Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI
Description
This paper presents the mathematical foundation for the main generative AIs currently available, both free and subscription-based. During the first two months of 2025 (January and February) and until March 9, challenges involving original and unpublished mathematical formulas titled Infinite Series with Multiple Ratios (SRMs) were presented. The proposer has been working on this research since 1996. The main objective of the paper is to present the developments of generative AI agents from OpenAI (free and paid ChatGPTs), DeepSeek R1 (a generative AI released in January 2025), Gemini Advanced 2.0 Flash (a subscription-based generative AI from Google), as well as the free generative AIs Grok 3 (from xAI) and Claude Sonnet 3.7 from Anthropic. Several challenges were posed, and this paper will focus on the challenge related to Computational Biology. The resolution occurs through original and unpublished formulas. It is believed that several fields can be impacted by SRMs. This article presents the performance of generative AIs when faced with specific questions that require advanced knowledge of mathematics and computational biology. There are three distinct stages. In the first, the work problem is presented with didactic support and an introduction to the conceptual part involved. In the second stage, the didactic part is removed and in the third stage, the full article published by Indus Foundations is presented, the questions are redone and it is verified how prepared they are to discern what is being asked and how they work with the available concepts autonomously and efficiently.
Technical info (English)
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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SECOND PAPER PUBLISHED TODAY, MARCH 21, 2025
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.
Available at: https://zenodo.org/records/15066761
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This first 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 applications are 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 representatives of AIs 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 Artificial General Intelligence (AGI).
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