Project summary

I have been developing Generative Triangle T independently since 2024. It is a foundational mathematical and physical framework in which causal structure, spacetime geometry, continuum behavior, internal spin-1/2-like structure, recursively stable particle-like structures, combinatorial mass, nonfactorizable joint compatibility, gravity without a primary gravitational field, physical consequences, and operational routes toward testing the framework are developed within one recursive architecture.

The manuscript and its separate symbolic and computational verification archive are already public. I am now seeking funding for two closely connected purposes: to continue the systematic development of Generative Triangle T and to expose the existing framework to serious independent technical scrutiny.

The work has reached a stage where its major sectors are already developed far enough to open substantially larger research programs. The next step is therefore not simply to add more speculative ideas, but to deepen the mathematical and physical consequences already obtained, test their internal and cross-sector consistency, connect them more fully with established physics, and obtain technically accountable external examination.

What are this project's goals? How will you achieve them?

This project has two closely connected goals: to continue the systematic development of Generative Triangle T and to subject the existing framework to independent technical scrutiny.

The manuscript contains an interconnected mathematical and physical construction rather than a single isolated conjecture. It develops causal structure, spacetime geometry and continuum behavior, internal structure, stable particle-like organization, combinatorial mass, statistical compatibility, gravity, physical consequences and operational tests within one recursive architecture.

These sectors are not independent phenomenological mechanisms added afterward. They arise from the same generative structure and constrain one another. Because of this, a correction, objection or extension in one sector may have consequences for later parts of the framework and must be traced through the full dependency structure.

The microscopic generative law is deterministic, but it does not prescribe a unique macroscopic history or predetermine which stable particle-like structures must arise. Stable structures are realized only on subsets of admissible histories for which the required conditions of recursive stability, causal localization and containment, stable internal organization, and asymptotic distinguishability are satisfied simultaneously. Different admissible subsets may therefore support different stable structures, or no stable structure at all, while obeying the same fundamental generative law.

The existing framework also develops consequences beyond the basic recursive construction. Distinct deterministic microhistories can become indistinguishable at finite macroscopic resolution, producing an effective statistical layer without introducing a fundamental stochastic generator. Joint recursive compatibility of stable structures can yield nonfactorizable normalized counting measures. The binary internal sector produces a two-state half-integer spin-1/2-like structure. Stable particle-like structures acquire quantitative characteristics including multiplicity and combinatorial mass.

The gravitational sector is developed without introducing gravity as a primary field. A localized stable structure changes the set and measure of stable causal continuations compatible with another structure while the fundamental causal cone and universal propagation bound remain unchanged. The manuscript develops an effective attraction regime, a causal-closure black-hole regime without requiring a fundamental singularity in its definition, and a nonstationary gravitational-wave-like regime.

The present work is therefore not merely a preliminary mathematical core waiting for physical interpretation to be added later. It already develops a broad interconnected mathematical and physical architecture. At the same time, the consequences of that architecture are far from exhausted.

My continued research will deepen the major sectors already opened by the framework. This includes further development of causal and continuum spacetime structure; the internal spin-like sector and its relation to the mathematical structures associated with physical spin; classification, dynamics and interactions of stable particle-like structures; the quantum implications of nonfactorizable compatibility; the relation to quantum field theory; quantitative gravitational dynamics and field-level descriptions; gravitational-wave consequences; and fixed operational mappings between the internal quantities of the model and measurable physics.

These developments are not claimed as completed results of the current manuscript. They are substantial research programs opened by structures already developed there.

In parallel, independent technical scrutiny will be used to examine the mathematical and physical construction critically.

Concrete objections will be reproduced and investigated. Where an error is established, the relevant result and dependent conclusions will be corrected. Where a result remains valid after detailed scrutiny, that provides a stronger technical basis for deeper work.

The project will therefore combine continued mathematical and physical development, independent technical examination, cross-sector consistency checks, further symbolic and numerical verification, and the preparation of additional technical results and publications arising from the framework.

How will this funding be used?

The main purpose of this funding is to give me dedicated research time to continue the development of Generative Triangle T.

I have developed the framework independently since Aug 2024 without institutional research funding. Reaching the present stage required sustained work across its mathematical foundations, causal and geometric structure, continuum limit, internal structure, stable particle-like organization, combinatorial mass, statistical compatibility, gravity, physical interpretation, operational consequences and computational verification.

The present manuscript establishes a broad interconnected architecture, but it also opens a much larger research program that cannot be exhausted within the current work.

Funding would allow me to devote substantially more time to the next stage of the research: extending existing mathematical results, deriving new consequences, developing the physical content of the different sectors, carrying out additional symbolic and numerical verification, preparing further technical papers, and working toward more detailed connections with established quantum theory, quantum field theory, gravitational physics and measurable observables.

A second use of the funding is to make serious external technical scrutiny and scientific collaboration more feasible. Where a concrete need arises, funding may support specialist technical work, research collaboration, scientific meetings, conference participation, computational work, or other activities that allow particular parts of the framework to be examined or developed with relevant expertise.

At the $15,000 minimum funding level, the funding would primarily provide a period of protected research time and cover the direct costs required to continue mathematical, physical and computational development of the framework.

At the $45,000 funding goal, it would allow a substantially longer period of concentrated research, broader development of several sectors of the framework, stronger symbolic and computational verification, preparation of additional publications, and greater ability to engage in meaningful technical collaboration and scientific discussion around the results.

Specific uses may include:

– my research time devoted to continued development of Generative Triangle T;

– mathematical and physical derivation of new results opened by the existing framework;

– further development of the causal, geometric, internal, particle-like, quantum-foundational, gravitational and operational sectors;

– symbolic and numerical verification and reproducibility work;

– preparation of further technical papers and public research materials;

– computational tools and research software where required;

– access to scientific literature and publication-related costs where necessary;

– participation in relevant scientific meetings or conferences where this creates a realistic opportunity for technical discussion;

– targeted collaboration or specialist technical work when a concrete research need arises.

The funding would therefore primarily support the continuation of the research itself, while also making it easier to expose the work to serious independent scrutiny and to develop technically meaningful collaborations around it.

Who is on your team? What's your track record on similar projects?

I am currently the sole author and researcher behind Generative Triangle T.

I began developing the framework independently. The underlying model, recursive architecture, mathematical structure, physical interpretation, and the connections between its different sectors have been developed through my own research.

The theory was not generated by artificial intelligence. Computational and AI-assisted tools have been used where useful for verification, consistency checking, numerical testing, editing and presentation, but they are not the source of the framework or its underlying scientific ideas. Responsibility for the mathematical and physical claims is mine.

The work has already produced a complete public manuscript, a separate symbolic and computational verification archive, and a public verification repository.

The verification program was developed chapter by chapter and includes symbolic checks, numerical tests, guards and negative tests designed to check mathematical statements independently of the prose of the manuscript.

The manuscript is publicly available at:

https://doi.org/10.5281/zenodo.22158676

Verification archive:

https://doi.org/10.5281/zenodo.22097675

Verification repository:

https://github.com/Stalnyi/generative-triangle-verification/tree/v1.0.0

I currently have no university, laboratory, grant or institutional research group supporting this work. Creating the conditions for sustained research, independent technical scrutiny and broader scientific development is one of the main reasons for this proposal.

What are the most likely causes and outcomes if this project fails?

There are several different ways in which this project could fail, and they would have different scientific meanings. Independent examination could identify a genuine mathematical error in one of the derived results. In that case, the result and any later conclusions that depend on it would have to be corrected or withdrawn. A mathematical result could remain valid while a proposed physical interpretation turns out to be unjustified or too strong. That would require narrowing or changing the physical claim without necessarily invalidating the underlying mathematics. A further possibility is that the framework cannot be connected consistently with some structure required by established quantum theory, quantum field theory, general relativity or experiment. Identifying such an obstruction would establish a real boundary on the physical development of the model. Some research directions opened by the framework may also prove substantially more difficult than expected or may require mathematical or operational structures that are not yet available. There is also a practical risk that researchers with the necessary expertise may remain difficult to engage because examining a large unfamiliar foundational framework requires substantial time. None of these outcomes would make the research meaningless. A precise mathematical error, a failed physical mapping, a demonstrated obstruction to a proposed extension, or a clear limit on the applicability of one sector would itself be a concrete technical result and would show exactly where the framework has to change. Conversely, results that withstand detailed examination would provide a substantially stronger basis for deeper research. I therefore do not define success as obtaining agreement that Generative Triangle T is correct. I define success as obtaining specific, technically accountable conclusions about what is mathematically established, what requires correction, which physical interpretations are justified, which predictions or operational mappings can be tested, and which research directions can be developed further.

How much money have you raised in the last 12 months, and from where?

I have raised $0 in external research funding during the last 12 months.

Generative Triangle T has been developed independently without grant funding, university funding or institutional research support.