Andrew Miller is UK editor of ESPNcricinfo. He tweets @miller_cricket
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"I suppose if you guys keep talking about it enough, he'll start believing it at some stage," Bayliss told reporters in Mumbai, in response to speculation that England's most-capped Test captain is on the brink of calling it a day.
It wasn't, in fairness, the ideal time for such an issue to bubble to the surface. England's surrender in the fourth Test was as bruising as any of the sizeable beatings they've endured in recent months - only two teams in history had previously managed to lose by an innings after posting 400 first time out - and they've still got a gruelling finale in Chennai to come.
But equally, it was disingenuous for Bayliss to dress the furore up as some sort of an end-of-a-losing-series scapegoat-seeking frenzy (as can, admittedly, be the case on some occasions).
After all, it was Cook himself who invited the line of enquiry with his pre-series admission that the end of his reign could be nigh, while Bayliss ramped up the inquisition, after England's defeat in the third Test, by revealing that he had 'stepped up' his presence in the dressing-room - an intervention that he must have known would be interpreted as a comment on Cook's passive leadership, particularly in Visakhapatnam and Mohali.
You can dress up the details in whatever finery you like (and nothing looks like being decided until Cook has sat down with his old captain and opening partner, Andrew Strauss, for a debrief in January) but there is no escaping the conclusion that a fork in England's path has been reached.
That much is as clear from England's itinerary as their statistics. Never mind the seven Test defeats that they have suffered in 2016 (one more in Chennai will equal their record for a calendar year), it is the seven long months of Test inactivity that are of greater significance to Cook and England. The team's attentions are about to turn to white-ball cricket on a scale never witnessed in their history - and who knows where that will leave the skipper, should he seek a return to his role against South Africa in July.
England have endured longer breaks between Test matches in the past - most recently the eight-month hiatus around the 2015 World Cup - but Cook, of course, was the ODI captain as well going into that spell, only to be jettisoned, with a cruel but overdue lack of ceremony, in the final run-up to the tournament. As a consequence, he is about to spend longer out of an England shirt than at any previous point in his career.
There's no point in conflating the events of that sorry winter with the circumstances of this one, except to point out that Cook's appointment as England's one-day captain - recalled from outside the squad after Strauss's resignation in 2011 - had been the ultimate symptom of the format's second-class status in the eyes of the ECB. And, by extension, his removal was the catalyst to the white-ball revolution that followed.
That upheaval came too late to salvage any dignity at the World Cup, but this coming period - culminating in a home Champions Trophy and a plausible shot at a first ICC global 50-overs trophy - is the first real test of the ECB's new resolve, ahead of the 2019 World Cup, to treat one-day cricket as an equal priority.
And with that in mind, if Bayliss is getting twitchy about the team's lack of "positivity" under Cook's leadership, albeit in a different format, then you'll just have to trust his judgment on that one, at least until there's sufficient reason to doubt it. After all, nine months ago, many of the same players who have been cowed into submission on this trip had so enjoyed their last visit to India that they came within four fateful deliveries of winning the World T20.
It may well be true that Australia's recent Test struggles expose the long-term folly of focussing too much attention on the white-ball game. But England have spent too many years swimming against the tide not to go with the flow while they can, and given that one of their most consistent performers in the last two Tests was Jos Buttler, a man who says that a lack of first-class cricket was the secret to his success, there seems already to be circumstantial evidence to back up Bayliss's attention to mindset.
Where all of that leaves Cook is both crystal-clear … and clear as mud. What cannot be in any doubt is his enduring importance as England's totem of Test batsmanship. Talking of mindset, when Cook sets his mind to bat all day, it becomes one of the most unbreakable substances known to man. He has not missed a Test match since his first visit to Mumbai in March 2006, and he is not scheduled to miss another until the date that he so chooses.
Cook will be 32 years young on Christmas Day, and it's still debatable whether he has yet broken sweat, let alone a bone, in the course of an extraordinary career. With 10,998 Test runs to his name already, he has the chance to set records that may never be challenged.
None of those remarkable facts, however, have any bearing whatsoever on Cook's aptitude as a leader, or indeed his suitability to be Bayliss's right-hand man in England's long-form planning, and those are the only aspects of his game that are up for debate as the India tour draws to its conclusion.
It is not that Cook even looks weary after four years as England's full-time Test captain - certainly not to the extent that his predecessors have tended to be after this length of time in charge. Only during his annus horriblis in 2014 did his seemingly limitless reserves of mental strength come flickering to the brink of exhaustion.
But nevertheless, he has carried himself with an air of … well, resignation, throughout this winter's tour of the subcontinent. Who knows what toll his personal life has taken on this trip - he met his newborn daughter for a matter of hours before jetting off to rejoin the squad in Bangladesh two months ago, and that is a sacrifice that would cut any family man to the quick. But Cook will know that his own returns haven't come close to the standards he sets himself, particularly in Asia, where his record as an overseas batsman is unrivalled.
Form-wise, Cook has drifted into what is, for him, an unusual limbo - neither drastically lacking in touch, nor capable of grinding his good starts into towering finishes; as a captain, he's clearly struggled to make the best of the men at his disposal, and there's no disgrace in that.
And yet, if you look at Cook's opposite number, Virat Kohli - in the form of his life with the bat, but living every moment in the field as India's most fired-up leader since Sourav Ganguly - or if you look back at the methods and mien of other recent England captains - the passion of Nasser Hussain, the tactical wit of Michael Vaughan, even the officer-class detachment of Strauss - you'd be entitled to wonder whether a squad with this much talent should be looking quite this defeated after a series in which they had moments of genuine opportunity in three of the four matches. As the People's Front of Judea might have asked of the Romans, "apart from a mountain of runs, a record-breaking run of appearances, two Ashes victories and famous series wins in India and South Africa, what exactly has Alastair Cook ever brought to the England captaincy?"
Well, his time as leader has spanned 58 Tests to date, the most by an England captain, and in winning 24 of those, he has already matched Strauss's mark and is two shy of Vaughan's all-time record of 26. However, he's also on the brink of a far less coveted record. Should England succumb to another defeat in Chennai, Cook would also overhaul Michael Atherton as the most defeated England captain in history.
Somewhere between those two figures lies a verdict on Cook's time as England captain. It's not that he has been a poor leader - far from it. If you were to take only his first full series in charge, his stunning assault on India's citadels in 2012-13, he would go down in history as the warrior-leader of one of England's greatest series wins of all time.
But for much of the rest of his reign, Cook has led with an imperceptible listlessness that has, at times, drawn brutal criticism - most notably from Shane Warne, though he's hardly been alone in his frustrations. Though cut from the same conservative cloth as his friend and predecessor Strauss, he has somehow never forged the same captaincy credentials. The ECB let him down terribly in their (mis-)management of the Pietersen affair, but even before that debacle, Cook had been struggling to forge an identity independent of his Essex mentors, Andy Flower and Graham Gooch. For a man of such singular resolve, it has remained a curious dichotomy.
Overall, Cook's batting hasn't suffered in the manner of his predecessors (in fact his average is a few decimal points higher when captain than not) which is one tenuous reason not to do anything so rash as to hand the reins to Joe Root before the Ashes. More tellingly, however, his runs haven't really contributed to any grander narrative. England haven't won three Tests in a row - even on home soil - since battling back from 0-1 down to beat India 3-1 in 2014, while Cook's overall record since 2015, the year in which he was left to focus on Test cricket, has been a decidedly limp: W12, L13.
That final statistic is perhaps the most galling, for it speaks of a failure to shore up England's standards in the form of the game that they still profess to hold most dear. Even last summer's Ashes redemption was punctuated by two of the most towelling defeats you could ever wish to experience in a winning cause.
There have been fleeting glimpses of what Cook's old-pro leadership could look like when surrounded by his team of young guns - most tantalisingly during his epic hundred against New Zealand at Lord's in 2015 - but for the most part, he's seemed either to try to lead where others cannot follow (take his Vizag rearguard, for instance), or, perhaps more worryingly, he's felt the need to adapt his own style to meet the new dressing-room imperatives. That way madness lies - the Cook of 2012-13 would never have danced out of his crease to be stumped for 46 from 60 balls, as he did on the first morning in Mumbai.
And for all his protestations about wanting to carry on working with Cook for the foreseeable future, these are issues that Bayliss (whose own Test record is a must-do-better W10 L11) knows he needs to address with less than a year to go until the next Ashes curtain-raiser in Brisbane.
"We have a chat before every day's play about what the message will be to the boys and the way we want to play," said Bayliss of his relationship with Cook. "Nothing is ever 100%, it's like selection, you don't want the same philosophy from every selector, you want different thoughts and ideas. So at different times we've come from a little bit of a different angle but, in the end, we go into the team singing from the same hymn-sheet."
Differences in style where captains and coaches are concerned are often a very good thing - Vaughan and Duncan Fletcher hardly seemed like natural bedfellows, after all. And nobody is seriously suggesting that England's Test brains trust are at each other's throats. But could it be that seeking consensus is precisely the wrong way to get the best out of a man as famously bloody-minded as Cook?
Or could it be that his ideal role in the final years of his career will come as a gnarled senior pro, clanking under the weight of his campaign medals and with the likes of Haseeb Hameed under his wing, who is given licence to grind out a ten-hour century on the second and third days in Adelaide and call bullshit at crucial moments when the coach's flights of attacking fancy get the better of him? Cook's defining series, the 2010-11 Ashes, came when he had nothing on his mind but the need to score mountains of runs. Why shouldn't he long for a return to such carefree days?