The continuous.ino example has the following code and comments in setup():
pinMode(READY_PIN, INPUT);
// We get a falling edge every time a new sample is ready.
attachInterrupt(digitalPinToInterrupt(READY_PIN), NewDataReadyISR, FALLING);
I think the comment saying that new data is ready on the falling edge of ALERT/RDY is based on diagram 7-8 in the datasheet, which shows the ALERT/RDY as being active high, with the sample being ready at the end of the 8usec positive pulse on the ALERT/RDY pin.
I was looking at the waveforms on an oscilloscope, though, and I saw that the ALERT/RDY behavior is active low, with a low-to-high transition at the end of the 8usec pulse.
I took a closer look at the datasheet and it says that the polarity of ALERT/RDY can be adjusted with the COMP_POL bit. The datasheet says that the default value of COMP_POL is 0b'0, which corresponds to active low.
It's confusing because the name COMP_POL suggests it's controlling only the comparator. However if you read the datasheet carefully, it does say that COMP_POL also affects the polarity of ALERT/RDY when it's being used to indicate the completion of a continuous sample.
As the continuous.ino example is written, the interrupt flag gets set on the falling edge of COMP_POL, which is the start of the 8usec pulse. The data isn't actually ready until the end of the 8usec pulse. It doesn't make a practical difference because it takes at least 8uSec to issue the I2C command to the ADS1115 that requests the data.
But if anyone else besides me hooks up an oscilloscope to their system, they will see the opposite polarity on ALERT/RDY vs. what's described in the example.