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School of Science, University of Management & Technology, Lahore, Pakistan
The current study presents the remodeling of General Relativity (GR) where gravitational effects are explained by phase dynamics in a two-dimensional time space instead of curvature of spacetime. It is based on previously modified formulation of special relativity, where motion of particles is linked to a unitary constraint of temporal velocity, and the relativistic effects have time dependence of an internal time phase. The study generalizes the principle of equivalence by supposing that gravitational interactions only act on the phase degrees of freedom of time and space but the geometry of spacetime is still flat. In this context, the study derives the principles of invariant action of phase evolution as well as the equations of motion of massive particles and photons in the time manifold. Additionally, the research obtained explicit solutions of inertial motion, uniform acceleration, and spherically-symmetric gravitational fields. The theory in the weak-field regime regenerates Newtonian gravity and standard results of GR. Meanwhile, the formulation is fundamentally different to Einstein’s gravity in that the curvature of spacetime is not a dynamical variable. This leads to the fact that there are no curvature singularities, and event horizons are well-defined. The findings indicate that relativistic gravitation can be systematically developed in phase evolution instead of spacetime geometry. This offers an alternative theoretical framework with a structure that can be extended appropriately in the future.
Copyright (c) 2026 Syed ali Mardan Azmi, Rodrigo Steinvorth https://creativecommons.org/licenses/by/4.0
Applications and Computational Varieties of Free Soft Trioids
Integrating soft set theory with multi-operational structures poses a foundational challenge In parameterized universal algebra,. In this paper, the theory of free soft trioids were developed establishing the existence and construction of free objects in the category SoftTrioid. Also we construct a non-restrictive definition of soft trioids equipped with pointwise operations with genuine context sensitivity. The free soft trioid being realized as a two-sorted term algebra prove the universal property and show that the word problem is decidable in linear time via a confluent rewriting system as the algorithmic implementations were supported by empirical validation. The relevance of our study were demonstrated by its applications in context-dependent type systems, formal verification, knowledge representation and access control thus situating soft trioid theory as a robust link between algebraic foundations and computational practice.
Copyright (c) 2026 Gülay Oğuz, David A. Oluyori https://creativecommons.org/licenses/by/4.0
Predictive Artificial Intelligence for Climate-Resilient Crop Breeding: Integrating Genomics, Phenomics, and Climate Modeling
Global food security is increasingly threatened by climate change, which intensifies both biotic and abiotic stresses on crops, leading to reduced yield stability and productivity. Conventional breeding approaches are insufficient to address these challenges due to long breeding cycles, strong genotype–environment interactions, and limited capacity to predict crop performance under future climate scenarios. Predictive artificial intelligence (AI) offers a powerful solution by integrating genomics, phenomics, environmental, and climate data to model complex traits, stress tolerance, and genotype performance across diverse agroecological conditions. This review synthesized recent advances in Machine Learning (ML), Deep Learning (DL), genomic prediction, high-throughput phenotyping, and climate modeling that collectively support the development of climate-resilient crop varieties. The application of predictive AI in plant breeding enhances selection accuracy, accelerates breeding decisions, reduces dependency on costly and time-consuming field trials, as well as improves resource-use efficiency. By enabling data-driven decision-making, AI-based approaches significantly improve the precision and scalability of modern crop improvement programs. Looking ahead, the integration of predictive AI with explainable modeling frameworks, multi-omics datasets, and genome-editing technologies holds significant promise for accelerating the development of high-yielding, resilient, and sustainable crops, thereby contributing to long-term food security under changing climatic conditions.
Copyright (c) 2026 Eizha Amir, Sumaira Mazhar https://creativecommons.org/licenses/by/4.0