Advanced computational mathematics and future point modeling of a predictive system: A collaborative scientific research between a human and a Generative AI.
Description
This paper is the third in an investigative series on the performance of the main generative AIs when faced with advanced computational mathematics, hard-level challenges, including unpublished authorial formulas. A system was presented with a jammed pressure valve, with very high risks of collapse, a scale with the evolution of pressure and the approach of the irreversible and catastrophic time. The mission of determining whether or not the company would authorize the repair in the available time frame fell to the AIs: Grok 3, ChatGPT o3 mini and model 4.0, DeepSeek R1, Gemini Advanced 2.0 Flash and Claude Sonnet 3.7. The solutions presented, the polynomial functions used, the proposed mathematical models and all development, were analyzed collaboratively by the author of this paper and the Generative AI Grok 3, which leads the ranking of AIs when it comes to hard-level computational mathematics, problems solved by very few humans and by some generative AI agents. The paper presents the complete resolutions of AIs, a modeling of the results in an impactful way due to the unprecedented collaboration between humans and a generative AI in the writing of a paper. The work ends with an overview of what is available on the market with a strong and consolidated mathematical basis and the new perspective of using AIs as a collaborative tool in the process of scientific research, and not only to answer questions formulated by users of all levels and purposes who underestimate their existential meaning.
Technical info (English)
Paper 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
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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
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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
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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
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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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Second paper v2 – published at 22th march 2025 - https://zenodo.org/records/15066761
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.
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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 is the third paper of a great physical and intellectual effort. The time between the papers is around 7 days. The first was published on March 12, 2025, the second on the 21st and this one on March 25, 2025. This dedication can be explained by two acronyms: SRMs and AGI. Just like most people who have been researching and using generative AI since 2022 and who have been able to follow the emergence of great models such as the Chinese DeepSeek R1, the various ChatGPT models, Google's efforts with Gemini, Anthropic with Claude Sonnet 3.7 and, logically, the most illustrious among Generative AIs, Grok 3 from the American company xAI.
It is the first record of collaborative research between a generative AI and a human
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