A Note from the Author

This work grew out of a personal project pursued in my own time, motivated by a long-standing curiosity about infinity, geometry, and the structure of the universe. While I have published in my own professional field, this project exists outside that discipline and beyond the scope of a conventional journal article. It is offered here as a transparent, self-published exploration: a technical web book and companion guide, an interactive model, and a record of the reasoning that led me here.

The guiding concern of this work is physical infinity. I do not believe infinities should be treated as physical realities simply because they are useful mathematical tools. While infinite space, infinite density, or parallel worlds may be mathematically productive, they do not necessarily describe the world we experience. In this model, an "infinity" is treated as a sign that a description has reached the edge of its domain, rather than as a literal feature of the universe.

This philosophical starting point leads to the finite deformable geometry model. This model preserves local tested physics while asking whether cosmological observations can be organized through "finite response registers"—essentially, measurement scales that respond to the geometry of the universe. The model keeps the local structure of General Relativity and quantum theory intact; instead, it proposes a new interpretation of how redshift, distance, gravity, and void structure behave on the largest scales.

The "Hubble tension"—the discrepancy in measured expansion rates—is a primary motivation for this work. My concern is not with Hubble’s discovery itself, but with the assumption that these different rates must all be forced onto one single, universal expansion scale. This book explores an alternative: that the universe may be finite, deformable, and internally measured, allowing different observational registers to remain linked without needing a single global ruler.

Use of AI Tools

AI tools helped make this project possible. They assisted with literature organization, coding, plotting, editing, figure development, and the testing of ideas that I might otherwise have found too discouraging to pursue. However, these tools did not create the work. All questions, assumptions, decisions, corrections, and physical interpretations are mine, and I take full responsibility for them.

AI is a powerful assistant only when supervised carefully. It can drift, lose sight of the goal, over-polish language, or invent confidence where there is none. Used carelessly, AI can damage a project; used with rigorous backups, citations, and clear workflow rules, it is an extraordinary tool.

This book and companion app are offered in that spirit: a way to make a difficult idea visible, testable, and easier to think through.