THEK Research Institute  ·  Guayaquil, Ecuador  ·  2025

Where formulas are not tools —
they are organisms.

Two original frameworks for mathematical discovery, equation generation, and the evolutionary theory of formulas. Twelve years of independent research. Now publicly available.

NFF · Nested Formula Framework FGET · Formula Genomics and Evolution Theory CC BY 4.0 · Open Access
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The THEK Framework Ecosystem

Two frameworks. One research programme.

NFF and FGET were developed as independent instruments, but share a single philosophical axis: the conviction that mathematical formulas are not static abstractions, but evolving structures that reconstruct the intrinsic pattern of any phenomenon.

NFF
Nested Formula Framework

A hierarchical methodology for mathematical modelling and equation discovery. Variables are introduced sequentially; at each level, the coefficients from the previous step become the dependent quantities to be modelled by the next variable. The result is a fully interpretable, physically traceable formula — never a black box.

Recursive coefficient nesting Hybrid architectures Gaussian · Gumbel Power law emergence xAI · Machine learning Seismology · Finance · Climate
THEK-WP-NFF-2025-001 · 18 pages · English and Spanish
FGET
Formula Genomics and Evolution Theory

A foundational philosophical and scientific framework proposing that mathematical formulas are abstract organisms inhabiting a potentially infinite evolutionary space. Matter, energy, and the laws of physics are not eternal constants — they are the tangible consequence of the genomic evolution of the formulas that constitute them.

Mathematical genome Evolutionary Formula Space Mathematical patterns Reverse engineering Evolutionary Platonism Mathematical natural selection
THEK-WP-FGET-2025-001 · 22 pages · English and Spanish
The NFF mathematical ecosystem
FIG. 1  ·  THE NFF MATHEMATICAL ECOSYSTEM — Functional families, hybrid architectures, and the emergence of power laws, Gaussian bells, and exponential towers through recursive nesting  ·  THEK Research Institute 2025
Formula Genomics and Evolution Theory

The scientist at the edge of the Evolutionary Formula Space

A scientist exploring the Evolutionary Formula Space — FGET
THE EFS — EVOLUTIONARY FORMULA SPACE

"Every existing phenomenon was shaped from its genesis by formulas. Our task is to uncover, level by level, the variables and coefficients of each genetic mutation of that formula."

FGET proposes that the universe is an infinite web of evolving mathematical patterns. What we perceive as matter and energy are stable manifestations of patterns that have achieved high evolutionary fitness within the EFS.

The NFF is the operational microscope of FGET — decomposing observable phenomena layer by layer, identifying at each level the coefficients and functions that shape the underlying pattern.

M.Sc. Marcelo Moncayo Theurer · THEK Research Institute · 2025

Science does not progress by accumulating data. It progresses by finding the formula. The NFF does not search for parameters within an assumed equation — it searches for the equation itself, architecture by architecture, level by level, until the intrinsic pattern of the phenomenon is reached.

M.Sc. Marcelo Moncayo Theurer · THEK Research Institute · 2025

The Fundamental Law of NFF — Nc = sn — was not postulated. It emerged from systematic derivation across six functional families. That makes it more compelling than a hypothesis: it is a consequence.

Open Access · CC BY 4.0

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Both papers are freely available under Creative Commons Attribution 4.0. Please register below — this helps us understand how these frameworks reach researchers and institutions worldwide.

NFF — Nested Formula Framework
THEK-WP-NFF-2025-001 · June 2025

18 pages. Explicit formulas for 6 functional families, 17 hybrid architectures, 3-level Gaussian and Gumbel NFF, connection to FGET. 27 references.

FGET — Formula Genomics and Evolution Theory
THEK-WP-FGET-2025-001 · June 2025

22 pages. Mathematical genome, 13 core definitions, research agenda 1–15 years, philosophical foundations. 26 references.

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Four ways to go deeper

These frameworks are not finished products — they are the opening moves of a long-term research programme. We actively seek researchers, practitioners and institutions who want to explore, apply, validate or build on them.

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Co-author papers, validate frameworks against real datasets, or extend NFF and FGET into new domains.

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APPLY NFF TO YOUR DATA OR INDUSTRY

The NFF has been applied to seismic risk assessment, attenuation law calibration, and structural modelling over twelve years. If your organisation works with complex multivariate data and needs models that predict and explain — write to us.

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Author

Marcelo Moncayo Theurer

M.Sc. Technische Universität München (TUM) IISEE-BRI — University of Tokyo Full Professor — University of Guayaquil THEK Research Institute — Guayaquil, Ecuador
ORCID: 0000-0002-8456-1571

Over twelve years of independent research in complex systems modelling, seismic risk assessment, and mathematical framework development. Founder of the THEK Research Institute and sole author of three original research frameworks: SERRA (seismic risk), NFF (nested formula methodology), and FGET (mathematical evolutionary theory).

NFF has been operationally applied to graduate theses and applied engineering projects since 2013. FGET was developed concurrently as the philosophical and theoretical foundation. Both frameworks are formally published under DOI on Zenodo (CC BY 4.0).

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