Published October 21, 2025 | Version v1
Preprint Open

SRMs & Few-Step Discrete Flows: Connections between Algebraic Determinism and Probabilistic Generation

Creators

  • 1. ROR icon Universidade Federal da Fronteira Sul

Description

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.

Technical info (En)

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 Grok 3 and the Authorial and Unpublished Mathematical Formulas as a learning tool for Generative AIs: Reactions and developments in the face of advanced calculations.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

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