Spectral Integrated Information

(C) 2026 Mark M. Bailey, PhD

A small Python package + CLI to compute Φ_spectral (spectral integrated information) on multivariate time-series, as defined in When Wholes Resist Decomposition: A Spectral Measure of Epistemic Emergence.

Install

pip install -e .

Input formats

The CLI expects an n_nodes × T matrix X (nodes/agents by time).

Supported on-disk formats:

• CSV: "wide" by default (columns are nodes; rows are time). If your first column is time, pass --drop-first-col.
• JSON:
  • dict of lists: { "node1": [...], "node2": [...] }
  • list of records: [{"t":0,"node": "a","value": 0.1}, ...] (use --format long)

You can always bypass parsing by saving a NumPy .npy file and using --input my.npy.

Common tasks

Compute Φ_spectral(t) with a sliding window:

phispectral compute --input data.csv --window 50 --step 5 --bins 8 --outdir outputs

Sweep across multiple window sizes and generate plots:

phispectral sweep --input data.csv --windows 10,20,50,100 --step 5 --bins 8 --outdir outputs

Generate toy-model data (random/transitional/synchronized/ctln), save it, and compute Φ:

phispectral simulate --model transitional --n 50 --T 150 --seed 7 --out data.csv
phispectral compute --input data.csv --window 10 --step 1 --bins 3 --outdir outputs

Output

compute writes:

• phi_timeseries.csv : time index, phi_raw, phi_norm
• phi_timeseries.png : Φ(t)
• mi_final.png : mutual-information matrix for the last window
• traces.png : trace heatmap + traces

sweep writes the above for each window and additionally:

• phi_vs_window.png : mean Φ vs window size (plus optional spread)

Citation

@misc{BaileySchneider2025,
  author       = {Mark M. Bailey and Susan L. Schneider},
  title        = {When Wholes Resist Decomposition: A Spectral Measure of Epistemic Emergence},
  note         = {PhilPapers preprint},
  year         = {2025},
  url          = {https://philpapers.org/rec/BAIWWR},
}