systemictau 2.0.0

Systemic Tau and Discrete Extramental Clock (RECD) implementation

Systemic Tau & Discrete Extramental Clock (RECD)

systemictau is a Python package implementing the mathematical and ontological framework of the Systemic Tau paradigm and the Discrete Extramental Clock (RECD), developed by Dr. Johel Padilla-Villanueva.

This package offers a novel, non-reductive approach for time series analysis in complex systems, shifting from classical variance-based early-warning signals to purely ordinal observables. It proves that time is not a homogeneous container (Chronos) but an emergent, generated metric dependent on the system's own structural reorganization (Kairos).

Core Concepts

The package operationalizes the three-layer ontological framework detailed in the Magna Synthesis:

1. Capa 1 (Local Intensification): Measures local persistence through hyper-persistence of ordinal states and structural trapping (RQA).
2. Capa 2 (Relational Coherence): Identifies Joint Episodes (relational kairoi) by measuring the anti-synchronization across modules.
3. Capa 3 (Ontological Ascent): Detects the exact moment of global structural reorganization through Kolmogorov-Smirnov contrasts and Frobenius norm shifts, indicating the emergence of a new law of temporal discreteness.

Installation

You can install the package directly from PyPI:

pip install systemictau

Quickstart

import numpy as np
import systemictau as st

# 1. Provide your multivariate time series data
# X = np.array([...]) # Shape: (T_steps, N_components)
np.random.seed(42)
X = np.random.randn(500, 4)

# 2. Compute the Systemic Tau over sliding windows
taus_global, taus_per_module = st.compute_taus(X, window_size=13)

# 3. Accumulate the Discrete Extramental Time (RECD)
T_series, dtk_series, gate_series, depths = st.accumulate_time(taus_global)

# 4. Extract Relational Windows (Joint Episodes)
hp_z, core_hyper = st.hyper_persistence(taus_global)
lam, tt = st.rolling_rqa(taus_global)
M_series = st.critical_mass_metric(hp_z, lam, tt)

A_series = st.compute_antisynchronization(taus_per_module)
episodes = st.extract_joint_episodes(A_series, M_series)

# 5. Detect Capa 3 Reorganization (Ontological Ascent)
t_frob, max_dist = st.detect_reorganization_frob(taus_per_module)
t_ks, max_ks = st.detect_reorganization_ks(dtk_series)
t_star = st.consensus_transition(t_frob, t_ks)

print(f"Capa 3 Transition detected at t* = {t_star}")

Citation

If you use this package in your research, please cite the foundational work:

Padilla-Villanueva, Johel. (2026). Síntesis Magna del Tau Sistémico. Version v6. Zenodo. DOI: 10.5281/zenodo.20576241

For a full list of references and mathematical proofs, consult the Zenodo Archive.

License

This project is licensed under the MIT License - see the LICENSE file for details. The underlying theoretical corpus is published under CC-BY 4.0.