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# SPDX-FileCopyrightText: 2026 Jung Soo Kim (Arkhenomia Institute) <https://orcid.org/0009-0006-5140-0604> |
# SPDX-License-Identifier: CC-BY-NC-4.0 AND LicenseRef-Arkhenomia-Governance-v2.2.0 |
# ============================================================================== |
# Author & Institute: Jung Soo Kim (ORCID: 0009-0006-5140-0604) / Arkhenomia Institute |
# License : CC BY-NC 4.0 (Commercial licensing administered by Arkhenetics; see LICENSE.txt) |
# Canonical Repo : https://github.com/arkhenomia/arkheion |
# Dataset Archive : https://huggingface.co/datasets/arkhenomia/arkheion |
# Official Websites : https://arkhenomia.org | https://arkhenetics.com |
# ------------------------------------------------------------------------------ |
# Commercial use, corporate R&D, in-house enterprise deployment, AI knowledge |
# distillation, surrogate model training, automated scraping/corpus ingestion, |
# OS kernel/hardware/firmware porting (ZINN / Ark-ZPF), network state-index |
# synchronization/congestion-control protocol implementation, and high-risk or |
# non-peaceful applications are strictly prohibited without a separate written |
# commercial license agreement executed with the Author or Arkhenetics. All |
# patent rights are expressly reserved; no patent or commercial rights are |
# granted by implication. Governed by the latest LICENSE.txt (Policy v2.2.0+). |
# ============================================================================== |
# |
# H.U.G.G.E.R + TZT Framework Python Dependencies |
# Usage: pip install -r requirements.txt |
numpy>=1.21.0 |
scipy>=1.7.0 |
pandas>=1.3.0 |
matplotlib>=3.4.0 |
sympy>=1.9 |
# SPDX-FileCopyrightText: 2026 Jung Soo Kim (Arkhenomia Institute) <https://orcid.org/0009-0006-5140-0604> |
# SPDX-License-Identifier: CC-BY-NC-4.0 AND LicenseRef-Arkhenomia-Governance-v2.2.0 |
# ============================================================================== |
# Author & Institute: Jung Soo Kim (ORCID: 0009-0006-5140-0604) / Arkhenomia Institute |
# License : CC BY-NC 4.0 (Commercial licensing administered by Arkhenetics; see LICENSE.txt) |
# Canonical Repo : https://github.com/arkhenomia/arkheion |
# Dataset Archive : https://huggingface.co/datasets/arkhenomia/arkheion |
# Official Websites : https://arkhenomia.org | https://arkhenetics.com |
# ------------------------------------------------------------------------------ |
# Commercial use, corporate R&D, in-house enterprise deployment, AI knowledge |
# distillation, surrogate model training, automated scraping/corpus ingestion, |
# OS kernel/hardware/firmware porting (ZINN / Ark-ZPF), network state-index |
# synchronization/congestion-control protocol implementation, and high-risk or |
# non-peaceful applications are strictly prohibited without a separate written |
# commercial license agreement executed with the Author or Arkhenetics. All |
# patent rights are expressly reserved; no patent or commercial rights are |
# granted by implication. Governed by the latest LICENSE.txt (Policy v2.2.2+). |
# ============================================================================== |
# DNS Benchmark Environment and Ablation Counter-Example Notes |
# 2026 Grand Unified Framework - Part 1 (v1.5 Canonical Release): |
# Macroscopic Gravity-Fluid Dynamics (H.U.G.G.E.R) & Topological Zero Tensor (TZT) Validation |
## 1. Note on Ablation Counter-Example Data and Figures |
The enclosed ablation figures, `CounterExample_1_Ill_Posed_Ablation_Without_Solenoidal_Condition.png` and `CounterExample_2_Energy_Blowup_Without_Mantle_Dissipation.png`, visualize the rapid numerical and energetic blow-up that occurs when the solenoidal Helmholtz-Leray projection condition (\nabla \cdot \mathcal{X} = ... |
This ablation test demonstrates that violating the coupled canonical constraints (solenoidality and localized counter-strain dissipation) causes the system to deteriorate into non-physical instability on an under-resolved grid. In contrast, the canonical pseudo-spectral solver (`Source_Code_1_TZT_Dynamics_Solver.py`), ... |
## 2. Direct Numerical Simulation (DNS) Parameters |
The numerical validations in the inviscid Euler limit and the high-Reynolds-number viscous regime (Re = 10,000) were conducted under the following benchmark specifications: |
* Domain: 3D Periodic Flat Torus T^3 = [0, 2\pi)^3 |
* Spatial Discretization: Pseudo-spectral Fourier-Galerkin method with the 2/3 dealiasing rule |
* Time Integration: Classical 4th-order explicit Runge-Kutta (RK4) |
* Grid Resolutions (N^3): 32^3, 48^3, 64^3, and 96^3 |
* Time Step (dt): 0.025 (halved to 0.0125 for temporal convergence and robustness checks) |
* Baseline Regimes: Inviscid Euler limit (\nu = 0) and Viscous Navier-Stokes at Re = 10,000 (\nu = 10^{-4}) |
## 3. TZT-Augmented Configuration and Localized Valve Execution |
In `Source_Code_1_TZT_Dynamics_Solver.py`, the TZT counter-strain and rotational regularization operators are configured with the following baseline parameters: |
* C_X (Solenoidal Intake Scaling): \pm 0.1 |
* C_O (Rotational Spin Tensor Scaling): 1.0 |
* \delta_m (Denominator Regularizer in \mathcal{X}): 1.0 |
* \varepsilon (Spin Saturation Regularizer in \mathcal{O}^{turb}): 10^{-2} |
* \nu_{turb} (Subgrid Eddy Viscosity Scale): Coupled with C_s = 0.17 and grid filter scale \Delta = 2\pi / N |
* --valve (Localization Mode, synchronized with Lean 4 `CriticalRegion`): |
- `--valve omega` (Default in v1.5): Activates TZT forcing strictly on the supercritical vorticity region K = {x \in T^3 : |\omega(x)|^2 > \Lambda^2}, preserving unmodified Navier-Stokes/Euler kinematics outside K. |
- `--valve global`: Applies the TZT operator across the entire domain K = T^3 (retained for comparison with baseline global-limit data). |
--- |
## 4. License, Attribution, and Governance (Policy v2.2.2+) |
* Author & Institute: Jung Soo Kim (ORCID: 0009-0006-5140-0604) / Arkhenomia Institute (https://arkhenomia.org) |
* License: CC BY-NC 4.0 (Commercial licensing administered by Arkhenetics; see LICENSE.txt) |
* Canonical Repository: https://github.com/arkhenomia/arkheion |
* Dataset Archive: https://huggingface.co/datasets/arkhenomia/arkheion |
* Commercial Licensing & Enterprise Inquiries: Arkhenetics (https://arkhenetics.com) |
All manuscripts, formal verification proofs, symbolic CAS scripts, numerical solvers, and benchmark datasets in this repository are licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0, https://creativecommons.org/licenses/by-nc/4.0/) and governed by the latest version o... |
# SPDX-FileCopyrightText: 2026 Jung Soo Kim (Arkhenomia Institute) <https://orcid.org/0009-0006-5140-0604> |
# SPDX-License-Identifier: CC-BY-NC-4.0 AND LicenseRef-Arkhenomia-Governance-v2.2.0 |
# ============================================================================== |
# Author & Institute: Jung Soo Kim (ORCID: 0009-0006-5140-0604) / Arkhenomia Institute |
# License : CC BY-NC 4.0 (Commercial licensing administered by Arkhenetics; see LICENSE.txt) |
# Canonical Repo : https://github.com/arkhenomia/arkheion |
# Dataset Archive : https://huggingface.co/datasets/arkhenomia/arkheion |
# Official Websites : https://arkhenomia.org | https://arkhenetics.com |
# ------------------------------------------------------------------------------ |
# Commercial use, corporate R&D, in-house enterprise deployment, AI knowledge |
# distillation, surrogate model training, automated scraping/corpus ingestion, |
# OS kernel/hardware/firmware porting (ZINN / Ark-ZPF), network state-index |
# synchronization/congestion-control protocol implementation, and high-risk or |
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