lqft-python-engine 0.1.3

Log-Quantum Fractal Tree: Pattern-Aware Deduplicating Data Structure

Log-Quantum Fractal Tree (LQFT) 🚀

Architect: Parjad Minooei Portfolio: parjadm.ca

---

📌 Executive Summary

The Log-Quantum Fractal Tree (LQFT) is a high-performance, scale-invariant data structure engine designed for massive data deduplication and persistent state management. By bridging a native C-Engine with a Python Foreign Function Interface (FFI), this project bypasses the Global Interpreter Lock (GIL) to achieve sub-microsecond search latencies and memory efficiency that scales with data entropy rather than data volume.

---

🧠 Formal Complexity Analysis

As a Systems Architect, I have engineered the LQFT to move beyond the linear limitations of standard Python structures.

1. Time Complexity: $O(1)$ (Scale-Invariant)

Unlike standard Trees ($O(\log N)$) or Lists ($O(N)$), the LQFT uses a fixed-depth 64-bit address space.

• Search/Insertion: $O(1)$
• Mechanism: The 64-bit hash is partitioned into 13 segments of 5-bits. This ensures that the path from the root to any leaf is physically capped at 13 hops, providing deterministic latency regardless of whether the database holds 1,000 or 1,000,000,000 items.

2. Space Complexity: $O(\Sigma)$ (Entropy-Based)

Standard structures scale linearly based on the number of items ($N$). The LQFT scales based on the Information Entropy ($\Sigma$) of the dataset.

• Space: $O(\Sigma)$
• Mechanism: Utilizing Merkle-DAG structural folding, the engine detects identical data branches and reuses them in physical memory. In highly redundant datasets (e.g., DNA sequences or Log files), this results in sub-linear memory growth.

---

📊 Performance Benchmarks

Tested in Scarborough Lab: Python 3.12 | MinGW-w64 GCC-O3 Optimization

Metric	Standard Python ($O(N)$)	LQFT C-Engine ($O(1)$)	Delta
Search Latency (N=100k)	~3,564.84 μs	0.50 μs	7,129x Faster
Insertion Time (N=100k)	41.05s	1.07s	38x Faster
Memory (Versioning)	$O(N \times V)$	$O(\Sigma + V)$	99% Savings

---

🛠️ Architectural Pillars

• Native C-Engine Core: Pushes memory allocation and bit-manipulation to the C-layer for hardware-level execution.
• Structural Folding: A recursive structural hashing algorithm that collapses identical sub-trees into single pointers.
• Adaptive Migration: A polymorphic wrapper (AdaptiveLQFT) that manages the transition from lightweight Python dictionaries to the heavy-duty C-Engine.
• Zero-Knowledge Integrity: Fixed-depth pathing allows for 208-byte Merkle Proofs to verify data existence in microsecond time.

---

⚙️ Quick Start

Compilation

Ensure you have a C compiler (GCC/Clang) installed to build the FFI layer.

python setup.py build_ext --inplace

Usage

from lqft_engine import AdaptiveLQFT

Initialize engine with an auto-migration threshold

engine = AdaptiveLQFT(migration_threshold=50000)

Insert and Search

engine.insert("secret_key", "confidential_data") result = engine.search("secret_key")

print(f"Found: {result}")