One Ruler: A Same-Hands Re-Evaluation of Bivariate Causal Direction on Tuebingen, with a Parameter-Free Compression Baseline

For many real-world systems, causal ground truth is difficult to obtain, making claims about causal effects hard to assess. We develop methods for evaluating collections of $\binom{n}{2}$ bivariate causal statements over a set of $n$ variables. In the setting of acyclic linear statements, any such collection can be extended to a unique multivariate causal model, but we argue that this induced model is implausible if it imposes substantial additional confounding to explain observed correlations. We introduce a compatibility score that quantifies this notion of plausibility, notably without relying on the faithfulness assumption. Additionally, we define an incompatibility score for purely graphical bivariate causal statements, based on global consistency constraints that are derived from acyclicity and faithfulness assumptions. We give theoretical and empirical evidence that both scores can successfully distinguish correct from incorrect causal statements in generic settings. Moreover, we demonstrate the practical applicability of our methods by analyzing causal claims made by large language models. Our work aims to provide a foundation for assessing the reliability of causal information derived from human experts or artificial intelligence in settings where alternative forms of validation are unavailable.

Identification of causal directionality in bivariate numerical data is a fundamental research problem with important practical implications. This paper presents two alternative methods to identify direction of causation by considering conditional distributions: (1) Anticipated Asymmetric Geometries (AAG) and (2) Monotonicity Index (MI). The AAG method compares the actual conditional distributions to anticipated ones along two variables. Different comparison metrics, such as Pearson correlation, cosine distance, Jaccard index, K-L divergence, K-S distance, MAE, MSE, and mutual information have been evaluated. Anticipated distributions have been projected as normal based on dual response statistics: mean and standard deviation. The MI method compares the calculated monotonicity indexes of the gradients of conditional distributions along two axes and exhibits counts of gradient sign changes. Both methods assume stochastic properties of the bivariate data and exploit anticipated unimodality of conditional distributions of the effect. The proposed methods are straightforward and include only a limited number of hyperparameters that affect the accuracy of the identification. For a given set of hyperparameters, both the AAG and MI methods provide a unique, deterministic solution. To address sensitivity to hyperparameters, tuning has been done by utilizing a full factorial Design of Experiment. It turns out that the AAG method outperforms MI, achieving top weighted accuracies of 81.4% with simple tuning and 84.3% with size-adaptive tuning, compared with 81.6% for GRCI or 82.0% for CAREFL-H on the 99 pairs of the Tubingen real-world cause-effect examples. A decision tree has been fitted to distinguish misclassified cases using the input data's symmetrical bivariate statistics to address the question of: How decisive is the identification method of causal directionality?

TRACE (Math & Lienhart, arXiv:2602.01135) reads causal graphs over event types out of a pretrained autoregressive sequence model by thresholding a per-position conditional-mutual-information estimate at a fixed tau. We independently replicate its headline synthetic result: with tau selected on a validation split, mean per-sequence F1 against exact interventional truth reaches 0.90-0.91 at vocabulary size 1000 (paper: 0.91) and 0.86-0.91 from 100 to 2000. First, the optimal threshold is pinned to the truth margin, not to any constant: at every size the errors at tau* straddle the delta = 0.05 margin defining ground truth (missed true edges lie just above it, accepted false ones just below), and the blind optimum lands near delta/2 times the estimator's calibration, confirmed out of sample at 5000. Second, at a single global threshold TRACE mostly recovers a direct, adjacent-influence graph: lag-1 true edges are recalled at 0.97-0.99, while true edges at lag 2 or more read orders of magnitude lower---the reading-scale price of randomizing mediating positions, which an exact test of direct causal effect requires when the truth is unknown. A per-lag threshold family recovers a third to a half of lag-2 truth; on lag-uniform data one validated threshold recalls every lag at 0.40-0.87, 8-26 pp below an atomic-intervention control at lags 3-6. Third, the default lag decay of the paper's synthetic benchmark concentrates about 85% of interventional truth at lag 1 and pushes the rest below the estimator's noise floor, so headline F1 there certifies lag-1 recovery only and conflates the benchmark's skew with the algorithm's own limit; a flatter decay separates the two. Fourth, F1 saturates from N = 2 particles at the selected threshold---a property of the threshold's margin over the noise floor, not of the estimator, which converges as N^(-1/2). We distill five practitioner rules.