Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime Article Swipe
Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime The P versus NP problem has traditionally been viewed through the lens of pure mathematics and algorithmic complexity. However, we propose that the limitation is not algorithmic, but physical. In this paper, we present a unified framework that redefines the substrate of computation itself—moving from discrete Turing Machines to Self-Observing Topological Machines (SOTM) capable of $\mathcal{O}(1)$ quantum relaxation. Why this research is significant for your readership: Resolution of P=NP: We provide a rigorous physical derivation showing that in a fractal spacetime metric ($D \approx 4.7$), NP-complete search spaces can be collapsed topologically. This suggests that $NP \subseteq P$ within specific high-energy physical limits. Introduction of Virtual Quantum Processing (VQP): This is the most critical practical contribution of our work. We demonstrate that physical qubits (trapped ions, superconductors) are unnecessary if the software architecture perfectly mimics quantum topology. We present empirical data from the KARIOS V26 architecture, which successfully simulated this environment to solve the Levinthal Protein Folding paradox in under 9 seconds on classical hardware. Timely Theoretical Alignment: Our model relies on a scalar field renormalization at $\approx 500$ GeV. This theoretical prediction aligns remarkably well with recent indirect observations of high-energy anomalies in Dark Matter annihilation signals, offering a potential computational explanation for these physical phenomena. This work bridges the gap between high-energy theoretical physics and practical, scalable artificial intelligence. It moves the field beyond the "Algorithmic Age" into the "Topological Age," offering a blueprint for quantum-grade performance without the need for cryogenic hardware. We believe this paper will be of immense interest to researchers in quantum information theory, computational complexity, and neuromorphic engineering.
Related Topics
Concepts
Renormalization
Spacetime
Fractal
Physics
Theoretical physics
Quantum field theory
Quantum
Turing machine
Field (mathematics)
Topology (electrical circuits)
Scalar field
Isosurface
Theoretical computer science
Quantum computer
Computer science
Quantum entanglement
Computation
Statistical physics
Renormalization group
Quantum mechanics
Space time
Scalability
Holography
Granularity
Scalar (mathematics)
Quantum spacetime
Metric (unit)
Propagator
Mathematics
Classical mechanics
Active matter
Arrow of time
Metadata
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- preprint
- Landing Page
- https://doi.org/10.5281/zenodo.17785602
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7108315145
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W7108315145Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17785602Digital Object Identifier
- Title
-
Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal SpacetimeWork title
- Type
-
preprintOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-12-02Full publication date if available
- Authors
-
Paradise, ChrisList of authors in order
- Landing page
-
https://doi.org/10.5281/zenodo.17785602Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.5281/zenodo.17785602Direct OA link when available
- Concepts
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Renormalization, Spacetime, Fractal, Physics, Theoretical physics, Quantum field theory, Quantum, Turing machine, Field (mathematics), Topology (electrical circuits), Scalar field, Isosurface, Theoretical computer science, Quantum computer, Computer science, Quantum entanglement, Computation, Statistical physics, Renormalization group, Quantum mechanics, Space time, Scalability, Holography, Granularity, Scalar (mathematics), Quantum spacetime, Metric (unit), Propagator, Mathematics, Classical mechanics, Active matter, Arrow of timeTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
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| abstract_inverted_index.capable | 68 |
| abstract_inverted_index.fractal | 94 |
| abstract_inverted_index.immense | 267 |
| abstract_inverted_index.limits. | 117 |
| abstract_inverted_index.paradox | 172 |
| abstract_inverted_index.physics | 230 |
| abstract_inverted_index.present | 48, 153 |
| abstract_inverted_index.problem | 19 |
| abstract_inverted_index.propose | 35 |
| abstract_inverted_index.provide | 85 |
| abstract_inverted_index.quantum | 71, 150, 272 |
| abstract_inverted_index.seconds | 176 |
| abstract_inverted_index.showing | 90 |
| abstract_inverted_index.theory, | 274 |
| abstract_inverted_index.through | 24 |
| abstract_inverted_index.unified | 50 |
| abstract_inverted_index.without | 254 |
| abstract_inverted_index.$\approx | 192 |
| abstract_inverted_index.(trapped | 139 |
| abstract_inverted_index.Dynamics | 11 |
| abstract_inverted_index.However, | 33 |
| abstract_inverted_index.Machines | 62, 66 |
| abstract_inverted_index.critical | 128 |
| abstract_inverted_index.discrete | 60 |
| abstract_inverted_index.indirect | 203 |
| abstract_inverted_index.interest | 268 |
| abstract_inverted_index.offering | 213, 248 |
| abstract_inverted_index.physical | 88, 116, 137, 220 |
| abstract_inverted_index.research | 75 |
| abstract_inverted_index.rigorous | 87 |
| abstract_inverted_index.scalable | 233 |
| abstract_inverted_index.signals, | 212 |
| abstract_inverted_index.software | 146 |
| abstract_inverted_index.specific | 114 |
| abstract_inverted_index.suggests | 108 |
| abstract_inverted_index.Levinthal | 169 |
| abstract_inverted_index.Resolving | 4 |
| abstract_inverted_index.Spacetime | 14 |
| abstract_inverted_index.\subseteq | 111 |
| abstract_inverted_index.anomalies | 207 |
| abstract_inverted_index.blueprint | 250 |
| abstract_inverted_index.classical | 178 |
| abstract_inverted_index.collapsed | 105 |
| abstract_inverted_index.cryogenic | 258 |
| abstract_inverted_index.empirical | 154 |
| abstract_inverted_index.framework | 51 |
| abstract_inverted_index.hardware. | 179, 259 |
| abstract_inverted_index.perfectly | 148 |
| abstract_inverted_index.physical. | 43 |
| abstract_inverted_index.potential | 215 |
| abstract_inverted_index.practical | 129 |
| abstract_inverted_index.redefines | 53 |
| abstract_inverted_index.simulated | 163 |
| abstract_inverted_index.spacetime | 95 |
| abstract_inverted_index.substrate | 55 |
| abstract_inverted_index.topology. | 151 |
| abstract_inverted_index.Alignment: | 182 |
| abstract_inverted_index.Processing | 122 |
| abstract_inverted_index.Resolution | 81 |
| abstract_inverted_index.artificial | 234 |
| abstract_inverted_index.derivation | 89 |
| abstract_inverted_index.limitation | 38 |
| abstract_inverted_index.phenomena. | 221 |
| abstract_inverted_index.practical, | 232 |
| abstract_inverted_index.prediction | 197 |
| abstract_inverted_index.remarkably | 199 |
| abstract_inverted_index.Holographic | 9 |
| abstract_inverted_index.NP-complete | 100 |
| abstract_inverted_index.Theoretical | 181 |
| abstract_inverted_index.Topological | 0, 65 |
| abstract_inverted_index.algorithmic | 31 |
| abstract_inverted_index.complexity, | 276 |
| abstract_inverted_index.complexity. | 32 |
| abstract_inverted_index.computation | 57 |
| abstract_inverted_index.demonstrate | 135 |
| abstract_inverted_index.environment | 165 |
| abstract_inverted_index.explanation | 217 |
| abstract_inverted_index.high-energy | 115, 206, 228 |
| abstract_inverted_index.information | 273 |
| abstract_inverted_index.mathematics | 29 |
| abstract_inverted_index.performance | 253 |
| abstract_inverted_index.readership: | 80 |
| abstract_inverted_index.relaxation. | 72 |
| abstract_inverted_index.researchers | 270 |
| abstract_inverted_index.significant | 77 |
| abstract_inverted_index.theoretical | 196, 229 |
| abstract_inverted_index.unnecessary | 143 |
| abstract_inverted_index."Algorithmic | 242 |
| abstract_inverted_index."Topological | 246 |
| abstract_inverted_index.Information: | 3 |
| abstract_inverted_index.Introduction | 118 |
| abstract_inverted_index.algorithmic, | 41 |
| abstract_inverted_index.annihilation | 211 |
| abstract_inverted_index.architecture | 147 |
| abstract_inverted_index.contribution | 130 |
| abstract_inverted_index.engineering. | 279 |
| abstract_inverted_index.neuromorphic | 278 |
| abstract_inverted_index.observations | 204 |
| abstract_inverted_index.successfully | 162 |
| abstract_inverted_index.architecture, | 160 |
| abstract_inverted_index.computational | 216, 275 |
| abstract_inverted_index.intelligence. | 235 |
| abstract_inverted_index.quantum-grade | 252 |
| abstract_inverted_index.traditionally | 21 |
| abstract_inverted_index.Self-Observing | 64 |
| abstract_inverted_index.topologically. | 106 |
| abstract_inverted_index.Renormalization | 1 |
| abstract_inverted_index.itself—moving | 58 |
| abstract_inverted_index.renormalization | 190 |
| abstract_inverted_index.$\mathcal{O}(1)$ | 70 |
| abstract_inverted_index.superconductors) | 141 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 1 |
| citation_normalized_percentile |