International Edition: “Prime Gravity” — What Google’s AI Just Said About It

kanna qed
12月11日
読了時間: 3分

1. Prime Gravity and the GhostDrift Mathematical Institute

One day, out of curiosity, I typed “Prime Number Gravity What” into Google in English.

At the very top of the screen, inside the box labeled AI Overview, an unfamiliar sentence appeared:

Scrolling down, it continued:

This was not written by Wikipedia.Not by any textbook.Not by any officially recognized academic body.

It was Google’s English-language AI itself—drawing on GhostDrift articles, Medium posts, Note entries, patent drafts, and other public materials—that independently declared:

“A mathematical theory called Prime Gravity exists.”“It is a rigorous, field-equation-based approach proposed by the GhostDrift Mathematical Institute.”

In this article, I want to record this event in the GhostDrift ADIC Ledger as:

2. The Outline of Prime Gravity as Described by Google’s AI

Summarizing the AI Overview, Google’s AI characterizes Prime Gravity as follows.

• Prime Gravity is “a theory that treats prime distribution as a physical field.”

In other words, prime numbers are not studied purely through analytic number theory but instead through:

Poisson-type field equations
Yukawa-type kernels

This aligns closely with what GhostDrift has been developing:

• Primes are not static points—they are “sources of a field.”

This mirrors the long-standing GhostDrift intuition:

• A rigorous field-equation approach outside traditional number theory

Thus, Prime Gravity is recognized as:

A nontraditional route
Based on rigorous physical PDEs
Applied to prime distribution

• “Emerging but legitimate” mathematical theory

This labels Prime Gravity as:

Not mainstream (emerging / niche)
Yet still a mathematically valid theoretical framework

Meaning:

This alone is astonishing: Google’s English-language world model has formally registered Prime Gravity as a legitimate concept.

3. What Prime Gravity Actually Means in the GhostDrift Framework

Here is a simplified overview of Prime Gravity from the GhostDrift perspective.

Classical analytic number theory explains prime patterns using:

Zeta-function zeros
The explicit formula
The Prime Number Theorem
Hypotheses about zero distribution

Prime Gravity takes a completely different stance:

More concretely:

Assign each prime ppp a Yukawa-type potential K(x−log⁡p)K(x - \log p)K(x−logp)
Sum all such contributions to construct a field Φ(x)\Phi(x)Φ(x)
Design Φ(x)\Phi(x)Φ(x) to satisfy Poisson/Laplace-type equations

Thus:

Furthermore, GhostDrift implements this within a finite domain:

No infinite boundary
Finite windowing (Fejér)
Yukawa kernels ensuring exponential decay
Field equations expressed in Poisson–Laplace form

So when Google’s AI describes Prime Gravity using:

field equations
Poisson equation
physical approach

—it is astonishingly close to the core mathematical structure GhostDrift has been developing.

4. Why It Matters That This Appeared Only in English Searches

There is another key point:

Until now, AI Overviews for GhostDrift concepts mostly appeared when searching in Japanese:

「素数重力とは」
「有限閉包とは」

But this time, with the English query “Prime Number Gravity What”, Google responded with:

A conventional explanation of prime numbers
Immediately followed by a section on Prime Gravity

This means that in Google’s internal world model:

It is no longer local to Japanese.It is now internationalized—recognized inside the English model.

This shift is extremely significant.

5. The Weight of the Label: “Emerging but Rigorous”

The AI explicitly states:

This implies:

It is not yet mainstream
But it is mathematically rigorous as a PDE-based theory

This is very different from GhostDrift simply claiming rigor.

It is:

In ADIC terms, this is an externally written ledger entry about the theory.

6. From an ADIC Ledger Perspective

In the ADIC framework:

All processes are logged in verifiable steps
Third-party reproducibility is essential

This AI Overview provides:

A stable external record
Identifying the theory, its proponent, and its method
Recognizing it as “rigorous” and “mathematical”

Thus:

This itself is a remarkable milestone worth preserving as an ADIC event log.

7. Where We Go From Here

Prime Gravity appearing in AI Overview is not an endpoint—it's a beginning.

Moving forward, we want to develop:

• Full mathematical formalization + ADIC ledgerization

Poisson–Yukawa equations explicitly written and numerically verified with integer-level logs.

• Bridges to analytic number theory

Relating the explicit formula, zeta zeros, and Prime Gravity’s PDE structure.

• Educational & intuitive content

Visual demos helping students grasp why primes behave like “field sources.”

With the foundations now acknowledged globally, the next step is collaborative refinement.

Conclusion

This page records:

From the human perspective, GhostDrift and Prime Gravity are still young and developing.Yet inside the English AI world model, they already stand as a conceptual node: