Chapter 354 - 293: I’m Just Saying It for Him

Chapter 354: Chapter 293: I’m Just Saying It for Him

Li Dong was the first to speak on the other end of the line.

"Teacher, please reject them all for me."

"The reason is the same for all of them."

"Tell them they aren’t rigorous enough."

E Weinan: "..."

He sighed to himself.

’If Li Dong keeps up this attitude, no one in this field will dare submit anything to him in the future.’

E Weinan took a breath and said.

"Li Dong."

"Let me tell you something."

"Don’t be hasty."

Li Dong: "Mm."

"Those other two journals... they aren’t quite the same as *Inverse Problems*."

"*Inverse Problems* only put out that public call for papers because they were forced to. They had already taken a tumble with the retraction of Engelhardt’s paper."

"Those other two journals haven’t had any incidents recently."

"Looking at their backlog of papers from the last decade or so, if you run them through your criterion, the proportion of problematic ones is lower than for *Inverse Problems*."

"We have to be objective about this."

"Before your criterion came out, nobody had a ruler."

"Without a ruler, everyone had a different feel for things. But as long as a paper could get by, as long as it passed the editorial department and the external review, it got published."

"It’s not that their entire stack of papers from back then got published by playing tricks."

"In that environment, you wouldn’t have been able to find the errors either."

"Now you’re taking a new ruler and going back to measure their old papers..."

E Weinan spoke with painstaking earnestness.

He had spent his entire life in applied mathematics.

He himself had his name on at least a dozen papers that used the little trick of circular weighting.

He wasn’t unaware that when this hammer fell, he too would have to be measured by the same criterion.

This speech wasn’t just for those two journals. It was also for all the old veterans in the field whose careers had been half-shattered by the "Ghost Wall."

But before he could finish...

Li Dong suddenly cut him off from the other end.

"Wait, Teacher E."

E Weinan: "Hm?"

"I’m not saying they weren’t rigorous enough because of what they did in the past."

Those words came from the other end of the line.

E Weinan froze.

He gripped the phone, unable to process it for a moment.

E Weinan: "Then are you saying...?"

Li Dong said from the other end.

"Teacher E."

"They aren’t being rigorous. Their lack of rigor is in their handling of the Li Criterion."

E Weinan: "A lack of rigor regarding the Li Criterion?"

He repeated the phrase subconsciously.

The Li Criterion was now the gold standard in the field of Inverse Problems.

It wasn’t that there was a problem with the criterion itself.

Li Dong’s "Comment" paper was crystal clear. Three lines of formulas, clean and simple.

People in the field had already taken the criterion to their own old papers, dredging up the entire field’s past mistakes.

’So how could they be "not rigorous"?’

He really couldn’t wrap his head around it for a moment.

Li Dong spoke again from the other end.

"Teacher."

"Logically speaking, this criterion shouldn’t even be called the Li Criterion."

E Weinan: "Oh?"

"It should be called the Gikhmanov Criterion."

The other end of the line went quiet for a moment.

E Weinan was completely frozen in place.

’The Gikhmanov Criterion?’

He couldn’t help but ask.

"What do you mean?"

"My criterion is actually..."

Li Dong paused.

"It was already in one of Gikhmanov’s early papers."

E Weinan: "..."

Li Dong continued on the other end.

"Teacher, go look at his foundational 1963 paper on regularization."

"Not the main text."

"The appendix at the end."

"At the very end of the appendix, he included a section called ’A Few Remarks on the Boundary Behavior of the Weight Function in Iterative Formats.’"

E Weinan’s mind went blank.

He’d lost count of how many times he had read Gikhmanov’s 1963 paper in his life.

He could recite sections of the main text from beginning to end with his eyes closed.

But the appendix...

To be perfectly honest...

Ninety-nine out of a hundred people in this field would flip to that page and skip right over it.

Back then, that section looked more like a rough draft. The formulas were fragmented, there were hardly any complete propositions, just scattered notes.

Gikhmanov himself never even cited that appendix in the main text.

Nor did he ever mention it on any other occasion.

In the field of Inverse Problems, that appendix was practically considered "scrap paper from the archives."

E Weinan held his breath.

"Are you saying...?"

Li Dong also spoke slowly.

"In that appendix, there’s an auxiliary operator called M_{α,c}."

"Gikhmanov only drew up the skeleton. He never finished fleshing it out."

"If you perform a local expansion of M_{α,c} along the boundary with respect to the second derivative of α, and then extract the dominant term from the expansion..."

"That coefficient you extract..."

"...is the very same coefficient in the Li Criterion."

E Weinan: "..."

"They’re identical."

"Off by only a constant factor."

On the other end of the line, something in E Weinan’s mind SNAPPED.

’To think the Li Criterion was hidden inside that rough draft—a draft Gikhmanov himself never even cited in his main text.’

He subconsciously glanced up at the Gikhmanov collection on the top shelf of his bookcase.

Li Dong was still talking on the other end.

"Teacher, if you look further down..."

"There are two more pages attached after the appendix."

"It’s a private letter Gikhmanov wrote in reply to a student."

"In the letter, he specifically mentioned that the matter of the weight function’s boundary behavior ’should be left for more detailed work by future generations.’"

E Weinan closed his eyes.

"’Should be left for future generations.’"

He was familiar with this phrase from Gikhmanov.

Everyone in their field had seen this phrase countless times.

It was the style of that older generation of Soviet scholars.

They’d toss out a sentence like that and leave the rest to posterity.

But that sentence, tossed out in 1963, had been left hanging until today.

Sixty years.

The cold case of "Gikhmanov’s circular Ghost Wall" had the entire community banging their heads against a wall in a dark tunnel for thirty years.

No one had ever thought to look through that appendix.

No one had ever thought that the skeleton for that coefficient had actually been drawn up all those years ago.

A skeleton that Gikhmanov himself had buried beneath a line of fine print.