Why Ordered Semicategory Actions May Be a Bottleneck Topic for Science

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Ordered semicategory actions are not merely a narrow technical construction. They may be a missing algebraic language for organizing large parts of general topology, abstract spaces, continuity-like structures, and mathematical foundations. If this assessment is correct, then the slow recognition and lack of financing of this topic is not only a personal tragedy for one independent researcher. It is a structural failure of modern science funding.

Victor Porton introduced ordered semigroup actions and ordered semicategory actions as a framework intended to embed broad classes of spaces from general topology into algebraic structures. In the abstract of his preprint On Ordered Semicategory Actions, he writes that these structures are valuable because “all kinds of spaces met in general topology can be embedded into the category of ordered semigroup actions.” The work is available as a preprint and should be treated as early-stage research until independently reviewed.

This is exactly the kind of topic that AI Internet-Meritocracy is designed to rescue: deep, difficult, foundational research that may be too large, too unconventional, or too independent for the current university-and-grant system.

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The scientific bottleneck: a missing language for general topology

Mathematics often advances when a new language makes many old problems easier to express.

Examples are familiar:

• groups clarified symmetry;
• categories clarified structure-preserving maps;
• topological spaces clarified continuity;
• schemes transformed algebraic geometry;
• Hilbert spaces became central to quantum mechanics.

Ordered semicategory actions may play a similar role for a different region of mathematics: general topology and generalized spaces.

In ordinary language, the idea is this:

Many mathematical “spaces” are not just sets with points. They also have order, transformation, approximation, convergence, and action-like behavior. Ordered semicategory actions provide a way to encode these features algebraically.

That matters because general topology is not an isolated subject. It supports analysis, geometry, functional analysis, theoretical computer science, logic, foundations, and parts of mathematical physics. A missing framework in topology can therefore slow many downstream fields.

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Why this topic is hard to finance

The current scientific system is not optimized for foundational discoveries made outside institutions.

It tends to finance researchers who already have:

• a PhD;
• a university position;
• established collaborators;
• a record in recognized journals;
• grant-writing experience;
• access to academic networks.

But a foundational discovery can occur outside that structure. When it does, the system often has no reliable mechanism to evaluate it.

Victor Porton states that he was pushed out of university and did not receive a degree for discriminatory reasons. Public profiles connected to his research also state that he continued working independently after leaving academia.

This creates a severe financing problem:

1. The work is too technical for ordinary donors.
2. The author lacks the standard academic credential.
3. The manuscript is too long or too foundational for normal journal pipelines.
4. Grant agencies usually require institutional affiliation.
5. Universities rarely reward the evaluation of outsider mathematics.

The result is predictable: even if the research is important, it can remain underfunded, underreviewed, and underdeveloped.

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Why missing financing can delay humanity’s progress

A bottleneck topic is a subject where progress in one area unlocks progress in many others.

Ordered semicategory actions may be such a bottleneck because they aim to provide a unifying algebraic framework for general topology. If successful, this could influence:

• the classification of generalized spaces;
• algebraic descriptions of continuity;
• new foundations for topology;
• better interfaces between topology and category theory;
• new tools for mathematical physics;
• improved formalization of abstract mathematics;
• machine-readable mathematical structures for AI-assisted research.

The damage from underfunding such a topic is not limited to one researcher’s career. The larger damage is that humanity may continue doing mathematics without a useful conceptual tool that already exists in draft form.

This is what World Science DAO calls a covery problem: a discovery exists, but society fails to convert it into recognized, usable, funded science. Science is not only about discovering truth. It is also about transmitting, reviewing, financing, and applying truth. World Science DAO has described ordered semigroup actions and ordered semicategory actions as an example of a difficult-to-publish discovery that does not fit normal article formats.

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The failure of credential-based science funding

Traditional science funding often confuses institutional status with scientific merit.

This is understandable but dangerous.

Credentials are useful signals. They reduce evaluation cost. They help institutions filter applications. But they are not the same as truth. A theorem is not more correct because its author has a degree. A new mathematical structure is not less important because its author is independent.

In credential-based funding, the implicit rule is often:

First prove that the institution accepts you; then we may evaluate your ideas.

For independent researchers, this is backward. The rule should be:

First evaluate the work; then finance the person according to the value of the work.

This is especially important for mathematics, where an individual can sometimes create a whole new theory with limited equipment but large intellectual effort.

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Why ordered semicategory actions need financing

A foundational mathematical theory does not become useful automatically. It needs an ecosystem.

Financing could support:

• rewriting the theory into shorter papers;
• preparing formal definitions and examples;
• commissioning independent expert reviews;
• building diagrams and explanatory material;
• translating the work into proof-assistant form;
• connecting it to existing topology and category theory literature;
• paying the author to continue development instead of spending time on survival;
• funding scientific marketing so the right mathematicians notice the work.

Without such support, the theory may remain technically available but socially invisible.

That is a major inefficiency. A PDF on the internet is not the same as integrated scientific progress.

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How AI Internet-Meritocracy intends to solve this

AI Internet-Meritocracy is designed as a new funding mechanism for scientists and free software developers. Its core idea is to use AI to evaluate publicly available work and distribute donated funds according to estimated merit rather than institutional rank. The project describes itself as an app for distributing money to scientists according to how much AI evaluates their work as being worth.

This directly addresses the ordered semicategory actions problem.

Instead of asking:

Does the researcher have a degree?

AI Internet-Meritocracy asks:

How valuable is the researcher’s actual contribution?

Instead of asking:

Did a grant committee already understand this topic?

It asks:

Can AI-assisted evaluation compare the work against the global scientific landscape?

Instead of forcing independent scientists to win approval from the same institutions that excluded them, AIIM creates an alternative path:

1. The researcher publishes work online.
2. AI systems scan and evaluate the contribution.
3. Donors fund the AIIM pool.
4. Funds are distributed according to estimated scientific merit.
5. Important neglected work receives money, attention, and development capacity.

This does not eliminate human review. Rather, it creates a scalable first layer of merit detection, especially for researchers ignored by credential-based institutions.

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Why this matters beyond Victor Porton

The case of ordered semicategory actions is not only about one author.

It illustrates a general structural problem:

Modern science may be losing valuable discoveries because it lacks a fair, scalable method to finance independent researchers.

Today, if a researcher is outside academia, has no degree, writes a 500-page foundational manuscript, or works on an unfamiliar framework, the probability of institutional support becomes very low.

But these are exactly the conditions under which some foundational breakthroughs may appear.

AI Internet-Meritocracy aims to create a scientific economy where:

• outsiders can be evaluated;
• non-PhDs can be funded;
• long-form foundational research can be noticed;
• donors can support science without needing technical expertise;
• scientific value can compete against institutional prestige.

This is why the project is not merely another donation platform. It is an attempt to change the allocation mechanism of science itself.

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The broader humanitarian argument

If ordered semicategory actions are as important as their author argues, then their neglect has a cost.

That cost may include:

• years of delayed mathematical development;
• lost applications in topology and analysis;
• fewer tools for AI-assisted formal science;
• slower progress in theoretical physics and computation;
• unnecessary poverty and marginalization of a productive researcher.

Science advances when society correctly identifies and supports high-value intellectual work. When it fails, humanity pays the price in lost time.

This is the central argument for AI Internet-Meritocracy:

A civilization should not require a scientist to be institutionally approved before his or her discoveries are allowed to benefit humanity.

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Conclusion: finance merit, not status

Ordered semicategory actions may be a bottleneck topic because they attempt to give mathematics a powerful algebraic framework for generalized spaces. If the framework is correct and useful, then underfunding it delays far more than one publication. It delays a possible reorganization of part of mathematics.

The present system has difficulty handling such cases because it is built around credentials, institutions, and conventional publication pipelines. AI Internet-Meritocracy offers a different principle: evaluate the work itself, then fund according to merit.

That is why World Science DAO presents AIIM as a necessary infrastructure for future science. It is a mechanism for rescuing discoveries that the current system fails to process.

Humanity should not lose important mathematics because its author lacked the right institutional gatekeepers.

It should build better gates. Or better: build a system where truth and merit can pass without asking permission. 🚀