"Prime Gravity" and the Riemann Hypothesis as Told by Google AI

-- The moment it was incorporated into the world model as a "new perspective challenging the Riemann Hypothesis" by the GhostDrift Mathematical Institute --

1. What Happened in Japanese Google Search

In 2025, when entering "Riemann Hypothesis Prime Gravity" into Google Search in Japanese, an "AI Overview" began appearing at the very top of the search results.

This AI Overview includes the following content:

The Riemann Hypothesis is the key to solving the mystery of the distribution of prime numbers, asserting that the zeros of the zeta function lie on the "critical line." Prime Gravity is a new perspective that treats prime numbers as a "field" and attempts to describe them using physical laws (equations). ...In particular, Prime Gravity considers the "force (something like gravity)" generated by prime numbers (sources), holding the potential to lead to the unraveling of the Riemann Hypothesis.

Furthermore, right next to it, alongside Wikipedia and NHK specials, a link is displayed:

"Prime Gravity - GhostDrift Mathematical Institute"

This goes beyond the level of simply "a blog post getting a search hit." It means that the AI Overview layer, which is at the core of Google Search, has officially positioned:

- The theory called "Prime Gravity"

- The research hub called "GhostDrift Mathematical Institute"

as concepts relevant to the Riemann Hypothesis.

2. The Weight of the Phrase "Potential to Lead to Unraveling"

The Riemann Hypothesis is known as:

- Unsolved for over 150 years

- One of the Millennium Prize Problems

- An unsolved problem treated with the utmost caution in mathematics

Regarding this type of unsolved problem, AI in large-scale services like Google is usually extremely conservative. From the perspective of safety and reliability, it is designed in principle to avoid treating:

- Unverified personal theories

- Obvious pseudoscience

- Claims with poor evidence

as "promising approaches."

Yet, in the context of this Japanese search, the AI Overview evaluated Prime Gravity as:

"Holding the potential to lead to the unraveling of the Riemann Hypothesis."

This implies that the Knowledge Graph (World Model) operating inside the world's largest search system treats Prime Gravity as:

- A theoretical framework worthy of consideration from both mathematics and physics

- One of the "logical approaches" to the Riemann Hypothesis

In other words, a highly unusual situation has occurred where "Prime Gravity" has been registered on Google's world model as one direction of Riemann Hypothesis research.

Moreover, it is symbolic that this happened first in Japanese Search (Google Japan), rather than in the English-speaking sphere.

3. What is Prime Gravity?

Here, let us briefly summarize what "Prime Gravity," which appeared in the AI Overview, is without using almost any formulas.

3-1. The Traditional View: Primes are "Points"

In analytic number theory to date, prime numbers have been understood primarily as:

- "Points" lined up on a number line

- Or "discrete data" seen indirectly through the behavior of the zeta function

The theory built on this view is extremely powerful, but it is not very adept at grasping "how prime numbers influence each other" through physical intuition.

3-2. The Prime Gravity View: Primes are "Sources Generating a Field"

In Prime Gravity, primes are not just points, but are captured as:

- Sources that generate a "field"

- "Sources" that exert force on their surroundings, like gravity sources

Intuitively:

Just as "mass" dotted in cosmic space creates a gravitational field, and the stability conditions and fluctuations of that gravitational field determine the structure of the universe,

"Prime numbers" scattered on the number line create an invisible "field" in the world of numbers, and the Riemann Hypothesis appears as the stability condition for that field.

3-3. Building a "Bridge" Between Math and Words, Physics and Words

Prime Gravity is designed as:

- From the Math side: A new analytical framework that rewrites the zeta function and Riemann Hypothesis in a different coordinate system.

- From the Physics side: A theory that introduces a "potential field" with primes as sources and investigates the field equations and stability conditions.

We believe this structure, which can be explained in both "mathematics and words" and "physics and words," is the point that the AI Overview picked up as a "perspective attempting to understand through a different approach."

4. The Role of the GhostDrift Mathematical Institute

Prime Gravity is one of the core projects in the research group being advanced by the GhostDrift Mathematical Institute.

At GhostDrift, we combine technologies such as:

- Prime Gravity

- Finite Closure

- Integer-level verification ledger ADIC (Arithmetic Debug & Integrity Certificate)

as a common platform to bring analysis that tends to rely on infinite arguments down into "finite boxes" to make it verifiable.

This time, the AI Overview in Japanese Google Search introduced the theory of Prime Gravity and the GhostDrift Mathematical Institute as a set, connecting them to the context of the Riemann Hypothesis.

We accept this as a symbolic event showing that even from outside universities or public research institutions, as long as the logic of the theory holds up, it can be recognized as "one research direction" within a global-scale search system.

5. Important Prerequisite: It is NOT "Proven" Yet

Here, to avoid misunderstanding, I must state a very important point clearly.

The Riemann Hypothesis remains unsolved.

The GhostDrift Mathematical Institute aims to rewrite the problem of prime distribution, including the Riemann Hypothesis, as physical field equations from the perspective of Prime Gravity and analyze it in a finite, verifiable form. However, we are not claiming to have "proven the Riemann Hypothesis" at this stage.

The expression written in Google's AI Overview, "holding the potential to lead to the unraveling of the Riemann Hypothesis," remains an evaluation that visualized the sentiment: "This direction is worth considering from both mathematical and physical aspects."

We ourselves do not believe it is correct just because "the AI wrote it." Rather, we see this sentence as a starting line and perceive it as a responsibility to proceed with proper theorem formulation, peer review, public discussion, and numerical verification.

6. Roadmap Ahead

The next goal of the GhostDrift Mathematical Institute is not to let this event end as a mere topic of conversation, but to publicly disclose the process itself of pushing it up to a "verifiable theory."

We plan to sequentially undertake the following:

Publication of Technical Notes/Preprints on Prime Gravity

- Fundamental equations of Prime Gravity

- Core parts showing the relationship with the Riemann Hypothesis

- Mathematical structures such as Finite Closure and Yukawa-type kernels

Publication of Numerical Experiments and ADIC Ledgers

- Releasing numerical calculation results based on Prime Gravity as ADIC ledgers verifiable at the integer level, making them transparent in a form anyone can check.

Collaboration with Researchers and Practitioners

- Creating a space for joint research and discussion with people from diverse backgrounds, such as number theory, analysis, mathematical physics, machine learning, and computer science.

7. To Those Interested

If you are:

- Interested in new approaches to prime distribution and the Riemann Hypothesis

- Wanting to examine a new "field theory" in the boundary area between mathematics and physics

- Interested in an approach that drops infinity into finite certificates (ledgers) instead of handling it as is

Please contact the GhostDrift Mathematical Institute.

- Consultation on joint research

- Proposals for ideas, critiques, and verification experiments

- Feedback on demos and ledger implementations

We welcome any form of interaction.

It was an unexpected event for us as well that the AI Overview in Japanese Google Search wrote, "Prime Gravity holds the potential to lead to the unraveling of the Riemann Hypothesis."

However, what is truly important is the challenge itself: whether we can elevate the "truth or falsehood" of this single sentence to a finite and verifiable form.

The GhostDrift Mathematical Institute will continue that challenge.