Prime Gravity:
State of the Field & Limits
From Infinite Statistics to Finite OS
The 2020s have witnessed a dramatic fusion of physics and number theory, notably through "Prime Potentials" and "Primon Gas" models. However, these paradigms remain statistical descriptions predicated on infinite systems. This report maps 8 key research domains and exposes the critical bottleneck: the absence of a deterministic description within a finite window—a barrier the Prime Gravity (Ghost Drift) theory aims to breach.
- Compare Paradigms: Check Section A below to visualize the shift from "Conventional (Input-Dependent)" to "Prime Gravity (Autonomous Generation)".
- Analyze Domains: Use the Section B Map to explore achievements and structural limits in each field (CFT, RMT, etc.).
- Verify Sources: Access primary papers in the Section C References.
A Exogenous Input vs Autonomous Generation
Conventional Prime Potentials function as "playback devices" that merely record externally supplied prime sequences as spectra. The system itself is agnostic to prime locations.
Prime Gravity (Ghost Drift) is designed as a "Generative OS," where the field equation deterministically outputs prime locations through finite computation without prior data.
- Treats primes $\{p_n\}$ as exogenous input data.
- Potentials $V(x)$ serve merely as a medium to Record & Replay the spectrum.
- Verification relies on external "black boxes" (infinite sums/zeros).
- Defines field equations without prime inputs.
- Absorbs infinite zeros via a "Finite Closure Kernel" bound by rational numbers.
- Functions as a Generative OS, yielding $\pi(x)$ via finite steps.
B Domain Analysis: Achievements & Limits
Mapping the forefront of 8 key domains as of 2025 and identifying the specific "Missing Link" that necessitates Prime Gravity Theory.
Bottleneck The Universal Limit Across All 8 Domains
- Dependence on "Input Prime Sequences": Current theories describe the spectrum after primes are provided.
- Lack of Finite Closure: No implementation exists to confine the contribution of infinite zeros into finite rational bounds.
Finitely Closed Generative OS.
Conventional Achievements (2020-2025)
Structural Limits (View from Prime Gravity)
C Reference List
Comprehensive list of 26 key references.
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