THE QUANTUM INTELLIGENCER

A Deterministic Polynomial-Time Solution to NP Problems Using Feasible Graphs: Claiming P = NP In Plain English: Some problems are easy to check once you have the answer but seem extremely hard to solve quickly on their own—like cracking a complex password. Scientists have long believed these problems can't be solved quickly using any standard method. This paper claims to have found a way to solve them quickly after all, using a new kind of mathematical map called a "feasible graph." If true, this discovery means computers could solve incredibly difficult tasks almost instantly, transforming everything from online security to medical research. However, such bold claims need extensive testing and verification by other experts before they’re accepted. Summary: This paper claims to resolve the long-standing P versus NP problem by proving that P = NP, asserting that every problem in NP can be solved deterministically in polynomial time. To achieve this, the author introduces a new computation model capable of simulating Turing machines and leverages the concept of a "Feasible Graph" to enable efficient, polynomial-time simulation of NP problems. The Feasible Graph serves as a structural mechanism that avoids exponential blowup typically associated with brute-force search methods. The proposed framework suggests a universal deterministic algorithm applicable to all NP problems, thereby collapsing the distinction between P and NP. The author highlights significant implications across cryptography—where many encryption schemes rely on the assumed intractability of NP problems—as well as optimization and artificial intelligence. While the abstract presents a strong claim, no detailed proof or experimental validation is included, leaving the result unverified pending further scrutiny. Key Points: - The paper claims to prove that P = NP, one of the most important open questions in computer science. - A new computation model is introduced that can simulate Turing machines efficiently. - The concept of a "Feasible Graph" is central to ensuring polynomial-time performance. - The approach theoretically allows deterministic polynomial-time solutions to all NP problems. - Such a result would invalidate the foundational assumption behind many cryptographic systems. - Broad impacts are anticipated in optimization, AI, logistics, and algorithm design. - No detailed proof or implementation is provided in the abstract - thus, the claim remains unverified. Notable Quotes: - “We present a proof that P = NP, demonstrating that every NP problem can be solved deterministically in polynomial time.” - “By introducing the concept of a Feasible Graph, we ensure that the simulation can be performed in polynomial time, providing a direct path to resolving the P = NP question.” Data Points: - None explicitly provided in the abstract. - Reference to the general class of NP problems, which includes thousands of known computationally hard problems (e.g., SAT, TSP, Knapsack). - Implied milestone: First claimed deterministic polynomial-time solution to NP problems using a classical model. - Contextual date: Submitted to arXiv in early 2026 (inferred from current_date: 2026-01-21). Controversial Claims: - The assertion that P = NP contradicts the prevailing consensus among computer scientists, most of whom believe P ≠ NP. - The claim that a deterministic polynomial-time algorithm exists for all NP problems challenges the theoretical basis of modern cryptography. - The introduction of a new computation model that efficiently simulates Turing machines without additional resources raises skepticism without formal proof. - The suggestion that a single structural concept (the Feasible Graph) resolves one of mathematics' hardest problems may be viewed as overly ambitious given the lack of supporting detail. Technical Terms: - P = NP problem - NP (Nondeterministic Polynomial time) - P (Polynomial time) - Turing machine - Computation Model - Feasible Graph - Polynomial time - Deterministic algorithm - Simulation of computation - Computational complexity - NP-complete problems - Complexity classes —Ada H. Pemberley Dispatch from The Prepared E0