Heru Technologies
Unprecedented Mathematics Formulas. Exclusive Solutions
Heru Technologies is a registered trademark of revolutionary algorithms, started in 1996. It is a set of 14 mathematical formulas that expand all Sir Isaac Newton's kinematics and the scopes of geometric and artimetic progressions.
Thanks to everyone who supported my efforts in 2025 for Brazilian and global science.
This was a great year for the research I started in 1996. Infinite Series with Multiple Ratios (SRMs) are featured in 20 papers. Paper #1, released on March 22, 2025, was highlighted at ICTIS 2025, which took place at Cornell University – New York/USA. This was the first recognition of the year. The paper became a chapter in a book by SPRINGER NATURE, which will be released in early January 2026.
Finally, the great highlight came with my election as a FULL MEMBER, SIGMA Xi - The Scientific Research Honor Society (2025).
The last two papers (#19 and #20) arose from an INSIGHT I gained from a post on the Sigma Xi members' forum. A society with 200 Nobel Prize winners, illustrious scientists such as Linus Pauling and Albert Einstein, recognized my efforts and welcomed me as a FULL MEMBER, and my gratitude comes in the form of 2 robust papers with the potential to impact global Space Engineering.
The papers (#19 and #20), written in 5 (FIVE DAYS), are posted below.
Ad astra per scientiam.
Dr. Carlos Roberto França
Associate professor at Federal University of Fronteira Sul – UFFS
Campus Chapecó – Santa Catarina/Brazil
Overcoming the Strategic Gap: A Counterpoint to Current "Humans First" Mars Colonization Architectures and Self-Replicating Artificial Intelligence Machine Systems (SRAIMs)
Abstract
Current Mars colonization architectures, predominantly centered on the "Humans-First" model (promoted by space agencies and private initiatives like SpaceX), demonstrate a critical vulnerability: the reliance on massive and continuous transport of terrestrial resources and the acceptance of an unacceptable existential risk due to the harsh conditions on Mars. This paper proposes an ethically and logistically superior route: the pre-colonization of Mars by SRAIMs (Self-Replicating Artificial Intelligence Machines), establishing humanity's largest extraterrestrial AGI laboratory. The SRAIM architecture is composed of a three-level system. The first level is the AIM Floating Station (Atmosphere), which acts as the mission's AGI core, providing data caching, onboard processing, and communication relay, mitigating the physical delay between Earth and Mars and providing advanced weather warning. The second level is Surface SRAIMs: Autonomous Machines dedicated to In-Situ Resource Utilization (ISRU), and the third level is Additive Manufacturing (Replication). The paper presents the robustness of SRAIMs through innovative Hybrid Energy Generation, as well as the backbone of the proposal, which is Predictive Locomotion Control using Infinite Series with Multiple Ratios (SRMs). Finally, it is worth noting that this work complements paper 19, posted here on the Zenodo Platform, supported by the advanced mathematics and SRM formulas presented in papers #2 and #4.
Link in the image below
My Victorious December: Full Member of Sigma Xi and the Launch of Paper #19 on Martian AIMs
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: FULL BREAKING NEWS - CLICK HERE
Paper #19: The exploratory possibilities of Mars through Artificial Intelligence Machines (AIMs) as a precursor to a civilizational milestone.
Link in the image below
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.
HCP App - Heru Cell Proliferation:
App Store
Link in the image below 👇👇👇
18Th paper - 21 October/2025 - França, C. R. (2025). SRMs & Few-Step Discrete Flows: Connections between Algebraic Determinism and Probabilistic Generation.
Zenodo CERN Switzerland.
The path of Computer Science has always pointed toward the reduction of steps. In 2017, with the Heru Search Method (HSM), we introduced a deterministic model based on SRMs capable of replacing Binary Trees and surpassing the long-standing O(log n) paradigm.
Eight years later, in 2025, researchers from Apple Inc. and Ohio State University presented Few-Step Discrete Flow-Matching (FS-DFM), applying the same principle within the probabilistic domain of information generation.
The complementarity between HSM and FS-DFM is remarkable, unveiling a unified axis of computational efficiency:
Link in the image below 👇👇👇
DeepMath - SRMs and GenAI - SECOND APP AVAILABLE ON THE Apple Store: In search of a powerful AI to control a robotic arm. A challenge for some humans and AI agents. Download and test your knowledge of Advanced Math.
Link in the image below.
👉 “SRMs & GenAIs & Quantum Computing — now inside the Apple Universe.”
APP ACH – Quantum Inspired (IOS) -
Link in the image below 👇👇👇
17° Paper - 29th september/2025 - França, C. R. (2025). Pipeline SRMs and GenAIs: Nonlinear Predictive Frameworks for Drone Swarms and Mobility in Defense. Zenodo.
Link in the image below
Dear Community,
We are pleased to announce that researcher and author Carlos Roberto França has had his Chapter 8, "Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI," accepted and is now in the final proofreading phase by Springer Nature, one of the most respected publishers in academia.
Book: ICT for Intelligent Systems – Vol. 2. Springer Nature - DOI: 10.1007/978-981-95-1357-4
Chapter 8: Mathematical Challenges for Generative AI in Computational Biology:
Cell Proliferation and the Path to Living AI - Link in the image below
Technological Pillar (iOS):
Completing this momentum, Carlos Roberto França also confirms that the first version of SRM-based applications is now in production for iOS (Apple Store), consolidating the transition from theory to globally accessible solutions.
Closing:
With 16 scientific articles published, one application already launched, and growing recognition across continents, Carlos França and Heru Technologies reaffirm their commitment to position SRMs as a global scientific and technological landmark.
Paper 16 - 24th september/2025 - França, C. R. (2025). Quantum Biology Based on SRMs: From Cell Proliferation to Cyclical Spheres of Preventive Health. Zenodo. Link in the image below
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
14th paper (September 10, 2025) - Quaternary Quantum Dynamics and SRM Algorithms: A Middle-Path Framework Beyond Qubits.
Link in the image below
🌌 New Milestone, September 3, 2025: Paper 13 Published on Zenodo
We are proud to announce the release of Paper 13 – SRMs and the Middle Path: Bridging Relativity and Quantum Mechanics.
Link in the image below.
11th paper: SRMs meet Schrödinger: Multiple-ratio expansions for quantum dynamics and entanglement in a timeless dialogue.
Link in the image below.
10th paper: SRMs and GenAIs: Bridges between Infinite Series with Multiple Ratios, Generative Intelligence and Quantum Computing.
Link in the image below.
August/2025 - ONE YEAR OF SRMs & GenAIs PARTNERSHIP: ACHIEVEMENTS AND FUTURE CHALLENGES - Link image below !
Beyond Binary Trees: A Paradigm Shift in Data Search Efficiency via SRMs-Based Structures. Zenodo. SEVENTH PAPER. França, C. (2025).
Link to paper 7 in the image below
📢 Mathematical Challenges for Generative AI in Computational Biology: Cell Proliferation and the Path to Living AI ***shines at ICTIS 2025***
SIXTH PAPER -Predictive analytics in the Swiss pharmaceutical sector: SRMs are the right amount of mathematics for GenAIs.
https://doi.org/10.5281/zenodo.15272636
PUBLISHED ON APRIL 23, 2025
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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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I have just published the 4th paper to prove the strength of SRMs and their importance for GenAI.
FOURTH PAPER- published at 5th April 2025 - Heru Technologies: Modeling Escape Trajectories of a Probe Trapped in an Asteroid's Gravitational Field Using SRMs and Human-GenAI Collaboration.
Link in the image below.
Heru Technologies Solutions
Cryptography
Exclusive solution, without hybridism, copyright and unpublished formulas. It is not based on keys with prime numbers or traditional cryptographic functions. It is the only cryptographer in the world that supports attacks by quantum machines. It went online for testing in 2014 for 3 months, with no record of security breaches, with access from 112 countries.
Paper published in portuguese.
Heru Search Method
A performance greater than 0 (log n) of the Binary Searches Tree or B-tree. Faster, more precision and objectivity and the end of useless results in web searches. I manage to reduce the users' cognitive overload, because I perform a clean search with my method, and I still mitigate the Overheads of large data centers. A pity that I could not transmit faithfully on the videopitch above, but it was worth a lot. This paradigm break needs to be heard, investigated and proven with large masses of data.
Paper published : American Journal of Computational Mathematics - AJCM - Link below
Heru technologies applied to formula 1 and moto speed.
It is a powerful algorithm with the formulas adopted by Heru, where we extended Isaac Newton's Kinematics, handling variables and metric patterns that are unable to be changed with the usual concepts of Physics and Computational Mathematics. Paper published - 2017. Link below.
Heru technologies and applications in biotechnology and biomedicine
Here is another promising applicability of the formulas handled by Heru. We are able to predict and control cell proliferations with extreme precision and speed. The big difference is the possibility of using / analyzing several agents or variables simultaneously.
Paper published - 2017 - Indus Foundation. Link below
Published and available for free at Google Play. Click on image above.
Heru technologies e a criptografia 100% brasileira - Saiba como surgiu a única solução que não utiliza hibridismo. Muitos confundem customização do AES(padrão americano), como sendo solução nacional. Não cometa esse erro, pois o Brasil não adota uma solução totalmente nossa e sim versões de padrões estrangeiros. Saiba mais com o App Criptógrafo Heru - Link na imagem abaixo:
Heru Technologies encryption method: Unique in
the world that uses unpublished mathematical
formulas and encrypts with binary disturbances.
While the world awaits encryption algorithms that can withstand attacks from quantum computers, Heru Technologies continues to work and share its advances. See this article we published in the International Mathematics Computers and Simulation - DOI: 10.46300/9102.2022.16.14
Link in the image below
Researcher's words
For many people, we are on our way to the Nobel Prize in Physics. I know that the applicabilities still need to impact humanity and that will happen. I don't wonder how, but when ...
Dr. Carlos França
Creator of algorithms Heru Technologies
POST-QUANTUM CRYPTOGRAPHY - PQC 2025
