Reference implementation of the TRIXEL calibrator system (SD, VD, VS) — minimum for maximum. TRIXEL Framework https://doi.org/10.5281/zenodo.20721811
T = (V, D, S) — a mathematical framework describing any system through three dimensions:
V (Existence) — what the system is
D (Dynamics) — how it changes
S (Structure) — the scale or form in which it exists
From these, three calibrators measure their mutual relationships.
What this is TRIXEL is an independent research project by Milan Takáč (Košice, Slovakia), developed collaboratively with AI assistance. The framework is not affiliated with any academic institution.
Latest preprint (v3.0): https://doi.org/10.5281/zenodo.20721811
Previous version (v1.0): https://doi.org/10.5281/zenodo.20610880
Installation bash pip install numpy scipy
Quick start python
import numpy as np from calibrators import compute_all, dominant_calibrator, check_algebraic_identity
S = np.linspace(0, 10, 500) V = np.exp(-0.5 * ((S-5)/1.5)**2) D = -np.gradient(V, S)
c = compute_all(V, D, S) print(f"VS range: {c['VS'].min():.4f} to {c['VS'].max():.4f}")
err, holds = check_algebraic_identity(V, D, S) print(f"Identity VD/VS = SD holds: {holds} (error: {err:.2e})")
dom = dominant_calibrator(c['SD'], c['n']) Example notebook: examples/basic_usage.ipynb
| Calibrator | Formula | Meaning |
|---|---|---|
| SD | |dD/dS| | How fast dynamics change with structure |
| VS | 1/|dV/dS| | Sensitivity of existence to structural change |
| VD | SD/n | Bridge between dynamics and existence |
Exact identity: VD / VS = SD
Dominance map In (log SD, log n) space, one calibrator always dominates:
VS dominant — existence highly sensitive to structure
SD dominant — dynamics change rapidly with structure
VD dominant — intermediate regime
Verified at 99.99% accuracy on a 600×600 grid.
Verified results Algebraic identity VD/VS = SD — exact
Dominance partition theorem — 99.99% accuracy
VS early warning — Burgers turbulence (90/90 runs, FP=0%, FN=0%)
Cross-domain validation — Lotka–Volterra ecology
Real tokamak data — VS identifies stable plasma phases in GOLEM (5 shots, metadata + raw oscilloscope data).
Not yet verified VS as disruption precursor on real tokamak data
VS early warning in 2D Navier–Stokes
VS on EEG seizure data
Rogowski coil calibration for GOLEM
Physical interpretation VS = 1/|dV/dS| drops when the system’s existence becomes rapidly sensitive to structural changes. This happens before global energy or amplitude changes become visible.
The mapping (choice of V, D, S) must be physically motivated.
How to apply TRIXEL Choose S (time, wavenumber, radius, position…)
Choose V(S) (energy spectrum, current, population…)
Choose D(S) (dE/dt, dI/dt, dN/dt…)
Run compute_all(V, D, S) and examine VS
Repository structure Kód trixel/ ├── calibrators.py ├── README.md ├── requirements.txt ├── tests/ │ └── test_identity.py └── examples/ └── basic_usage.ipynb Citation bibtex @misc{takac2026trixel, author = {Takáč, Milan}, title = {TRIXEL 3.0 — Scale-Adaptive Metric Framework}, year = {2026}, doi = {10.5281/zenodo.20721811}, url = {https://doi.org/10.5281/zenodo.20721811} } License MIT License.
Contact Milan Takáč, Košice, Slovakia https://doi.org/10.5281/zenodo.20721811