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PreprintCC BY 4.0Zenodo

The Frictionless Incompleteness Theorem: Meta-Mathematical Independence of Dynamic and Conformal Limits in First-Order Set Theory

  • August Tudor
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Abstract

We establish the Frictionless Incompleteness Theorem: any first-order axiomatic formal system (\mathbf{Sys}, including \mathsf{ZFC}) that models computation, dynamical systems, and field theory under the postulates of zero process cost (\underline{\operatorname{Cost}} \equiv 0), infinite phase-space information density (\rho_{\text{info}} \equiv \infty), and cost-free state transitions (\Delta Q_{\text{Landauer}} \equiv 0) is structurally incapable of deciding asymptotic stability, spectral localization, mass generation, or complexity class separation for open recursive processes.

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Cite

BibTeXRIS
BibTeX
@misc{tudor2026frictionless,
  title = {{The Frictionless Incompleteness Theorem: Meta-Mathematical Independence of Dynamic and Conformal Limits in First-Order Set Theory}},
  author = {August Tudor},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23547001},
  url = {https://zenodo.org/records/23547001},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Frictionless Incompleteness Theorem: Meta-Mathematical Independence of Dynamic and Conformal Limits in First-Order Set Theory
AU  - August Tudor
PY  - 2026
DA  - 2026/10/21
PB  - Zenodo
DO  - 10.5281/zenodo.23547001
UR  - https://zenodo.org/records/23547001
AB  - We establish the Frictionless Incompleteness Theorem: any first-order axiomatic formal system (\mathbf{Sys}, including \mathsf{ZFC}) that models computation, dynamical systems, and field theory under the postulates of zero process cost (\underline{\operatorname{Cost}} \equiv 0), infinite phase-space information density (\rho_{\text{info}} \equiv \infty), and cost-free state transitions (\Delta Q_{\text{Landauer}} \equiv 0) is structurally incapable of deciding asymptotic stability, spectral localization, mass generation, or complexity class separation for open recursive processes.
ER  -