Post Zero: What I’m Releasing and Why

A Note on Process:

I come up with ideas and share my opinions across mathematics, AI architecture, cosmology, and business concepts, its what i do. None of these ideas are a push towards following a strictly line of reasoning but instead an attempt to ask different questions and accepting that 90% could hold no ground and realizing that whether I'm comfortable with sharing or not.. With that in mind, 10% of every idea I come up with is far greater a statistic than 10% of what i am comfortable with sharing.

Philosophy:

Over the past year, I’ve come to the realization that an idea in the pocket is one that would follow me to the grave and I developed the belief that whether good, bad, right, wrong, or incomplete i would release all of my ideas. I would reather that my ideas have the potential to spark curiosity enough in someon that they find it usefull somewhere in life. While that has been a goal of mine I did realize that my technical understandings and presentation skills are "lacking" so i began utilizing tools such as LLM's in order to formalize my ideas and philosophies while still having control over the final product. This one (Boundary-Naive Set Theory: BNST and Boundary-Native Language Models: BNLM) emerged from noticing an inconsistency in how we treat paradox across domains, then formalizing that observation through collaboration with Claude.

Call:

If you want to follow the other frameworks as I develop them, that’s what this blog is for. I’m treating idea-sharing itself as an experiment, what happens when you release frameworks freely instead of hoarding them? I plan to open this up as i get more free time in the future and try to allow for maximum participation.

“This work demonstrates what human-AI collaboration can achieve: rapid formalization of philosophical insights into rigorous mathematics and practical architecture. The framework stands on its formal merits.”

Over the next 20 days, I’m releasing a complete framework that connects pure mathematics, AI architecture, and experimental validation. This is my first attempt at a full research paper, and I tried to brake into digestible pieces. I don't know about you but I don't like newsletters or mass amounts of emails, so there will not be newsletter updates on the releases.

What This Is

Over a few weeks, I developed Boundary-Naive Set Theory (BNST) - a mathematical framework that formalizes paradox instead of prohibiting it - through intensive collaboration with Claude (Anthropic’s AI). Then I applied it to artificial intelligence, creating Boundary-Native Language Models (BNLM) - an architecture that attempts to prevents AI systems from validating claims using only the claims themselves.

The work includes:

∙ Formal mathematics (axioms, proofs, theorems)

∙ AI architecture design (five computational layers)

∙ Experimental validation (testing whether it actually works)

∙ Practical implications (for AI safety and deployment)

This emerged from rapid, iterative human-AI collaboration. I brought the philosophical insights, framework vision, and final say on the framework. Claude helped formalize the mathematics, structure the architecture, and articulate the implications. The results are better than I could have achieved alone, and if I could do something like this utilizing AI as a tool for articulation and formalization then i believe anyone could come up with things just as goo and 100% better.

Why I’m Releasing It This Way

Free and open: This work is released under Creative Commons Attribution 4.0 and Apache License, Version 2.0. Use it, build on it, cite it, modify it. Knowledge should be given and not waisted. My insights, whether valuable or not will never never have had be be questioned by me on whether I should have build this over that.

Daily releases: One section per day for 20 days. This gives you time to digest each piece and lets discussion develop as we go.

Complete at the end: On day 20, I’ll release the full paper as a single PDF. But the daily structure helps make mass amounts of technical content approachable, at least for me.

What I’m Hoping Happens

I want to see what occurs when you release a complete theoretical framework freely:

  • Do researchers engage with the mathematics?
  • Do AI practitioners test the architecture?
  • Do critics find holes I missed?
  • Does anyone build on this?

I’m treating this as an experiment in idea-sharing itself.

How to Follow Along

If you’re a mathematician: Pay attention to Part II (days 5-11). That’s where BNST is formally developed. I want your critiques on the axioms and proofs.

If you’re an AI researcher: Focus on Part III (days 12-16). That’s the BNLM architecture. I want to know if it’s implementable and what I’m missing.

If you’re philosophically inclined: Start with Part I (days 1-4). That’s the argument for why we should formalize paradox rather than prohibit it.

If you’re practical: Jump to Part IV (days 17-20). That’s experimental validation and real-world implications.

If you want everything: Just wait until day 20 and grab the complete PDF.

What This Costs You

Nothing monetarily - the work is free.

There’s a $1/month commenting fee to prevent spam and bots as well as help cover the cost of the website, I will lower it if i can once i find a provider that can accommodate low cost subs. If you want to engage in discussion, that’s the only cost. If you just want to read and take the ideas, they’re yours.

What I’m Doing Next

While this releases, I’m working on:

  • Theory of Everything AI - a broader framework BNST is part of
  • Geometric redistribution theories - collapsing formal physics into geometric frameworks
  • Business Ideas - turning theoretical work into practical value

A Request

If this work helps you, feel free to cite:

Pendry, S. (2025). From Russell's Paradox to Boundary-Native Intelligence:

A Complete Framework. Halfhuman Draft.

And if you build something from it, let me know, it would be cool to see if anything come about from one of my ideas and the collab of others.

What’s Coming

Each section will be released as its own post following a formal TOC.

PART I: PHILOSOPHICAL FOUNDATION

[§1] Introduction and Motivation

[§2] The Inconsistency in Paradox Treatment

[§3] Historical Context and Response

[§4] The Case for Formalization Over Prohibition

PART II: BOUNDARY-NAIVE SET THEORY

[§5] Naive Set Theory Baseline

[§6] The Boundary Complement Operator

[§7] Russell Boundary Set and Validity Predicate

[§8] Conditional Complement: Validity-Gated Operations

[§9] Formal Properties and Theorems

[§10] Comparison to Existing Approaches

PART III: BOUNDARY-NATIVE LANGUAGE MODELS

[§11] The Self-Referencing Validation Problem

[§12] BNST as Architectural Solution

[§13] Five-Layer BNLM Architecture

[§14] Training Methodology

[§15] Implementation Considerations

PART IV: EXPERIMENTAL VALIDATION

[§16] Experimental Design and Protocol

[§17] Results and Analysis

[§18] Implications for AI Communication

[§19] Discussion and Future Work

[§20] Conclusion

© 2026 HalfHuman Draft - Pendry, S
This post is licensed under Creative Commons Attribution 4.0 (CC BY 4.0).
Code examples (if any) are licensed under the Apache License, Version 2.0

See /license for details.