SUPER PAPER # 21 - 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.

 

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.

My Christmas gift to humanity. 

Link:👉👉👉 SUPER PAPER # 21 

Mars: Why Bravery Isn't Enough. The Engineering of Survival and the Launch of Paper #20

 

Dear Community

Today marks a significant milestone in my scientific journey. Those who follow my work know that I have been deeply immersed in the mathematical and computational challenges of our era. However, in recent days, I was provoked by a much larger challenge: the future of humanity on Mars.

We all watch the modern space race with enthusiasm. We see reusable rockets and ambitious plans to send human settlers as quickly as possible. But as a scientist and mathematician, I looked at the numbers and found what I have termed the "Strategic Gap."

Sending humans to a frozen, radioactive desert, while dependent on a continuous supply chain from Earth, is not just risky; it is logically unsustainable.

The Question No One Wants to Ask: Why send fragile biological bodies to build critical infrastructure when we can send Self-Replicating Artificial Intelligence?

The Answer: Paper #20 - The SRAIM Architecture

Today, inspired by high-level debates at Sigma Xi, I have officially published my new paper on Zenodo: "Overcoming the Strategic Gap."

In this work, I present the SRAIM (Self-Replicating Artificial Intelligence Machine). This is not science fiction; it is robust engineering based on three pillars:

1. The AIM Floating Station: A "brain in the clouds" of Mars to manage weather prediction and communications, mitigating the delay with Earth.

2. In-Situ Replication: Robots that use Martian soil to build more robots and human habitats before we even arrive.

3. Advanced Mathematics (SRMs): The application of my Infinite Series With Multiple Ratios to ensure these machines move with near-perfect energy efficiency ($O(1)$ complexity), saving battery power where every watt counts.

The Invitation

This paper is a technical manifesto proposing a shift from a "suicidal adventure" to an "intelligent occupation." I invite all of you, engineers, programmers, mathematicians, and dreamers, to read the full document.

The colonization of Mars will not be achieved by those who get there first, but by those who can sustain themselves there. And to survive, we need SRAIMs.

👇 Access the full Paper and download the PDF here: 

[Link in the image below:

 

Let’s discuss in the comments: Would you trust your life to a base built by AI before leaving Earth?

Best regards,

My Victorious December: Full Member of Sigma Xi and the Launch of Paper #19 on Martian AIMs / Meu Dezembro Vitorioso: Membro Pleno da Sigma Xi e o Lançamento do Paper #19 sobre AIMs Marcianas)

Prezada Comunidade / Dear Community 

 

Este mês marca um ponto de inflexão na minha jornada de pesquisa, unindo o reconhecimento de excelência acadêmica com o lançamento de um trabalho que explora a fronteira da inteligência artificial e da exploração espacial.

Honoring 140 Years of Scientific Excellence: Sigma Xi

I am deeply honored to announce my election as a Full Member of Sigma Xi, The Scientific Research Honor Society.  

Founded in 1886, Sigma Xi boasts a nearly 140-year history of recognizing research excellence across all scientific disciplines. The Society counts among its members icons such as Albert Einstein and over 200 Nobel Prize laureates. To be recognized by this distinguished body is to join a legacy of profound scientific contribution.

My election was specifically in the area of Computational Mathematics and Educational Technologies, a direct validation of my life's work. This honor is the crowning achievement of a year dedicated to innovation, bridging the gap between theoretical mathematics and practical technological solutions.

Paper #19: The Direct Result of International Peer Recognition

The momentum of this recognition immediately catalyzed my newest publication:

Paper #19: The exploratory possibilities of Mars through Artificial Intelligence Machines (AIMs) as a precursor to a civilizational milestone.

This paper is the first direct scientific product to emerge from my engaging interactions with fellow Sigma Xi members, particularly in a forum that inspired the core ethical and logistical questions addressed.

• The Core Thesis: The work argues that AI-Driven Machines (AIMs) must achieve extreme autonomy—an AGI Marciana—using my Infinite Series with Multiple Ratios (SRMs) algorithms to manage the multi-variable complexity of the Red Planet.

• The Foundation: The research stands on the shoulders of the 18 papers previously generated, and the formal presentation of the SRMs research at Cornell University (NY, USA) in May 2025.

A Testament to Hard Work and Peer Validation

This December, 2025, represents the culmination of a journey that began in 1996 with the initial development of the SRMs. My election to Sigma Xi and the rapid publication of Paper #19 (available as an open-access preprint on Zenodo) are a powerful international acknowledgment of the effort expended by researchers who commit to rigorous work.

The AIMs paper is a call to action for the scientific community to debate the ethical and legal void surrounding self-replicating AI before they colonize Mars.

Viva a Ciência! Cheers to those who recognize and value the efforts of researchers worldwide. 

Viva a Ciência! Viva os que reconhecem e valorizam os esforços dos pesquisadores e pesquisadoras! 

Link do paper 19 na imagem abaixo 

Link to paper #19 in the image below

 

APP ANDROID - MORSE CODE - TEXT AND AUDIO: It is an educational application entirely developed in English, designed to teach and convert Morse code through two integrated modes: Text-to-Morse conversion (visual learning)

 Dear community,

It is with immense pride that I present the 184th Android App from the Educational Technologies Research Group of the Federal University of Fronteira Sul - GTED/UFFS.

I emphasize that this approval was achieved within a few hours of submission. I congratulate the Google Play team for their respect and professionalism. I made this App available on the other platform, which, incidentally, WAS THE LAST ONE. I don't produce for money, but for the passion to do GOOD FOR THE SAKE OF GOOD. No DEVELOPER deserves the negligence of the Apple support team, with submissions waiting for more than 60 days. I apologize to iOS users; I made 21 Apps available there and WILL NOT MAKE ANOTHER SUBMISSION. I respect those who respect educational technologies. Apple only aims for profit and its own self-interest.

Below you will find the link to the 184th App from GTED/UFFS. Download, share, and help us bring knowledge to people in a respectful way, just as we have been doing since 2021.

Link in the image below: 👇👇👇

 

RMQ - RELATIVIDADE E MECÂNICA QUÂNTICA - 14° APP QUE DISPONIBILIZAMOS GRATUITAMENTE NA APP STORE. EM TEMPOS DE TEMPESTADES SOLARES, VISITANTES INTERESTELARES MISTERIOSOS E ATÍPICOS, O MELHOR A SE FAZER É ESTUDAR E SE INFORMAR. AQUI ESTÁ A ASTROFÍSICA PARA PESQUISADORES E ENTUSIASTAS DA ÁREA.

RMQ - RELATIVITY AND QUANTUM MECHANICS - 14th APP WE OFFER FOR FREE ON THE APP STORE. IN TIMES OF SOLAR STORMS, MYSTERIOUS AND ATYPICAL INTERSTELLAR VISITORS, THE BEST THING TO DO IS STUDY AND STAY INFORMED. HERE IS ASTROPHYSICS FOR RESEARCHERS AND ENTHUSIASTS IN THE FIELD. 

 

App - RMQ - Portuguese and English - Link in the image below

 

App - RMQ - Português e Inglês - Link na imagem abaixo  

 

 

Paper 1: Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI - Chapter 8 of ICTIS - Vol 2, to be released in January 2026 by Springer Nature, now presented as the HCP App - Heru Cell Proliferation - App Store - To further revolutionize the field, I'm sharing the approval of NINE more iOS apps (FREE on the App Store) on November 7th, 2025. This is science with responsibility, quality, and accessible to everyone.

 

From Cornell University to Cupertino:
The ICTIS 2025 / Springer Nature recognition meets Apple’s App Store approval.
SRMs & GenAIs cross the scientific frontier — from computational biology to global technology.

What began at Cornell University under the ICTIS 2025 Conference (Springer Nature) has now reached Cupertino through Apple’s App Store — a historic fusion of science, mathematics, and innovation.

The SRMs & GenAIs research line, authored by Prof. Carlos França and Gabriel Altman (OpenAI), transcends academic borders to become a living ecosystem of educational and scientific applications. Each app reflects decades of dedication, connecting generative intelligence, quantum computing, and biological reasoning.

SRMs & GenAIs & Quantum Computing — From Cornell University to Cupertino, 2025.

🔬 HCP – Heru Cell Proliferation
Da Cornell University à App Store (Apple Inc.)

Nesta tarde de 7 de novembro de 2025, a Apple Inc. aprovou oito aplicativos científicos da Heru Technologies, consolidando a ponte entre pesquisa científica e tecnologia educacional. O destaque é o HCP – Heru Cell Proliferation, baseado no paper apresentado na Cornell University (ICTIS 2025 / Springer Nature). Abaixo segue a lista completa dos aplicativos aprovados, todos inspirados na teoria das SRMs & GenAIs & Quantum Computing.

Aplicativo	Link direto / Ícone
🧬 HCP – Heru Cell Proliferation	Ver na App Store
♾️ Ciclo Hamiltoniano Interativo	Ver na App Store
📈 Progressões Matemáticas	Ver na App Store
🔢 Fatores Primos de um Número	Ver na App Store
🧮 Geometria Total	Ver na App Store
❤️ ECG – Escala de Coma Glasgow	Ver na App Store
⚛️ ACH – Quantum Inspired	Ver na App Store
📊 Md_dvp_GTED_UFFS – Medidas de Dispersão	Ver na App Store
🎯 LREG – Regressão Linear	Ver na App Store
🧩 Sistemas e Equações Lineares	Ver na App Store

Cada aplicativo é um fragmento de uma jornada científica que começou em 1996 e agora atravessa as fronteiras entre Matemática, Biologia Computacional e Computação Quântica. A Heru Technologies agradece à App Store Review e à comunidade científica por este marco histórico.

SRMs & GenAIs & Quantum Computing – Heru Technologies, 2025.

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SRMs & GenAIs — From Cornell University to Cupertino

ICTIS 2025 / Springer Nature → Apple App Store, November 2025

What began at Cornell University during the ICTIS 2025 Conference (hosted by Springer Nature) has now reached Cupertino through Apple’s App Store. This marks a historic bridge between academic science and global technology — a living testimony of how mathematics, biology, and generative intelligence converge into one unified field.

Led by Prof. Carlos França (Heru Technologies / GTED-UFFS) and Gabriel Altman (OpenAI), the SRMs & GenAIs research evolves from theoretical foundations to applied innovation, integrating Quantum Computing, Computational Biology, and Generative Intelligence. Each approved app embodies years of research and symbolizes a paradigm shift in human–AI collaboration.

Approved Scientific and Educational Applications — November 7, 2025

Application	App Store Link
🧬 HCP – Heru Cell Proliferation	View on App Store
♾️ Interactive Hamiltonian Cycle	View on App Store
📈 Mathematical Progressions	View on App Store
🔢 Prime Factors of a Number	View on App Store
🧮 Geometria Total	View on App Store
❤️ ECG – Glasgow Coma Scale	View on App Store
⚛️ ACH – Quantum Inspired	View on App Store
📊 Md_dvp_GTED_UFFS – Measures of Dispersion	View on App Store
🎯 LREG –Line Regression	View on App Store
🧩 Systems and Linear Equations	View on App Store

SRMs & GenAIs & Quantum Computing — Heru Technologies 2025
From Cornell University to Cupertino 🌎

Paper 2 Surpasses 1K Downloads — November 6, 2025 - Thank you, Zenodo / CERN – Switzerland

 

Dear community,

 

Paper 2: 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.

This paper has been crowned with the seal of quality and recognition from the international scientific community.
It has now surpassed one thousand downloads — becoming the second preprint in the SRMs series to achieve this distinction.

Paper 1, already exceeding 2K downloads, was presented by me at ICTIS 2025 – Cornell University – Springer Nature, and undoubtedly marked the beginning of this current research phase that I started back in 1996.
Nearly three decades of recognition from universities in Brazil and Canada, along with many other achievements already shared across the portals GTED and Heru Technologies, have brought us to this moment.

I sincerely hope this milestone will draw the attention of the App Store Review team.
I have submitted 13 apps, 11 of which remain in the review queue for several weeks.
The Heru Math app, directly inspired by this Paper 2, presents SRM-based challenges that are complex even for Generative AI systems (GenAIs).

The app has been under testing since September 30, 2025, currently in its 5th version (submitted October 17, 2025), and still awaits publication.
Here lies a valuable opportunity for the reviewers: Challenge 1 is fully solved in this very Paper 2 — already downloaded and studied by more than 1,000 researchers worldwide.
The remaining challenges will demand intellectual strength and deep understanding of the peculiarities of the Infinite Series with Multiple Ratios (SRMs).

Once again, I express my gratitude to the Zenodo Platform / CERN Switzerland, as well as to everyone who has already recognized the power of SRMs & GenAIs & Quantum Computing — each, within their own cognitive time.

The link to the paper is in the image below.