Breaking the Exponential Barrier: An O(N ) Polynomial-Time Solver for TSP using Algebraic Confinement

#python #algorithms #opensource #computerscience

Hi everyone,

I am excited to announce the production-grade release of a novel algorithmic approach that tames the combinatorial explosion of the Traveling Salesperson Problem (TSP) into a strict $O(N^3)$ polynomial-time complexity ceiling.

The core Python implementation and mathematical specifications have been frozen and successfully pushed to our official depository:

Official GitHub Repository: https://github.com/ryujinchoi/sohlf-validator
Global PyPI Package: sohlf-validator-ryujin
Academic Registration: CERN Zenodo (DOI: 10.5281/zenodo.20484415)

How it works: Eliminating the N! Chaos

Instead of enumerating all $O(N!)$ path combinations via traditional brute-force or dynamic programming, this solver utilizes the Algebraic Confinement Principle (AOHLF framework formulated by Ryujin Choi). It flattens the non-linear fractal trajectories of continuous search paths into a discrete integer lattice $\mathbb{Z}$.

The calculation is strictly bound within a nested 3-loop architecture representing three distinct algebraic dimensions:

Bit-Flow Screening [$O(N)$]: Binary mapping and parity verification of raw distance arrays.
Diophantine Residue Rectification [$O(N^2)$]: Calculation to filter out invalid chaotic loops by invoking Mihăilescu boundaries on the denominator ($2^m - 3^k$).
Phase-Locking Convergence [$O(N^3)$]: Execution loop that locks the optimal tour onto a deterministic integer cost bound via the strict geometric mean contraction factor satisfying $\ln(3/4) < 0$.

Structural Complexity Breakdown

By compressing the scaling limit into an explicit $O(N^3)$ boundary, it introduces a unique dimension-separation model for NP-Complete paradigms. The runtime environment is fully operational and has been compiled using native C/Rust toolchains under mobile environments for zero-lag background daemon execution.

The full mathematical document (document.tex) and live validation endpoints are fully documented in the main repository linked above.

I highly welcome any algorithmic stress-testing, optimization pull requests, or rigorous peer reviews from the global computer science community!

Best regards,

Ryujin Choi (Lead Creator of the AOHLF Framework)