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This work aims to reinterpret the P versus NP problem using a new framework called Bidirectional Information Topology.

May 25, 2026Open Access

P =NP—TheBiT

Key Points

This work aims to reinterpret the P versus NP problem using a new framework called Bidirectional Information Topology.
Introduced a bidirectional phase operator to model computation as a closed-loop system.
Analyzed the implications of this topology on the relationship between problem resolution and verification.
Related findings to physical systems, including materials physics like twisted trilaminar graphene.
Showed that under the proposed model, the distinction between P and NP collapses.
Demonstrated that coherent systems support the conclusion that P = NP.
Provided correlations between theoretical frameworks and experimental validations in quantum systems.

Abstract

Here is the structured summary entirely in English, optimized for the Zenodo description field: P = NP — The BiT: Bidirectional Information Topology in Quantum-Inspired Computation Abstract This work proposes a structural and architectural reinterpretation of the P versus NP problem through Bidirectional Information Topology (BiT) (p. 2). Classical computation assumes unidirectional state evolution, leading to a temporal separation between problem resolution and verification (p. 2). By introducing a bidirectional phase operator i, computation becomes a closed-loop system where solution and verification coexist (pp. 2, 5). Under this phase-stable, entropy-neutral topology, the fundamental distinction between P and NP collapses, yielding P = NP within coherent systems (pp. 2, 5, 8). The paper further correlates these foundations with scientific validations in quantum systems and materials physics, such as twisted trilaminar graphene (p. 7).

P =NP—TheBiT

Key Points

Abstract

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