Description

Abstract (English)

This article presents the reactions of the generative AI Grok 3 to an unprecedented and original mathematical tool, never published in printed or digital book. The learning of AIs through interactions with users is partially or fully viable, and these are points discussed in this article. Other points emerged during the research with great relevance, mainly in the context of the complexity of algorithms and the computational cost to execute the actions demanded by users. The work was developed in three distinct moments and in the same way with new prompts and chats to avoid doubts about what was retained by the generative AI in this attempt to train from interactions with the user. This article is an unfolding of the challenges of AIs organized by this same author and socialized in the form of an article. The best performance among the AIs was from Grok 3, surpassing its competitors ChatGPTs, all free and paid models, Gemini Advanced 2.0 Flash, Claude 3.7 and DeepSeek R1. Grok 3 finished with 75% accuracy and for this reason it is the only participant of the generative AIs in this article. The main objective is to verify if there is consistency in the execution and learning of the original and unprecedented formulas called Infinite Series with Multiple Ratios (SRMs). Finally, a comparison is made between the resolutions with the mathematical tools of Grok 3 domain and how difficult or simple the handling with the SRMs was. This paper also explores possible applications of SRMs in areas such as finance, engineering, biology, physics, and computer science, highlighting their versatility and efficiency.

Technical info (English)

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

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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

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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

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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

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Paper 13: França, C. R. (2025). SRMs and the Middle Path: Bridging Relativity and Quantum Mechanics. Zenodo. https://doi.org/10.5281/zenodo.17069526

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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

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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

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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

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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

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📌 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)

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SEVENTH PAPER.  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

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Dear worldwide scientific community, This is the 6th and last paper I publish to highlight the importance of Infinite Series with Multiple Ratios (SRMs) for GenAIs. The evidence in this 6th paper in 40 days, perhaps a WORLD RECORD, is a gigantic effort to show the world that there is something "NEW" and still unheard of in mathematics. In this paper 6 you will observe how no GenAI has been able to solve and the reason is simple. SRMs are not yet part of the repertoire of my favorite GenAI (Grok 3) or the others. I did what I could. I hope you like it and continue supporting and sharing my papers. Thanks to everyone!

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 

PUBLISHED ON APRIL 23, 2025

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This is the fifth paper to demonstrate the power of SRMs and GenAIs. Judging humanity's greatest invention as a "digital statistical parrot" is a grave and unprecedented mistake. My FIVE papers prove the opposite and also present Infinite Series with Multiple Ratios (SRMs), authorial formulas that enhance GenAIs and the search for AGI. The links to the other papers are below.

FIFTH PAPER - 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

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I have just published the 5th paper (in 36 days) to prove the strength of SRMs and their importance for GenAI.

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FOURTH PAPER - 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

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Third paper v1 – published at 25th march 2025 – https://doi.org/10.5281/zenodo.15083825

Advanced computational mathematics and future point modeling of a predictive system: A collaborative scientific research between a human and a Generative AI.

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First paper v2 – published at 15th march 2025 - https://zenodo.org/records/15033127

Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI

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This second paper presents the performance and reactions of the Generative AI Grok 3 when faced with authorial and disruptive mathematical formulas. The reader will have contact with a tool prepared to impact several areas. The highlight is the training for Generative AIs to recognize and act with large amounts of cyclical and periodic data. The applicability is immeasurable and this article presents some in the areas of finance and biology, among others. This is the second article published here in preprint format. The first was about the challenges of AIs with issues of computational biology, but specifically cell proliferation. The main Generative AIs participated (ChatGPTs, all models), Gemini Advanced 2.0 Flash, Claude Sonnet 3.7, DeepSeek R1 and the big winner was Grok 3 from the company xAI. This is the reason why it was chosen as the AI representative in this second article. I hope you like it, share it with your contact networks and let's do our part in the search for the much dreamed of Artificial General Intelligence (AGI).