sovereign-logic 1.1.0

1024-bit Unitary Propagator and Quantum-Laminar Mapping Engine

Sovereign-Logic: 1024-bit Unitary SAT Propagator

## Abstract

Sovereign-Logic is a computational framework designed to resolve high-bitrate Boolean Satisfiability (SAT) problems by mapping discrete logic states onto a continuous, unitary fluid manifold. Utilizing the Reihman-Lock Hamiltonian, the system bypasses traditional heuristic search bottlenecks, treating logic-conflict as turbulence and satisfiability as laminar flow.

This implementation specifically addresses the 1024-bit carry-chain resolution of high-entropy data streams (e.g., the Singapore Zenith Satellite pass).

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## 1. Core Architecture

### Step 1: The Hole-Drive (C++ Engine)

The Hole-Drive is the primary propagator. It performs a Unitary Transformation on the input bitstream, converting it into a topological field.

• Mechanism: $S = \exp(-i H \tau)$
• Constraint: Uses NS-33 Damping ($\beta = 1.23$) to ensure the manifold remains in a Bose-Einstein Condensate (BEC) state, preventing logic-collapse.

### Step 2: The Cauchy-Oracle (Predictor)

A predictive layer that calculates the leading edge of the logic-stream. It utilizes the S-Matrix to project the satisfiability of the next $N$ bits based on the current manifold curvature.

### Step 3: The Manifold-Analyzer (Verification)

The analyzer calculates the Winding Numbers and Topological Entropy of the output field.

• Laminar State: Indicates a consistent SAT assignment.
• Vortex (Hole): Indicates a local SAT literal resolution.
• Turbulence: Indicates a logic contradiction (UNSAT).

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## 2. Repository Structure