Search follows one path, but an ordered scan walks the tree in key order. The scan result is recomputed from the compiled tree, then rendered as a sequence. Note: the sequence appears only in the diagram.
in order scan
Tree source
The source tree has recomputed height 2 and key count 9. Note: the same compiled tree feeds the scan.
h=2,k=9
a page models a node; real B-trees tune fanout to disk pages; tiny exact trees prove structure/search behavior only - no I/O or perf claims.
Rendered scan
The recomputed scan emits 9 keys. Note: the render shows the sorted sequence without prose hand-typing it.
scan keys=9
a page models a node; real B-trees tune fanout to disk pages; tiny exact trees prove structure/search behavior only - no I/O or perf claims.
Summary
An ordered scan is deterministic because it is an in-order walk of the recomputed tree. Note: a page models a node; real B-trees tune fanout to disk; no I/O or perf claims.