Terminology Map

Two independent lines of research arrived at the same structural decomposition of the Collatz problem. Paper 1 frames everything through dropping times and affine orbits, while Paper 2 uses stopping times and geometric correspondence. The underlying mathematics is identical; only the names differ.

The table below maps equivalent concepts between the two papers.

Paper 1 (Dropping)	Paper 2 (Stopping)	Same concept?
Dropping Time	Stopping Time	Yes — steps to first value $< n$
Dropping Destination	Stopping Destination	Yes — first value $< n$
Dropping Set$_k$	Stopping Class$_k$	Yes — all $n$ with time $= k$
Dropping Modulus	Stopping Modulus	Yes — inner subsets
Dropping Index	Stopping Page + Offset	Related
Dropping Genus $(S,M,I)$	Stopping Signature $(T,P,O)$	Analogous tuples
Orbital Oddity	—	Paper 1 only

Convention

This site primarily uses Paper 1 (dropping) terminology, as the affine orbit framework was developed in that context.