Notable P vs. NP proof attempts.

The Emergence Dynamics: The Paradigm of Continuous Measurement and Non-deterministic State Flows – Toward P versus NP and the Boundary of Computation

This repository was setup to help people who believe that they solved the P vs NP problem and to help the people who review proposed solutions.

Formal verification of the logical incompatibility between the P=NP hypothesis and the Witten-Helffer-Sjöstrand tunneling theorems in spectral geometry. Implemented in Lean 4.

python implementations of algorthims for the boolean satisfiability problem, including one to solve 3SAT in polynomial time

A comprehensive Python framework for parsing, transforming, and benchmarking CNF files for SAT solving research.

Machine-verified proof (0 sorries, 2 axioms) that P ≠ NP via exponential circuit lower bounds for Hamiltonian Cycle. Lean 4 formalization with Mathlib. Proves SIZE(HAM_n) ≥ 2^{Ω(n)} using frontier analysis, switch blocks, cross-pattern mixing, recursive funnel magnification, continuation packets, rooted descent, and signature rigidity.

OPEN PROBLEMS WANT TO STAY OPEN

Unity Equilibrium Theory (UET)

An interactive graph coloring game with progressive levels and customizable random graphs.

P != NP

P vs NP — Conditional Certificate. 223 Lean bricks. 3 barriers formalized. Cook-Levin proved. Theorem: IF SAT ∉ P THEN P ≠ NP — certified. 0 sorry. 0 axiom. Separation hypothesis named.

Labs for the Advanced Algorithms course

An experimental greedy heuristic for graph 3-coloring using a custom Matrix Sorting Machine priority structure, with benchmarking and graph visualization.

Reproducible proofs for P vs NP, Yang-Mills Mass Gap, and Riemann Hypothesis using parameter-free Jabri Identity Zₜ=1. Zero fitted parameters. Python code, data, and Zenodo DOI included. Author: Abdulla Al-Jabri.

Reframing the P vs NP Problem

Novel mathematical framework connecting P vs NP to the golden ratio phi via witness space geometry. Part of the unified E8/H4/phi theory.

Structural analyses of 11 Millennium-Class challenges (01/30/2026). Using the XYAKANYAA System, the repository documents how expanded observational context yields harmonic stabilization. Experimental, reproducible, and open to refutation.

"Formal Audit and Systematic Convergence of the Millennium Prize Problems using the 107.19 Master Space-Lock with the raw .0214- .03 latency from the average of the magnetic field and .67 Logic Gate."

All assignments for CS 218: Design and Analysis of Algorithms, Spring 2021, IIT Bombay