Each "Readiness Indicator" has it's own set of requirements. The Drive Cycle should catch most of them, but not always.
If you fail the Cat Efficiency Test, you'd be logging a P0420 or P0430 code. Good news is that you haven't (yet) failed the test. But for some reason you haven't successfully completed the test the required two times sequentially and passed both times since doing a computer reset as a result of disconnecting your battery. So you need to work on setting up the optimum conditions to achieve a pair of passes.
Without getting into too much detail, the Cat Test runs one time per drive cycle, about 5 to 10 minutes or so after a cold start. Once everything is up to temperature, and if you are driving on a relatively level road (as determined by a load ratio calculation) at a fairly constant speed (40-45 mph works on many cars), the test begins.
In the Catalytic Efficiency test, the ECU actually momentarily leans out the mixture by up to 30% and evaluates the waveform output response of the rear (post cat) sensor in relationship to that of the front AF sensor. It then returns to the stoichiometric point and watches the rear settle out. It then richens the mixture by up to 30% and compares the waveforms again. So it is monitoring the cat’s ability to store up excess oxygen during a lean period and hold on to it, and then release it on demand to cope with an extended rich mixture condition.
The whole deal takes maybe 10 seconds or so, but as I said, it only takes place once per drive cycle, and it takes two runs of this to log a pass and set the readiness indicator. If your whole commute were say stop and go traffic, you might NEVER achieve a green flag.
Hope this helps!