nested-recd 0.1.0

Nested ordinal RECD: Φ1–Φ3 conjunction levels and λ-weighted Discrete Extramental Clock

nested-recd

Nested ordinal RECD — pure-NumPy implementation of nested ordinal conjunction levels (Φ₁, Φ₂, Φ₃) and λ-weighted Discrete Extramental Clock (RECD) accumulation.

This is the standalone library behind the nested-time structure used in the CCTP/SDDB cardiac pilot and the experimental design in Conversación de la naturaleza del tiempo.

Install

pip install nested-recd

From source:

pip install git+https://github.com/johelpadilla/nested-recd.git

Quick start

import numpy as np
from nested_recd import compute_recd_from_conjunctions, compute_weighted_contributions

# Multivariate series: shape (T, N)
rng = np.random.default_rng(0)
X = rng.normal(size=(800, 3)).cumsum(axis=0)

out = compute_recd_from_conjunctions(X, m=3, d=4, theta3=0.10)

print("mean Φ1:", float(np.nanmean(out["phi1"])))
print("mean Φ2:", float(np.nanmean(out["phi2"])))
print("Φ3 active fraction:", float(np.nanmean(out["phi3"] > 0)))
print("final T_recd:", float(out["T_recd"][-1]))

w = compute_weighted_contributions(out)
print("frac level-3 contribution:", w["frac_contrib3"])

Optional: supply a Systemic Tau series tau_s (aligned in time) so that λ is derived empirically:

out = compute_recd_from_conjunctions(X, tau_s=tau_s)

Or fix the regime weight with a scalar / array override:

out = compute_recd_from_conjunctions(X, lam_override=0.5)

What it computes

Symbol	Meaning
Φ₁	Co-occurrence of identical ordinal symbols across variable pairs
Φ₂	Persistence of pairwise ordinal relations over lag d
Φ₃	Higher-order synergy proxy (total-correlation excess + joint surprise)
λ	Chaos / reorganization intensity (from τ_s or lam_override)
α(λ)	Level weights: α₁ decays with λ; α₂, α₃ grow with λ
ΔRECD	α₁Φ₁ + α₂Φ₂ + α₃Φ₃
T_recd	Cumulative sum of ΔRECD (nested-time clock)

Ordinal symbols use Bandt–Pompe patterns (m=3 by default).

Surrogates

from nested_recd import phase_shuffle_independent, random_permutation_independent

X_null = phase_shuffle_independent(X, seed=42)   # IAAFT per column
X_perm = random_permutation_independent(X, seed=42)

API surface

from nested_recd import (
    compute_recd_from_conjunctions,
    compute_phi1, compute_phi2, compute_phi3,
    compute_lambda, alpha_weights, regime_lambda_proxy,
    compute_weighted_contributions, high_level3_rate,
    generate_multivariate_symbols,
    phase_shuffle_independent, generate_surrogate_ensemble,
)

Relation to other projects

Project	Role
systemictau	Full Systemic Tau library (τ_s, platform, studio)
cctp-sddb-systemic-tau	Cardiac VF pilot using this nested RECD pipeline
This package	Lightweight, installable nested-time / ordinal RECD core

Citation

If you use this software, please cite the CCTP/SDDB pilot archive:

Padilla-Villanueva, J. (2026). CCTP/SDDB: Systemic Tau and ordinal RECD before spontaneous ventricular fibrillation (v1.0.1). Zenodo. https://doi.org/10.5281/zenodo.21270699

And the theoretical nested-time / RECD framework as appropriate for your venue.

@software{padilla_nested_recd_2026,
  author  = {Padilla-Villanueva, Johel},
  title   = {nested-recd: Nested ordinal RECD levels},
  year    = {2026},
  url     = {https://github.com/johelpadilla/nested-recd},
  version = {0.1.0}
}

License

MIT © 2026 Johel Padilla-Villanueva
ORCID: 0000-0002-5797-6931