systemictau 4.6.0

Systemic Tau, gate RECD, and optional nested ordinal excess³ (via nested-recd)

Systemic Tau & Discrete Extramental Clock (RECD)

systemictau implements the Systemic Tau paradigm and the Discrete Extramental Clock (RECD) for ordinal multivariate time-series analysis (early-warning, regime reorganization, multi-scale structure).

Current library version: 4.6.0

Installation

pip install systemictau
# Level-3 nested ordinal RECD / continuous excess³:
pip install "systemictau[nested]"   # pulls nested-recd>=0.2

From source:

git clone https://github.com/johelpadilla/systemictau
cd systemictau
pip install -e ".[nested,dev]"

Two RECD notions (do not confuse)

Name	API	What it is
Gate RECD	compute_recd_increments, accumulate_time	Clock from τ_s + Feigenbaum gate
Nested ordinal RECD / excess³	compute_nested_recd → nested-recd	Φ₁–Φ₃ on Bandt–Pompe; excess³ = 0.6·Syn + 0.4·Surp primary Level-3

Canonical Level-3 methods: DOI 10.5281/zenodo.21385937 · github.com/johelpadilla/excess3

Quick start

import numpy as np
import systemictau as st

np.random.seed(42)
X = np.random.randn(500, 4)

# Systemic Tau
taus_global, taus_per_module = st.compute_taus(X, window_size=13)

# Gate RECD
T_series, dtk_series, gate_series, depths = st.accumulate_time(taus_global)

# Nested ordinal RECD / continuous excess³ (requires nested-recd)
if st.has_nested_recd():
    nested = st.compute_nested_recd(X, tau_s=taus_global, m=3, theta3=0.10)
    print("mean excess³:", float(np.nanmean(nested["excess3"])))

# Full pipeline with optional Level-3
res = st.run_full_analysis(X, window_size=13, compute_nested_recd=True)
print("t* =", res.t_star)
if res.nested_recd_results:
    print("mean excess³:", res.nested_recd_results["mean_excess3"])

Studio (optional)

pip install "systemictau[studio]"
systemictau-studio
# or: PYTHONPATH=src streamlit run src/systemictau/studio/app.py

Related packages

Project	Role
nested-recd	Canonical Φ₁–Φ₃ + excess³ core
excess3	Methods + intro ES + primer
systemictau-web	Streamlit analytical app

Citation

Padilla-Villanueva, Johel. (2026). Síntesis Magna del Tau Sistémico. Zenodo. DOI: 10.5281/zenodo.20576241

For excess³ / Level-3 claims, also cite:

Padilla-Villanueva, J. (2026). excess³ methods. DOI: 10.5281/zenodo.21385937

License

MIT © Johel Padilla-Villanueva
ORCID: 0000-0002-5797-6931