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stops and stop flattened the path twice, once for the points and once for its length, and stop did both before rejecting an index past the last object. place validated the path with attachable_path first, and transform measured the old and new paths up to three times each. A private Measured value now holds the flattened first subpath with its length and closed flag, and path_length, stops, stop and transform use it. stop returns None for an out-of-range index without measuring, and a move of the group measures no path. attachable_path now uses path_length, so a path whose length overflows to infinity is no longer offered as one objects can attach to when placement cannot measure it.