Treffer: Formal Proof that P = NP via Logical Tabular Machine (LTM)

This repository contains a formal, constructive proof that the complexity classes P and NP are equal, established through the construction of a universal deterministic algorithm known as the Logical Tabular Machine (LTM). Rather than relying on brute-force, symbolic formulas, or resolution methods, the LTM approach encodes any NP problem as a finite system of local constraints. Each constraint is expressed as a small truth table over 2–3 variables, and a deterministic propagator mechanism eliminates incompatible rows through local table intersections. The main components include: A fixed number of constraint tables (with up to 8 rows each), A propagation engine that enforces consistency across overlapping variables, A halting condition based on the exhaustion or stabilization of all tables. We prove: That this method terminates in polynomial time $O(m^2 \cdot n)$, That it handles all 21 classic NP-complete problems (e.g., 3-SAT, CLIQUE, COLORING, KNAPSACK), And that it is implementable as code or hardware (e.g., FSM, logic processor). The archive includes: A PDF of the full proof, The LaTeX source (.tex) of the proof, A sample implementation of LTM in Python, Demonstrative test cases, Licensing and README documentation. This work represents an original contribution to the theory of computational complexity and offers a constructive path to resolving one of the most fundamental open problems in computer science. Keywords: P vs NP, Logical Tabular Machine, NP-complete, polynomial-time algorithm, constraint propagation, proof theory, SAT, structural logic, Sanal Ednyashev