Descend Field Theory — A Variational Law of Physical Stability (v3 Verification Suite & Boundary Clarification)

This manuscript presents the Descend Field Theory, a unified variational formulation for physical stability.The theory defines a field-level functional Φ combining entropy, flux–force power, and correlation terms, governed by dΦ/dt = −κ₁ (dS/dt) − κ₂ (J·X) − κ₃ (dI/dt) ≤ 0. This inequality expresses the monotonic descent of Φ, ensuring that any physical system evolves irreversibly toward a stable steady state (Φ̇ = 0).The framework reproduces the H-theorem, Onsager reciprocity, Noether symmetry-drift constraints, and RG-scale monotonicity within one compact law.Appendix A provides full derivations, mainstream physical limits, and a reproducibility protocol suitable for peer-review validation.No simulations or external data are included in this release.Scope: pure physics (thermodynamics + field theory only). – Peer-review ready; appendix contains mainstream derivations.– No numerical data or simulation files required.– Prepared in Nature Physics manuscript format. Title:Descend Field Theory — A Variational Law of Physical Stability (v2 Replication Kit Update) Description:Version 2 adds the full replication kit verifying the universal Φ̇ ≤ 0 stability law of Descend Field Theory.The included calibration dataset, audit scripts, and results files reproduce all figures and statistics from the paper.All tests confirm strict stability across pointwise and coarse-grain scales, demonstrating reproducibility of the variational stability principle.Licensed CC BY-NC 4.0 (public theory); private IP modules excluded under DFOS IP Shield v2. Note: The optional generator script mentioned in early documentation (`generate_phi_inputs_calibration.py`) is not included in this release. All essential files required to reproduce the Φ̇ ≤ 0 verification are present in v2. All numerical replication artifacts for the Φ̇ ≤ 0 stability law are publicly available in the Zenodo v2 Replication Kit (DOI 10.5281/zenodo.17379829.v2). Title:Descend Field Theory — A Variational Law of Physical Stability (v3 Verification Suite & Boundary Clarification) Description: This release provides the full Colab-ready verification suite for Descend Field Theory (DFT v3) — the third-stage replication and falsifiability confirmation of the variational stability law Φ̇ ≤ 0. It extends the earlier v2 Replication Kit by adding:• Five independent model verifications (Ising, gradient descent, diffusion, stochastic, and coarse-graining).• Boundary-violation demonstrations confirming Φ̇ > 0 only when assumptions are broken (e.g., dt > dx² / 2κ, η > 2/Lₘₐₓ).• A full README with the OU (KL) Numerical Clarification addendum documenting grid-truncation effects and their correction. The package includes the complete Python source, logs, plots, and documentation — reproducible in Google Colab without dependencies. License: CC BY-NC 4.0 (non-commercial research and education). Suggested citation:Norman S. (2025). Descend Field Theory — A Variational Law of Physical Stability (v3 Verification Suite & Boundary Clarification). Zenodo. DOI: [to be assigned].