Step 1: Build a simple round by round elimination table for Vitezlav Vesely instead of eliminating clue by clue in prose.
List the six rounds as columns: R1, R2, R3, R4, R5, R6, and mark each one Possible or Not Possible as the clues are read.
Step 2: Mark R1 and R2.
Clue (i) explicitly excludes Vitezlav (one of the other two athletes besides Neeraj) from having a medal winning throw in rounds 1 and 2. Mark R1 = Not Possible, R2 = Not Possible.
Step 3: Mark R6.
Clue (ii) says Vitezlav's round 6 throw was a foul, so it could not have been counted as his best. Mark R6 = Not Possible.
Step 4: Mark R5.
Clue (iii) says Vitezlav's position and best throw were already fixed by the end of round 4 and did not change afterward, meaning nothing in round 5 (or 6) could be his best. Mark R5 = Not Possible.
Step 5: Mark R4.
Clue (iv) attributes the best throw of round 4 to Jakub Vadlejch specifically, distinguishing round 4 as Jakub's standout round rather than Vitezlav's. Mark R4 = Not Possible.
Step 6: Read off the surviving column.
Table state: R1 Not Possible, R2 Not Possible, R3 Possible (untouched by any clue), R4 Not Possible, R5 Not Possible, R6 Not Possible. Only R3 remains marked Possible.
Step 7: Conclude.
Vitezlav Vesely's best throw must have occurred in the third round, the only round not excluded by any of the four given observations.
\[ \boxed{\text{Third}} \]