1. França, C. R. (2025 p1). Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI. Zenodo. https://doi.org/10.5281/zenodo.15033127 2. França, C. R. (2025 p2). Grok 3 and the Authorial and Unpublished Mathematical Formulas as a learning tool for Generative AIs: Reactions and developments in the face of advanced calculations. Zenodo. https://doi.org/10.5281/zenodo.15066761 3. França, C. R. (2025 p3). Advanced computational mathematics and future point modeling of a predictive system: A collaborative scientific research between a human and a Generative AI. Zenodo. https://doi.org/10.5281/zenodo.15083825 4. França, C. R. (2025 p4). Heru Technologies: Modeling Escape Trajectories of a Probe Trapped in an Asteroid's Gravitational Field Using SRMs and Human-GenAI Collaboration. Zenodo. https://doi.org/10.5281/zenodo.15151423 5. França, C. R. (2025 p5). SRMs and GenAI applied to the stock market: Predictive system and projections of future points for industrial expansion and finance. Zenodo. https://doi.org/10.5281/zenodo.15252352 6. França, C. R. (2025). Predictive analytics in the Swiss pharmaceutical sector: SRMs are the right amount of mathematics for GenAIs. Zenodo. https://doi.org/10.5281/zenodo.15272636 7. França, C. (2025). Beyond Binary Trees: A Paradigm Shift in Data Search Efficiency via SRMs-Based Structures. Zenodo. https://doi.org/10.5281/zenodo.15602787 8- França, C. R. (2025). Método de criptografia Heru Technologies: único do mundo que utiliza fórmulas matemáticas inéditas autorais e que criptografa com perturbações binárias. Zenodo. https://doi.org/10.5281/zenodo.15653585 9 - França, C. R. (2025, junho 23). Heru Technologies encryption method: unique in the world that uses unpublished mathematical formulas and encrypts with binary disturbances. https://doi.org/10.5281/zenodo.15717868 10 - França, C. R. (2025). SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing (Second version). Zenodo. https://doi.org/10.5281/zenodo.16888353 11 - França, C. R. (2025). SRMs meet Schrödinger: Multiple-ratio expansions for quantum dynamics and entanglement in a timeless dialogue. Zenodo. https://doi.org/10.5281/zenodo.17017967 12 - França, C. R. (2025). GenAIs and SRMs: A Guide to Conceptual Bridges and Practical Applications in Quantum Computing. Zenodo. https://doi.org/10.5281/zenodo.17042186 13 - França, C. R. (2025). SRMs and the Middle Path: Bridging Relativity and Quantum Mechanics. Zenodo. https://doi.org/10.5281/zenodo.17069526 14 - França, C. R. (2025). Quaternary Quantum Dynamics and SRM Algorithms: A Middle-Path Framework Beyond Qubits. Zenodo. https://doi.org/10.5281/zenodo.17095495 15 - França, C. R. (2025). ACH – A Quantum Inspired Annealing Cloud Application Powered by SRMs & GenAIs. Zenodo. https://doi.org/10.5281/zenodo.17163200 16 - França, C. R. (2025). Quantum Biology Based on SRMs: From Cell Proliferation to Cyclical Spheres of Preventive Health. Zenodo. https://doi.org/10.5281/zenodo.17188874 17 - França, C. R. (2025). Pipeline SRMs and GenAIs: Nonlinear Predictive Frameworks for Drone Swarms and Mobility in Defense. Zenodo. https://doi.org/10.5281/zenodo.17220829 19 - França, C. R. (2025). The exploratory possibilities of Mars through Artificial Intelligence Machines (AIMs) as a precursor to a civilizational milestone. (1° Version). Zenodo. https://doi.org/10.5281/zenodo.17886639 20 - França, C. R. (2025). Overcoming the Strategic Gap: A Counterpoint to Current "Humans First" Mars Colonization Architectures and Self-Replicating Artificial Intelligence Machine Systems (SRAIMs). Zenodo. https://doi.org/10.5281/zenodo.17925369 21 - França, C. R. (2025). Deep Math is proof of the viability of Self-Replicating Artificial Intelligence Machine Systems (SRAIMs) and the level of excellence of some of the leading GenAIs. Zenodo. https://doi.org/10.5281/zenodo.18049949

This paper proposes a unifying interpretation between two fields that, although born in different times and contexts, move toward the same fundamental principle: few-step computational optimization. In 2017, the Heru Search Method (HSM), based on Infinite Series with Multiple Ratios (SRMs), was published in the American Journal of Computational Mathematics, presenting a deterministic method capable of replacing binary trees and breaking the century-old O (log n) paradigm. In 2025, Few-Step Discrete Flow-Matching (FS-DFM) emerged, developed by researchers at Apple Inc. and Ohio State University, introducing, in the domain of probabilistic generation, the same logic of discrete jumps with minimum procedural entropy. The objective of this article is to demonstrate that such systems — the deterministic (SRMs-HSM) and the probabilistic (FS-DFM) — are complementary expressions of the same universal law of efficiency: the Principle of Discrete Transition in Few Steps. The convergence proposed here does not aim to superimpose models, but to reveal the dual nature of the same mathematical-computational phenomenon: the transformation of the traversal into a jump.