The future belongs to those who build it.
I build systems that amplify the best of humanity with AI — at enterprise scale, from first principles, and against the kind of adversarial scrutiny that separates the work that lasts from the work that doesn't.
An instrument, not a metaphor.
Power residues on Z/NZ
Choose a modulus.Patterns are computed live.
Each cell shows aⁿ mod N. Brighter cells are fixed points — values where raising the base lands back on the base. The shaded columns mark attractor patterns — recurrences the integers fall into without being told to. This is a fragment of the structure my research program — Marithmetics — works from. Finite. Periodic. First-principles.
The work, in three directions.
Recent.
Foundations that hold.
An independent program in finite, periodic arithmetic. The thesis: the integers carry more native structure than mainstream mathematics treats them as carrying. The continuum is a derived object built over a finite substrate. Most barriers in modern math are artifacts of method — not properties of the underlying objects.
The program is called Marithmetics. It has its own canonical site at marithmetics.com, where every claim is paired with a deterministic demonstration, a published paper, and a public attack surface.
The work is conservative on purpose. Every claim has to compress to a finite, checkable object before it leaves the workshop. Every demo is reproducible. Every paper has a published method of falsification. Audit-grade, applied to mathematics instead of accounting.
Selected artifacts.
Step-Response Admissibility
A sharp characterization of when periodic-convolution smoothers preserve bounded ranges on Z/NZ, with constructive worst-case witnesses for the cases where common diagnostics give a wrong answer.
Fejer-Type Smoothing
A self-contained reference: explicit ℓ¹ and ℓ² norms for a Fejer-type kernel on Z/NZ, uniform bounds in N, and a smoothed discrepancy estimate for downstream quantitative work.
Marithmetics
The full canonical site — 28 deterministic demos, 16 papers, 3 published attack vectors, zero free parameters. Every prediction is a dimensionless ratio.
Finite Infinity
Twenty-three small books on Plato's missing substrate. The general-reader entry point — six or seven pages per book, fifteen minutes to read, the work of many years.
public-arch / Marithmetics
The companion repository. Computational demonstrations, derivation notebooks, every result hyperlinked to its source. The receipts.
Finite Infinity.
"What follows is a series of small books. Each one is short — six or seven pages — and each one does one thing. They are meant to be read in order, but they do not require it. You can begin anywhere."
Each book reads in fifteen minutes. The whole volume is the work of many years. The time difference is not an accident.
Table of contents.
Operator-grade ROI.
AI fails when it's applied as substitution. It compounds when it's applied as leverage on what humans are already doing well. My framework: find the friction, strip the noise, amplify the people. The returns follow.
AI to ROI: Your friction is your opportunity.
A long-form leadership briefing with Alex Jarett at the Technology Executives Club. A repeatable framework for moving from AI experimentation to defensible business value — built for the senior executives who are done with hype and ready to deploy.
Leveraging AI for Business Results
Featured speaker at the Chicago Technology Executives Club AI in the Enterprise Summit. A working framework for AI executives who actually have to deliver, not just announce.
Cincy AI Week — three sessions
Three sessions across three days at Union Hall during Cincinnati's inaugural AI Week. From "AI to ROI: Business First" to the operational realities of enterprise adoption.
AI accelerator portfolio launch
Once an organization deploys AI into their environment, we can guide them through the organizational change management needed to ensure a successful return on their investment. When organizations license AI tools for their entire workforce but users fail to fully leverage them, they miss out on the transformative potential AI can deliver. — Press release · April 2025
AI infrastructure: modern data management for insight-driven strategy.
A grounded look at what AI actually requires from data infrastructure — and where executives most often skip the steps that determine whether the investment compounds or stalls.
A servant operator.
I lead AI & Analytics for a large enterprise, run an independent research program, and wrote a book on what Plato called the missing substrate. The through-line is the same in every domain: strip the noise, build from the foundation, amplify the humans doing the work. The future belongs to those who build it.
The work looks scattered until you see the method. In the enterprise, that means leading transformation across nine functional domains — data engineering, applied AI, architecture, change management — with the discipline of an operator and the bearing of a servant leader. In research, it means treating mathematical objects as exact finite sets rather than statistical approximations, and pushing every claim to closure or rejection rather than to summary. In writing, it means showing rather than arguing — six or seven pages at a time, fifteen minutes per book, the work of many years.
I believe in signal as a strategic asset. In an era of noise, the operators who learn to extract it compound. The ones who can't, don't. AI is the single highest-leverage instrument for that extraction ever built — provided you use it on humans, not against them.
I live near Cincinnati. I read carefully. I think slowly on purpose.
— Credentials
- Harvard UniversityGraduate study
- University of CincinnatiStatistics & economics
- Senior Director · AI & AnalyticsEnterprise — current
- Independent researcherMarithmetics · MARI · DRPT
— Recent talks
- AI in the Enterprise SummitSchaumburg · Nov 2025
- Cincy AI Week — three sessionsCincinnati · Jun 2025
- Tech Talk · AI in RetailDec 2024 · with Wes Chaar
- Capacity/Lucy — KM & AIOct 2024 · with Scott Litman
— Profiles
- LinkedInProfessional
- GitHub · public-archRepositories
- arXivPreprints
- Marithmetics.comResearch program
— Contact
- hello@justingrieshop.comCollaboration · speaking · press
- research@justingrieshop.comAcademic correspondence
Currently building.
A short note, updated monthly, on what's in front of me.
— Updated · May 2026 —
Finite Infinity is being mailed to a short list of academics and writers ahead of public release. The next two papers in the DRPT sequence are being prepared for arXiv — the layered architecture established before the projection result lands.
At the enterprise, my team and I are scaling a Claude rollout from pilot into governed deployment. The framework I keep returning to in those rooms is the one I gave at the Technology Executives Club — AI ROI lives in the friction, not in the roadmap. The work that compounds is the work that amplifies the people who are already there.
Reading less than usual. Writing more. Trying to do the next thing well rather than the next ten things at once.