lin-0080

5.8 The three IC compatibility tests

The infinitesimal-causality calculus contains three differently typed tests.

Test	Object tested	Vanishing means	Does not imply
Normalization or marginal test	signed kernel derivative	mass conservation or declared first-order marginal invariance	finite-scale causal irrelevance
Copy test	kernel coderivation defect \(B_D\)	first-order preservation of declared copyable information	generic stochastic compatibility
Bracket test	normal component of \([u,v]\)	visible intervention distribution is involutive	absence or identification of latent causes

Table 5.1 The three tests share a compositional grammar but not a common type.

These tests resemble infinitesimal analogues of deletion, duplication, and reordering rules, but they are not a derivation of Pearl’s do-calculus [ Pearl , 2009b ] . That stronger comparison would require a category of causal models carrying the relevant graph surgery, stochastic semantics, and a tangent construction compatible with both.