Functional Decoupling Framework for p-adic Hamiltonian Models of Granular Field Interactions

In the paper's words

The reconciliation of continuous temporal evolution with discrete physical granularity remains a central challenge in theoretical physics, requiring novel mathematical approaches to model localized action within unbroken fields. This study introduces a functional decoupling framework that divides the total Hamiltonian into localized workers, delocalized signals, and a mathematically rigorous interaction term. We employ p-adic heat equations and subhyperbolic dynamics to model continuous time over discrete space.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Synthesizing this discrete scattering theory with the dynamics of the system is a key challenge, one that requires an understanding of entropy and evolution in these exotic spaces (Hsia, Nie, & Wu, 2025).

   from 2.3 Discrete Wave

2. In standard Minkowski space, causality is strictly bound by the light cone metric $c^2 \Delta t^2 - \Delta x^2 \ge 0$, an Archimedean assumption that struggles to explain quantum entanglement (Peterson, 2025).

   from 6.3 Implications for

3. Our non-Archimedean approach, by explicitly isolating the worker and signal dynamics, provides a higher-fidelity model of fundamental interactions (Vladimirov & Volovich, 1989).

   from 6.6

How it is done

1. While standard models often rely on Archimedean approximations that break down at fundamental scales (Crespo & Pelayo, 2025), our approach integrates these disparate domains through a rigorous, evidence-based structure.

   from 1.1 Context and Motivation

2. This approach moves beyond models that conflate these roles (Antoniouk & Kochubei, 2025), allowing for a precise, balanced description of their interplay.

   from 1.4 The Functional Decoupling

3. The necessity of a non-Archimedean approach is well-established (Vladimirov & Volovich, 1989), yet a robust framework for applying it to coupled systems has been missing.

   from 1.5 Identified

4. Rather than claiming a definitive universal resolution, this paper will substantiate our thesis by first reviewing the foundational literature, then formally defining the theoretical framework and its components.

   from 1.7 Thesis Statement

What would falsify it

1. By acknowledging these limitations, we ensure the framework remains open to refinement and empirical falsification.

   from 6.5 Epistemic

Where the claim stops

1. While standard models often rely on Archimedean approximations that break down at fundamental scales (Crespo & Pelayo, 2025), our approach integrates these disparate domains through a rigorous, evidence-based structure.

   from 1.1 Context and Motivation

2. This paper argues that the common practice of smoothing over this granularity with Archimedean approximations, as noted by Peterson (2025), is a primary obstacle to a unified theory.

   from 1.2 The Core Tension:

3. It was only later that physicists recognized their potential for modeling the fractal nature of spacetime at the Planck scale, a concept that challenges the assumptions of smooth evolution (Hsia, Nie, & Wu, 2025).

   from 1.3 Historical

Where to read

1. Addressing211 words · 1 min
2. 1.0 Introduction861 words · 4 min
3. 2.0 Literature Review809 words · 4 min
4. 3.0 Theoretical Framework793 words · 3 min
5. 4.0 Methodology680 words · 3 min
6. 5.0 Results694 words · 3 min
7. 6.0 Discussion771 words · 3 min
8. 7.0 Conclusion530 words · 2 min
9. Appendices1,383 words · 6 min