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When ArcMap creates a new feature using the Oracle Spatial Linear Referencing System (LRS), it sets the measures to NAN instead of "0" for HP and RedHat Linux. According to the Oracle 8.1.7 documentation, this would be an invalid feature. The values should be set to either NULL, or some measure.
On HP, Oracle's OCI does not handle NaN's correctly. Oracle is aware of the issue (TAR# 2232230.996)
On RedHat Linux, the functionality was not ported over by Oracle.
Both these platforms will be fixed once the underlying DBMS functionality is available.