"We won’t touch the manuscript for now, nor will we issue any public statements."
"We need to be sure of where we stand."
The editors exchanged a glance.
Finally, the eldest editor spoke.
"Alright."
"Let’s conduct our own review."
No one else in the conference room spoke.
A light rain began to fall outside.
Torres picked up his teacup and took a sip.
The tea had grown a bit cold.
The same thing was happening almost simultaneously at *Numerical Mathematics*, *SIAM Journal on Numerical Analysis*, and *Mathematics of Computation*.
Munich University of Technology.
Department of Applied Mathematics, third floor, the small, unmarked conference room at the very end of the hall.
Three men sat in the room.
Albrecht, the head of that large research group under Max Planck.
Engelhardt, the first author of "A Hybrid Tikhonov-Variational Regularization Scheme for Ill-Posed Inverse Spectral Problems—Residual Phase Coupling with Cyclic Weights."
The overall coordinator for mathematical inversion in Albrecht’s group, Hoffman.
Albrecht sat at the head of the table.
He was usually a very elegant, elderly German scholar.
But at this moment, he raised his head and looked coldly at Engelhardt across from him.
"Mueller."
Engelhardt’s name was Mueller Engelhardt.
"I’ll just ask you one thing."
"When you substitute your family of cyclic weights into the Li Criterion, where do the coefficients fall?"
Engelhardt’s lips twitched.
He kept his head down.
After several seconds, he finally looked up.
"Professor Albrecht."
"I didn’t substitute it."
Albrecht: ...
Engelhardt quickly added.
"It’s not that I was unwilling to."
"It’s that the Li Criterion itself... is still controversial."
"Lindgren from Copenhagen has already publicly questioned it."
"The family of cyclic weights in my paper was derived from my own algorithm."
"My own derivation is solid."
"My six numerical simulations all ran successfully."
"Until Lindgren’s challenge is resolved, I have no reason to use a ’still controversial’ criterion to pass judgment on my own paper."
Albrecht watched him coldly.
"Mueller."
"Whether the criterion is controversial or not isn’t for you to decide."
"Nor is it for Lindgren to decide."
"The results will speak for themselves once you substitute it."
"Only after you’ve substituted it can we discuss it."
"If you don’t, we can’t even begin to have a discussion."
Hoffman, the overall coordinator sitting beside Albrecht, hadn’t said a word. He just sighed.
The other two men in the room heard it.
Albrecht’s gaze shifted from Engelhardt to Hoffman.
Hoffman didn’t look at him either.
He simply lowered his head and gently closed the copy of the Comment in front of him.
Albrecht understood.
His overall coordinator for mathematical inversion had already passed judgment.
Engelhardt’s path was no longer worth the group’s continued investment of energy.
It wasn’t a question of whether Li Dong was right or wrong.
Even if they assumed Li Dong was wrong, their group had been pushing forward with Engelhardt’s family of weights for nearly two years.
Every step was clearly correct.
All the data looked great.
But they still couldn’t get a breakthrough.
The younger members of their group had long been whispering among themselves.
"Is there something wrong with Professor Mueller’s path?"
Before, no one dared to say it out loud.
Now, Li Dong had posted this Comment.
It was as if they were using Li Dong’s ruler to finally give measure to the words they had kept buried for over a year.
That sigh from Hoffman was for this very reason.
Albrecht looked out the window.
Outside, the Munich sky was a dreary gray.
Silently, he thought.
’Engelhardt...’
’Our work on this path... we have to put it on hold.’
Hecheng.
University of Science and Technology of China, National Research Center for Microscopic Matter Science.
Third floor, Director’s office.
Wang Shen, Xie Yi, and Mateo Levan were gathered around a table.
On the table was a printed copy of Li Dong’s Comment.
Beside it was a stack of draft paper handwritten by Levan himself.
Wang Shen had been sitting in this room all morning.
He hadn’t said a single word.
He just sat there, watching Levan.
Since last evening.
Levan had locked himself in the visiting professor’s office next door.
He hadn’t come out all night.
At one point, Wang Shen had knocked on the door, but Levan didn’t answer.
Wang Shen knocked again, and Levan opened the door just a crack to say one thing.
"Director Wang, just give me half a day more."
After hearing that, neither Wang Shen nor Xie Yi disturbed him again.
In truth, both of them already had a bad feeling about it.
Here in Hecheng, the two hundred million special project had been stuck for several years.
The most promising path finally chosen for the entire project was mathematical inversion.
They had brought Levan over specifically to break through on this path.
If Li Dong’s criterion was really correct...
Then this path was fundamentally flawed.
The entire project would have to find a new direction from scratch.
This was no laughing matter.
So they had to let a true expert in the field make the call.
Levan opened his mouth.
In the end, he spoke only five words.
"This judgment of Dong’s... is correct."
Hearing this, Wang Shen suddenly sighed.
"This path... it’s a dead end."
The same thing was happening in more places as well.
Over a dozen research groups across the globe, almost in unison, took up the Li Criterion and measured it against the stacks of drafts on their desks.
After they were done.
They all sighed.
That sigh actually contained two things.
One was relief.
The group from Max Planck in Germany, Albrecht’s group, the one that had gotten the furthest—it turned out they were stuck there too.
They hadn’t truly broken through either.
The other was worry.
The path of mathematical inversion was, for the past few years, universally acknowledged by the entire field as the one closest to "plucking the star."
Now, that path was impassable.
So where were the remaining paths?
No one knew.
At least, no one in their field knew.
—Except for one group.

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