Spectral Dynamics and Thermodynamic Stability in the Arithmetic Quantum Framework

In the paper's words

The scalability of fault-tolerant quantum computing is currently obstructed by a “Thermodynamic Wall,” where the entropy generated by active error correction (QEC) cycles scales exponentially with the number of logical qubits. This research addresses the crisis by proposing a transition from active, entropy-driven maintenance to passive, geometry-driven protection within the Arithmetic Quantum Framework. We establish a rigorous isomorphism between the p-adic ultrametric geometry of the Bruhat-Tits tree and the physical requirements for macroscopic information storage.

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

Numbers it reports

1. Langevin simulations confirm ultrametric trapping with a time-dependent slope reduction (0.59 $\to$ 0.30), proving asymptotic logarithmic “freezing.” We acknowledge a 10nm ultraviolet cutoff in physical strain engineering.

   from Abstract

2. While the 10nm lithographic cutoff limits the tree depth, the ballistic speedup and logarithmic stability remain robust.

   from 6.0 Conclusion: Toward Arithmetic Quantum Materials |

3. Our simulations grounded in these parameters demonstrate that for $10^5$ qubits, active QEC generates heat loads that exceed the 10-20 $\mu W$ cooling capacity of standard dilution refrigerators at 10mK (Quni-Gudzinas, 2025a).

   from 1.1 The

4. This confirms that the “Fractal Egg-Carton” potential (Quni-Gudzinas, 2025b) provides a stable substrate, provided the system is initialized below the 10mK phonon bottleneck.

   from 5.1 Passive

5. p-Adic statistical field theory (SFT) models exhibit $O(N)$ parameter scaling, a significant improvement over the $O(N^2)$ complexity of Euclidean networks (Zúñiga-Galindo et al., 2023).

   from 3.1 O(N) Parameter Efficiency

6. The mapping of the Activation Function to the Vladimirov Derivative Threshold is grounded in the operator’s ability to localize signals within specific p-adic balls, effectively acting as a multi-scale “gate” that prunes noise while preserving hierarchical features (Zúñiga-Galindo et al., 2023).

   from 5.2 The Holographic

How it is done

No section of this paper is shaped like a method, so no method sentence is quoted.

What would falsify it

The paper's text states no explicit falsification criterion; the limits below are what it says about where the claim stops.

Where the claim stops

1. Future work must extend these results to non-abelian sectors for universal logic.

   from 6.0 Conclusion: Toward Arithmetic Quantum Materials |

2. However, physical realization in strain-engineered materials faces a hard ultraviolet (UV) cutoff.

   from 1.2 Ultrametric

3. This approximation treats the walker’s movement along the radial coordinate while averaging lateral scattering, allowing for the simulation of ballistic scaling without the $O(p^D)$ memory wall.

   from 2.1 Bruhat-Tits Tree

Where to read

1. Reconciling22 words · 1 min
2. Abstract197 words · 1 min
3. 1.0 Introduction:264 words · 1 min
4. 2.0113 words · 1 min
5. 3.0 Results I:72 words · 1 min
6. 4.0 Results II:77 words · 1 min
7. 5.0 Discussion: Solenoidal140 words · 1 min
8. 6.0 Conclusion: Toward Arithmetic Quantum Materials |67 words · 1 min
9. Appendices400 words · 2 min