A Toroidal Geometric Rectifier: Empirical Disproof of Linear-Response in Plasma Confinement

Plain-language summary

This work shows, in a clean numerical experiment, that a particular toroidal geometry combined with two simple feedback mechanisms produces a structured energy state that does not respond linearly to input drive and does not undergo a phase transition. Push the system with 5% noise, push it with 80% noise — it sits in the same place. Across a 16× change in input, the output stays within 7% of itself.

Four additional stress tests subject the same mechanism to the kinds of imperfections a real instrument would impose: only a few sensors instead of perfect information, delayed control commands, a slow amplifier, magnetic-field irregularities. The structured state survives all of them. The mechanism is small, deterministic, and inspectable.

Scientific summary

A 3D toroidal numerical experiment (Tolkamak) demonstrates a drive-independent attractor produced by an engineered Reynolds-stress accumulator and phase-sensitive coherent reinjector, layered on a Hasegawa-Wakatani-style drift-wave substrate with bad-curvature drive and a parametric safety-factor profile. Across a 16× span of stochastic drive amplitude, every measured steady-state energy quantity in the active-mechanism arm is invariant to within 4–7% while the control arm scales by two decades.

A four-stage "Dirty Digital Twin" benchmark sequence further demonstrates that the attractor survives realistic sensor sparsity (down to 4 discrete probes), control-loop latency (smooth ~5%/step graceful degradation), actuator slew limits down to a hardware-relevant threshold, and a 40% q-profile ripple — both in the original perpendicular-dominant regime (10⁻⁶-level effect) and in a physically representative parallel-dominant regime with parallel-to-perpendicular coupling ratio ≈ 11 (0.24% effect, two orders of magnitude inside pre-registered pass thresholds).

The findings constitute the empirical disproof, in this geometry and under this mechanism, of two assumptions widely applied to driven dissipative systems on toroidal manifolds: linear response of steady-state to input drive, and discrete-state bifurcation as the mechanism of self-organization.

What's open, what's proprietary

The paper, figures, parameter regimes, experimental design, and aggregated results data are open and reproducible. The exact accumulator and reinjection kernel implementations are held proprietary pending IP review. Supplementary CSV files in this deposit contain the full aggregated experiment data with mechanism-revealing columns redacted; the redaction policy and the script that produced the cleaned files are included.

Companion to: TOU Engine — Toroidal Self-Organization in a 3D Wave Manifold (Zenodo, January 2026, DOI: 10.5281/zenodo.18450491).

Project Black Box LLC (CAGE Code 11FU4) · Source: https://github.com/projectblackboxllc