Algorithmic Information Bounds for Causal Structure Discovery — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Causal structure discovery is fundamentally constrained by algorithmic information loss; permutation-based methods and Kolmogorov complexity provide the measure-theoretic backbone for separating signal from noise in causal graphs. | MATH: Kolmogorov complexity K(x) = minp {|p| : U(p)=x}; algorithmic mutual information IA(x;y) = K(x) + K(y) − K(x,y); causal Markov condition P(v1,…,vn) = ∏i P(vi | pa(vi)); integrated information Φ (Tononi) — lossless variant requires K(Φ) ≈ K(system) (no compression below intrinsic complexity); permutation search space size n! over DAGs, with intervention targets unknown → complexity grows as O(n! · 2m) for m latent targets. | CONNECTION: The golden ratio appears implicitly in the trade-off between algorithmic compression and causal fidelity — the optimal partition of information into "mechanism" vs "noise" follows a fixed-point where \(K(\text{model}) / K(\text{
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026algorithmic,
title = {{Algorithmic Information Bounds for Causal Structure Discovery — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635637},
url = {https://zenodo.org/records/23635637},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Algorithmic Information Bounds for Causal Structure Discovery — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635637
UR - https://zenodo.org/records/23635637
AB - FINDING: Causal structure discovery is fundamentally constrained by algorithmic information loss; permutation-based methods and Kolmogorov complexity provide the measure-theoretic backbone for separating signal from noise in causal graphs. | MATH: Kolmogorov complexity K(x) = min_p {|p| : U(p)=x}; algorithmic mutual information I_A(x;y) = K(x) + K(y) − K(x,y); causal Markov condition P(v_1,…,v_n) = ∏_i P(v_i | pa(v_i)); integrated information Φ (Tononi) — lossless variant requires K(Φ) ≈ K(system) (no compression below intrinsic complexity); permutation search space size n! over DAGs, with intervention targets unknown → complexity grows as O(n! · 2^m) for m latent targets. | CONNECTION: The golden ratio appears implicitly in the trade-off between algorithmic compression and causal fidelity — the optimal partition of information into "mechanism" vs "noise" follows a fixed-point where \(K(\text{model}) / K(\text{ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -