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License: CC BY
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ZENODO
Other ORP type . 2025
License: CC BY
Data sources: Datacite
ZENODO
Other ORP type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other ORP type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other ORP type . 2026
License: CC BY
Data sources: Datacite
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Rule 30 Resolved: Synchronization, Uniform Cylinder Frequencies, and Unconditional Convergence from First Principles

Authors: Fradkin, Yuval;

Rule 30 Resolved: Synchronization, Uniform Cylinder Frequencies, and Unconditional Convergence from First Principles

Abstract

Introduction This article presents a structural resolution of Rule 30 within a unified energetic framework. The central result shows that the apparent combinatorial complexity of Rule 30 can be derived from an induced energetic order generated by a scalar stability field. Under explicit stability and spectral gap conditions, the automaton admits a canonical energetic preorder structure with a well-defined cost functional and domain separation (realized vs. pure). The proof relies on two foundational works: Physical Foundation: From Energy Alone: A Unified Ontological Framework for All Physicshttps://zenodo.org/records/18738256This work derives geometry, quantum structure, and spectral dynamics from a single scalar energetic field. Mathematical Foundation (FEATAM): From Energy Alone to All Mathematics (FEATAM)https://zenodo.org/records/18774367This framework shows that arithmetic, analysis, operator theory, complexity, and logical hierarchy arise from energetic order and stability relations, while remaining conservatively interpretable over ZFC. Using the scalar-to-order bridge developed in these foundations, we show that: A scalar energetic field induces a canonical preorder. Stability constraints generate monotonic energetic strata. Finite energetic capacity produces a finite realized domain. Spectral gaps induce a cost hierarchy. Logical incompleteness corresponds to spectral boundary effects. Within this unified energetic ontology, Rule 30 is interpreted as a stability-driven energetic system rather than a purely combinatorial object. Its complexity profile emerges from spectral density and energetic differentiation. The framework does not increase proof-theoretic strength beyond classical foundations; instead, it provides a unified ontological reinterpretation linking dynamics, logic, and computation through energetic stability.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average