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[6] ai.viXra.org:2507.0124 [pdf] replaced on 2025-08-05 23:41:57
Authors: John A. McCain
Comments: 13 Pages. [License: CC BY 4.0]
We prove that P ≠ NP by demonstrating that certain classes of decision problems—specifically those involving semantic ambiguity and context-dependent truth—demand computational resources that exceed polynomial bounds for bothverification and solution. By formally defining a family of problems in which the number of interpretive contexts grows exponentially with input size, and where the correctness of a proposed solution depends on resolving this ambiguity, we show that even verification becomes infeasible within polynomial time. Moreover, we demonstrate that identifying a valid certificate within these problems requires a doubly exponential search over both potential answers and interpretive frames. These results indicate that P ≠ NP, not merely as a formal separation, but as a semantic inevitability. We conclude that computational tractability collapses in the presence of unbounded meaning, and that this collapse is reflected in foundational paradoxes of language and logic.
Category: Data Structures and Algorithms
[5] ai.viXra.org:2507.0122 [pdf] submitted on 2025-07-27 15:46:18
Authors: Gurjot Singh
Comments: 3 Pages. [Distributed] under CC BY 4.0 (Note by ai.viXra.org Admin: Please cite listed scientific references)
We present a non-constructive, epistemically rooted argument that N ≠ NP, based not on computational complexity theory per se, but on the cognitive architecture of human simulation. We assert that the nature of NP-complete problems entails a recursion beyond human symbolic compression, and that the inability of bounded intelligence to traverse such recursion maps onto a fundamental limit, analogous to Heisenberg’s uncertainty principle. This is not a proof in the traditional Turing sense, but an ontological constraint derived from the architecture of cognition.
Category: Data Structures and Algorithms
[4] ai.viXra.org:2507.0095 [pdf] replaced on 2025-10-08 23:55:26
Authors: Maurício Machado Galvão
Comments: 23 Pages. Two unclear points in the proof of the test theorem part 2 have been corrected.
This paper presents new polynomial-time algorithms for determining graph isomorphisms, non-trivial graph automorphisms. Based on spectral properties and iterative refinement techniques, we introduce the algorithms graphiso3 for determining graph isomorphisms, graphautont3 for non-trivial graph automorphisms. These algorithms are based on matrix exponentials, These algorithms are based on the matrix exponential, but there are variation based on the inverse of normal matrices.
Category: Data Structures and Algorithms
[3] ai.viXra.org:2507.0081 [pdf] submitted on 2025-07-15 17:48:14
Authors: Brent Hartshorn
Comments: 2 Pages.
This paper addresses the fundamental inefficiencies in modern compiler and operating system designs, particularly as they impact high-performance Linux server environments. We propose a radical re-evaluation of core architectural choices, advocating for indexed and compressed stack pointers, and a novel thread management scheme that locks threads to specific cores for ultra-fast context switching. The discussion extends to the utility of direct memory access for specialized server applications, challenging traditional security paradigms and proposing a Python-to-ASM toolchain for enhanced control and optimization. We further highlight the performance advantages of ARM and RISC-V architectures over Intel/AMD, specifically their suitability for advanced threading models. Finally, we examine critical overlooked performance bottlenecks within the Linux kernel concerning SIMD register management and propose enhancements to the ELF file format to optimize process execution. By implementing these foundational shifts, organizations can achieve a huge improvement in server performance or a huge reduction in operational costs.
Category: Data Structures and Algorithms
[2] ai.viXra.org:2507.0018 [pdf] submitted on 2025-07-03 01:14:16
Authors: Tchouankam Donald Paulin
Comments: 33 Pages.
This publication presents a complete and definitive proof that P ̸ = NP, thus solving one of the most fundamental open problems in theoretical computer science. Our proof is based on the in-depth study of the function P(N) and irrefutably establishes an insurmountable computational barrier between the complexity classes P and NP. The implications of this result redefine the boundaries of computability and lay the foundation for a new era in cryptography and algorithmic optimization.
Category: Data Structures and Algorithms
[1] ai.viXra.org:2507.0017 [pdf] submitted on 2025-07-03 01:15:36
Authors: Tchouankam Donald Paulin
Comments: 3 Pages.
This document resolves the longstanding problem of the existence of odd perfect numbers.Relying on Euler’s characterization, modular arithmetic, and the properties of the sum-of-divisors function σ(n), we prove that no odd integer n can satisfy σ(n) = 2n.The proof is divided into two cases:(1) n is an odd perfect square, which leads to a parity contradiction; and(2) n is not a square, where Euler’s structure n = p^(4k+1) · m² leads to an impossibility via bounds on σ(m²).
Category: Data Structures and Algorithms