# Layer L0: Primordial

## Overview
The foundation layer of the Research Stack. Contains pure mathematics, fixed-point arithmetic, braid fields, and core computational primitives.

## Status
✅ **Implemented** - 746 modules, 3529 build jobs, 0 errors

## Key Components

### Q16.16 Fixed-Point Arithmetic
- Core number system for all computation
- Deterministic across all substrates (CPU, GPU, FPGA, ASIC)
- Canonical constructors: `ofNat`, `ofRatio`, `ofInt`
- Forbidden: `ofFloat` in compute paths

### Braid Fields
- 8-strand braid topology (BraidStorm)
- Sidon labels: powers of 2 (1,2,4,8,16,32,64,128)
- Yang-Baxter relation for order invariance
- Crossing matrix C with contractive weights

### PIST/DIAT Shell
- Core computational framework
- Quaternion-based rotations
- Torsional dynamics

### SSMS_nD
- n-dimensional state space machine
- Cross-dimensional transitions
- State space compression

## Formal Proofs

### Core Theorems
- [[Q16.16 Arithmetic Correctness]]
- [[Braid Field Properties]]
- [[Eigensolid Convergence]]
- [[Receipt Invertibility]]

### Recent Additions
- [[Burgers 4-Theorem Attack Plan]] - Energy dissipation, CFL stability, mass conservation, complexity regularization

## Documentation
- [[Arithmetic Specification]]
- [[Braid Topology Reference]]
- [[PIST Implementation Guide]]

## Hardware
- [[FPGA Implementation Status]]
- [[ASIC Design Considerations]]
- [[Cross-Substrate Verification]]

## Receipts
- [[Build Receipt]] - Compilation verification
- [[Test Receipt]] - Test suite results
- [[Arithmetic Receipt]] - Number system validation

## Subdirectories
- [[01-Formal-Proofs]] - Mathematical proofs
- [[02-Documentation]] - Technical documentation
- [[03-Receipts]] - Validation receipts
- [[04-Hardware]] - Hardware extraction

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#layer-L0 #primordial #fixed-point-arithmetic