Where there is Virat Kohli there is hope. There are not many causes for Indian optimism as they chase a target of 444 but one of them ended the day unbeaten on 44, and for as long as he remains so will their belief. At stumps Mohammed Shami certainly seemed surprisingly relaxed as he smiled and declared: “We will win the match tomorrow.”

They are 164 for 3 overnight, with Kohli batting alongside Ajinkya Rahane, and must still score 280 if they are to win, on a ground where no Test side has ever successfully chased more than 262.

Related: Cummins’ lack of intent shows sharp contrast of styles before Ashes | Andy Bull

However bleak India’s position it was clear from the start of their innings there was no lack of belief, either in the stands or on the pitch, but in a run chase where they needed everything to go their way it took just over seven overs for them to receive conclusive evidence that it would not, as Shubman Gill fell victim to another spectacular diving catch by Cameron Green.

There was some doubt as to whether the ball had been grounded as Green fell to earth. This is the second Test to be played since the International Cricket Council stopped the use of soft signals and without any guidance the TV umpire, Richard Kettleborough, forced an extended delay while he watched the same few camera angles enough times to be absolutely certain that he had no idea what to do. “He could have taken more time,” Shami said. “It’s the World Test Championship final, not a normal game. He should have checked better, zoomed in.” Either decision would have been entirely understandable – in the end he just had to make one.

Gill trudged from the field to a chorus of “Cheat! Cheat! Cheat!” from the stands, and later tweeted a still picture of the ball apparently grounded, along with two magnifying glass emojis and a facepalm. “I knew I caught it straight away,” Green insisted. “I know it looks a bit weird but I knew straight away I caught it. In the heat of the moment I thought it was clean.”

India had clearly decided that if a positive result was to prove out of reach they would at least go down swinging. In the first 55 balls of their innings they hit as many fours as Australia had in the entire morning session, and a bonus six to boot.

Gill’s departure did little to change their methods, with Cheteshwar Pujara hitting three boundaries in his first nine balls. After 19 overs they had scored 91 runs, and if victory remained a tiny speck on a distant horizon they were at least charting the right course. Then Australia brought on Nathan Lyon.

Related: Despite the fury, Cameron Green’s catch leaves no grounds for complaint | Geoff Lemon

Five balls into the off-spinner’s first over Rohit Sharma swept, missed and was irredeemably lbw. In the following over Pat Cummins bowled short at Pujara, who attempted to help the ball over the cordon and instead tickled an attempted upper cut into the gloves of Alex Carey. They felt like a decisive few minutes.

In the circumstances it is hard to criticise Australia’s approach, but their performance with the bat on the fourth day was, if not bad, then certainly not very interesting. Since arriving in this country their players have been incessantly asked for their thoughts on the current England team’s high-octane approach to Test cricket, generally coming up with diplomatic responses. But here it felt like they spent the best part of half the day wordlessly producing the cricketing equivalent of two raised middle fingers and a couple of bared arse-cheeks towards Brendon McCullum. “We have to entertain and captivate kids,” the New Zealander said last week. Er, I think you’ll find we don’t, Australia responded.

What momentum Australia had in the opening session was provided by Carey, who scored 41 of their 68 runs and looked calm and fluent.

“He’s batting beautifully,” said Green, who himself took 95 balls to score 25. “He’s obviously put so much time in the last few months to get into a really good space. He’s back to his aggressive and positive self and he’s been looking to show intent from ball one.”

In the morning Carey scored at 4.03 runs an over while Green, Marnus Labuschagne and Mitchell Starc trundled along at a combined 1.7.

• Download the Guardian app from the iOS App Store on iPhone or the Google Play store on Android by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the Menu button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

There was a slight acceleration after lunch, notably from Starc, and when Cummins finally declared – waiting until he himself was dismissed a few balls after drinks – Carey, the only Australian to impress in both innings, stood unbeaten on 66.

Perhaps a certain fatalism had by then descended over India as they toiled in the field. Good bowling often went unrewarded; Australia twice got boundaries by edging the ball through a fielder’s legs; Carey sent the ball flying between second and third slip, neither of whom moved – Pujara was nearest but was caught cold (ironically, given the temperature was 29C and he was wearing a jumper). India are down, but they are not yet out.