The numbers are not adding up. IRCC's statements if reconsidered supports the 1st theory:
* The highest ranked candidates are invited during rounds of invitations. If we issue 3,500 invitations during a round, the system will pick the top 3,500 candidates at that time. The cut-off for the round is set by the CRS and submission date of the 3,500th candidate.
* If more than one candidate has the lowest score, the cut-off is based on the date and time they submitted their Express Entry profiles.
From the above statements, referencing the last draw tie-breaking date, of 31/12/17: this indicates the profile submission date of the 3750th ITA recipient with a score of 441 (hence the oldest profile with 441). So, this implies that nobody with 441 is left prior to the tie breaking date. Assuming 3650 candidates scored above 441, starting from the oldest profile 3750th ITA on 441, to similar 99 profiles forward into 2018 to complete 3750 ITAs. So, a couple of profiles on 441 might have received ITA post the so called 'tie-breaking date' of 31/12/17.
Should this be the case, the draw on 08/08/18, will make a lot of people happy. Perhaps, almost all of 441 will be cleared, in fact a very few 440 might get ITA with an increase in draw size to 4000.
Once again, if you're reading this and you know someone who got ITA on the 25/07/18 and entered the pool with a score of 441 after 31/12/17 tie breaking date, please let us know.