6.7 From Democritus to BRIDGE and SKFM

Democritus constructs local causal models from discourse and records their variables, claims, contexts, and provenance in a categorical atlas. Its local causal object is graph-like. Infinitesimal causality replaces a finite edge claim by a smooth response direction generated by a declared protocol. The infinitesimal database does not discard the earlier atlas; it expands it:

BRIDGE and SKFM, developed in Chapter 11, currently use bracket non-closure to prioritize latent-confounded causal discovery [ Mahadevan , 2026b ] . The database layer adds persistence and compositional memory. It can retain bracket witnesses across sources and regimes, compare alternative visible spans, record which extraction or estimation pipeline produced each field, and determine whether one repair explains several local failures.

The division of labor is therefore:

Infinitesimal causality

supplies the intervention semantics and closure criterion.

BRIDGE/SKFM

estimates fields and uses bracket geometry for causal search.

Database layer

organizes the resulting objects, comparisons, queries, provenance, and repair history.

None of the three layers certifies causal identification by itself. A bracket row says how registered fields interact under a declared model and protocol; its causal interpretation still depends on the grounding and identification assumptions of Chapter 5.