"I am confident that I will be able to prove my majority on the floor of the House and provide a stable government," Mr Yeddyurappa says in his letter on Wednesday. This was Mr Yeddyurappa's second letter to the governor; the first one sought an appointment to "stake claim" before the results were declared on Tuesday.
Governor Vala right away invited Mr Yeddyurappa on this claim on Tuesday and gave him 15 days to prove his majority in the assembly, triggering a barrage of protests.
The Congress complains that the governor's invite and the long grace period was "a licence to poach" lawmakers from the Congress-Janata Dal Secular alliance, which had the support of 117 legislators.
The BJP says there was nothing wrong in the governor's invite since the people of Karnataka had delivered a clear mandate against the previous Congress government led by Siddaramaiah and gave the BJP the maximum seats.
Mr Yeddyurappa's letter made a similar point.
"Being the single largest party, BJP has a rightful claim to form the government... is required to be invited to form the government," the letter says.
This is the one of the two letters that the Supreme Court wanted to see when it started the post-midnight hearing on the Congress petition against Mr Yeddyurappa's swearing-in. Former attorney general Mukul Rohatgi had then said he couldn't produce the letters because he wasn't representing Mr Yeddyurappa but two BJP legislators.
The court had responded by issuing notice to Mr Yeddyurappa and asking him for the letters.
At today's hearing, Mr Rohatgi was representing Mr Yeddyurappa and produced the two letters sent to the governor.
The first letter, sent on Tuesday evening, shows that Mr Yeddyurappa had staked claim to form the government even before the results for all the 222 seats on which elections were held, had been announced.
"This is to submit to that we request your appointment this evening at 5 pm this evening, May 15, 2018 to stake claim to form the government in Karnataka (sic)," the BJP's request for the appointment said. The Election Commission declared all the seats around midnight on Tuesday. The formal notification was only issued the next day.
If the BJP only had 104 seats, how did the party or the government expect this number to reach 112 seats... "Magic?" asked Congress leader Abhishek Singhvi, who led the Congress legal team that is contesting the invitation in the Supreme Court.
The BJP won 104 seats in the Karnataka election, eight short of the majority mark. The Congress emerged second but quickly tied up with the Janata Dal Secular (JDS) and extended support to its leader HD Kumaraswamy.