable
+```
+
+### Clone and Build
+Clone the repository and build the workspace:
+```bash
+git clone https://github.com/your-username/Entropyk.git
+cd Entropyk
+cargo build --workspace
+```
+
+## 2. Running Your First Simulation
+
+The best way to understand Entropyk's capabilities is by running the **Water Chiller Demo**.
+
+### Run the Demo
+```bash
+cargo run --bin chiller
+```
+
+### What's Happening?
+The `chiller.rs` demo sets up a complete refrigeration cycle:
+1. **Water Side (Circuit 1)**: Pump moves 12°C water at 0.5 kg/s through an evaporator.
+2. **Refrigerant Side (Circuit 0)**: R410A flows through a compressor (2900 RPM), condenser (air-cooled at 35°C), expansion valve, and evaporator.
+3. **Thermal Coupling**: The evaporator exchanges heat between the water and refrigerant circuits.
+
+The output displays the **Point de Design** (COP, power consumption, heat transfer).
+
+## 3. Using the Visual UI
+
+Entropyk includes a web-based interface to build systems without writing code.
+
+### Launch the UI Server
+```bash
+cargo run -p entropyk-demo --bin ui-server
+```
+
+### Build a System Graphically
+1. Open [http://localhost:3030](http://localhost:3030).
+2. **Palette**: Drag and drop components (Pump, Compressor, Pipe, etc.) onto the canvas.
+3. **Configure**: Click a component to adjust its parameters (fluids, polynomials, geometry).
+4. **Connect**: 
+   - Click "Relier" in the toolbar.
+   - Click a **Source** (orange port) and then a **Target** (green port).
+5. **Simulate**: The UI sends the configuration to the Rust backend, which performs calculations using real thermodynamic models.
+
+## 4. Coding with the Library
+
+Here's how to create a simple unit-safe model using the Entropyk crates.
+
+### Basic Physical Quantities
+```rust
+use entropyk_core::{Pressure, Temperature};
+
+let p = Pressure::from_bar(3.5);
+let t = Temperature::from_celsius(25.0);
+
+println!("Pressure: {} Pa", p.to_pascals());
+```
+
+### Creating and Connecting Ports
+Entropyk uses the **Type-State Pattern** to prevent uninitialized connections.
+```rust
+use entropyk_components::port::{Port, FluidId};
+
+// 1. Create disconnected ports
+let p1 = Port::new(FluidId::new("Water"), p, h);
+let p2 = Port::new(FluidId::new("Water"), p, h);
+
+// 2. Connect (returns Result of connected ports)
+let (mut c1, mut c2) = p1.connect(p2).expect("Incompatible ports!");
+```
+
+## 5. Next Steps
+
+- **[EXAMPLES.md](../EXAMPLES.md)**: Explore code snippets for every component (Heat Exchangers, Pumps, Fans, etc.).
+- **[Crates Documentation](../crates/entropyk/README.md)**: Deep dive into the library architecture.
+- **[Story 1.3 README](../README_STORY_1_3.md)**: Technical details on the port and connection system.
+
+Happy simulating!

docs/index.md

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+# Directory Index
+
+## General Documentation
+
+- **[README.md](../README.md)** - Main project overview and getting started guide.
+- **[TUTORIAL.md](./TUTORIAL.md)** - Step-by-step guide to using Entropyk (CLI & UI).
+- **[EXAMPLES.md](../EXAMPLES.md)** - Comprehensive usage examples for all library components.
+- **[README_STORY_1_3.md](../README_STORY_1_3.md)** - Technical details of Port and Connection system implementation.
+
+## Project Subdirectories
+
+### demo/
+
+- **[demo/README.md](../demo/README.md)** - Documentation for demo applications and system simulations.
+
+### crates/
+
+- **[crates/entropyk/README.md](../crates/entropyk/README.md)** - Specific documentation for the main Entropyk library crate.
+
+## Assets
+
+- **[docs/katex-header.html](./katex-header.html)** - KaTeX configuration for rendering mathematical formulas in documentation.

docs/katex-header.html

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