**************************************************************** Paper 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 ************************************************** Paper 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 **************************************************** Paper 18 - França, C. R. (2025). SRMs & Few-Step Discrete Flows: Connections between Algebraic Determinism and Probabilistic Generation. Zenodo. https://doi.org/10.5281/zenodo.17406902 *************************************************** Paper 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 ************************************************ Paper 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 ************************************************* Paper 15 - França, C. R. (2025). ACH – A Quantum Inspired Annealing Cloud Application Powered by SRMs & GenAIs. Zenodo. https://doi.org/10.5281/zenodo.17163200 ************************************************ Paper 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 ************************************ Paper 13: França, C. R. (2025). SRMs and the Middle Path: Bridging Relativity and Quantum Mechanics. Zenodo. https://doi.org/10.5281/zenodo.17069526 ************************************ Paper 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 ************************************ Paper 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 ************************************ Paper 10: SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing França, C. R. (2025). SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing. Zenodo. https://doi.org/10.5281/zenodo.16888353 **************************************************************** PAPER 9 ORIGINAL PUBLISHED IN 2022 INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTERS IN SIMULATION VOL 16 - Heru Technologies encryption method: unique in the world that uses Unpublished mathematical formulas and encrypts with binary disturbances. França, C. R. (2025, junho 23). https://doi.org/10.5281/zenodo.15717868 ***************************************************************** 📌 Foundational Cryptographic Work (2018) For readers interested in the original cryptographic concepts that inspired this research line, a foundational chapter was written in 2018 and has now been officially published on Zenodo with a dedicated DOI. This work introduces the earliest applications of the Infinite Series with Multiple Ratios (SRMs) in the field of binary perturbation cryptography. ⚠️ Note: The publication is in Portuguese, as it was originally published in a national academic book in Brazil. The author has made it available internationally for documentation and historical record purposes. 🔗 Método de criptografia Heru Technologies (2018)(Heru Technologies encryption method: the only one in the world based on unpublished mathematical formulas and capable of encrypting with binary perturbations) *********************************************************************************** 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

Abstract: This is the seventh paper written in the context of Infinite Series with Multiple Ratios (SRMs), driven by Generative Artificial Intelligences (GenAIs). Previous papers presented advanced mathematical challenges with no record of resolutions by humans, where some GenAIs managed to achieve success. Paper 1, which addresses computational biology, more specifically, cellular profiles, is the most notable and publicly recognized. This work will not have a mathematical challenge per se, but the socialization of the breaking of the Binary Trees (B-Tree) paradigm and its algorithmic complexity in the order of O(log n). The Heru Search Method (HSM) is another development of Infinite Series with Multiple Ratios. In this paper, you will find the main aspects involving data structures that aim to optimize binary searches, the most recognized by GenAIs being the so-called Hash Table. We will address the positive and negative aspects of adopting Hash Tables as a database management tool, particularly regarding data searches in a database based on a hash function. Data will be presented that indicate that HSM is a more versatile structure and is suitable for fulfilling functions that Hash Tables do not deliver with the desired efficiency and that traditional B-Trees consume more computational processing and execution time. It will be up to the reader to decide whether the Heru Search Method deserves an opportunity to become a product that is disseminated and used worldwide. This task was eased with the collaborative writing between humans and GenAIs, which even allows for the title of co-author of this paper.