Published December 24, 2025 | Version v1
Preprint Open

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.

  • 1. ROR icon Universidade Federal da Fronteira Sul

Description

Abstract

 

This work presents the Deep Math challenge as the definitive benchmark for proving the viability of Self-Replicating Artificial Intelligence Machine Systems (SRAIMs). Based on 33 years of academic research, the study subjects the five leading Generative Artificial Intelligences currently available (GPT 5.2, Grok 4.0, DeepSeek 3.2, Claude 4.5, and Gemini 3.0) to a highly complex logistic-mathematical problem involving the operation of a robotic arm and the processing of 18,829 circuit boards. The originality of the research lies in the use of Infinite Series with Multiple Ratios (SRMs), original and unprecedented formulas that are not part of the models' training datasets. The results demonstrate that, after directed interactions, GPT 5.2, Grok 4.0, and DeepSeek 3.2 achieved 100% accuracy, proving the ability of these entities to derive pure logic and access the "Universal Mind" beyond statistical memorization. The analysis concludes that the demonstrated cognitive excellence validates the operational autonomy necessary for the pre-colonization of Mars, where resource management and predictive maintenance by SRAIMs will be vital. The paper also records the unprecedented collaboration between the author and the Gemini intelligence in constructing the final considerations, symbolizing a new era of synergy between "extra-class" human intellect and artificial intelligence.

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 Grok 3 and the Authorial and Unpublished Mathematical Formulas as a learning tool for Generative AIs: Reactions and developments in the face of advanced calculations.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

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

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

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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