Chapter 349 - 291: Public Call for Submissions

Chapter 349: Chapter 291: Public Call for Submissions

The table was divided into three columns.

The first column: paper title and authors.

The second column: Li Criterion coefficient.

The third column: conclusion, either [Stable] or [Pseudo-Convergence Anchor].

In less than twenty-four hours after the table was posted, it had been forwarded to every professional mailing list in the field of inverse problems.

Out of one hundred papers, a total of thirty-seven were labeled [Pseudo-Convergence Anchor].

Thirty-seven percent.

And among those thirty-seven papers, eleven had once been in the top ten of the inverse problems field rankings.

The very night Sutton posted that table,

Over at ETH Zurich, Ahmed Schmidt, a professor nearing sixty who had spent his entire life researching inverse problems, posted a message on his personal homepage.

"I took the Li Criterion today and went over my own 1998 paper on cyclic regularization."

"The coefficient falls within the anchor interval."

"I apologize to all the peers who have cited that paper of mine over the years."

Once this message was posted, everyone in the inverse problems field fell silent.

In the days that followed, similar "self-review statements" began to pop up one after another.

Some came from Paris.

Some came from Kyoto.

Some came from Tel Aviv.

Even at Moscow State University, which typically avoided getting involved in such matters, an old professor publicly retracted one of his papers from the nineties.

At this point, the Li Criterion was no longer just a "criterion."

It had become a hurdle that every researcher in the inverse problems field who still wanted to work with dignity had to clear first.

...

But amidst this chorus of self-reviews, there were still a few who remained stubbornly defiant.

The first was Eric Lindgren of Copenhagen.

He was the first to jump out and question the Li Criterion.

The second was Leonard Hartwig of Purdue University.

The third was Hubert Rasko from an old engineering institute in the southern suburbs of Paris.

The three were of similar seniority, in their early fifties, had been in the field for over twenty years, each led a large research group, and served as the principal investigator for a national-level project.

But the angle of their defiance was no longer the desk-pounding protest of "I’ve been doing this for twenty years and couldn’t figure it out, so how could you?"

They had adopted a new posture.

Hartwig was the first to speak out.

He posted a short article on LinkedIn with the title:

"A Few Questions Regarding the Physical Realizability of the ’Pseudo-Convergence Anchor’ Concept."

In the article, he didn’t deny the mathematical correctness of the Li Criterion itself.

He simply raised three points.

First, while "pseudo-convergence anchor" is a clean concept mathematically, as a physical concept, there is currently no direct experimental evidence that the real-world scenarios it corresponds to actually exist.

Second, the fact that everyone has been using that little trick "seemingly well" for the past thirty years might suggest that the vast majority of practical engineering scenarios don’t fall into the anchor interval at all. In other words, while the Li Criterion is mathematically elegant, it might be a criterion that is "almost useless" in practical engineering applications.

Third, in light of the above two points, he advised his peers not to rush into using this "ruler" to re-evaluate the past thirty years of work, especially papers that were classified as [Pseudo-Convergence Anchor] but whose numerical results at the time "looked perfectly normal."

After Hartwig’s piece came out, Lindgren immediately shared it on his blog.

Rasko didn’t write an article. Instead, he directly sent private messages to the editors-in-chief of several journals in the inverse problems field, suggesting that they "suspend the acceptance of any submissions that use the Li Criterion as their core argument until this storm passes."

The three of them, a coordinated one-two punch.

Their angle of attack was quite clever.

They didn’t dare to directly challenge the mathematical correctness of the Li Criterion.

They bypassed the mathematics to attack its "engineering significance."

In the past thirty years, this move would have been enough to fool a great many people.

But this time, it wouldn’t work.

Less than twenty-four hours after Hartwig’s LinkedIn article was posted, Sutton posted a new table on his X account.

This table listed the papers Hartwig himself had published over the past fifteen years that used the cyclic weight trick.

Nine papers in total.

The Li Criterion coefficients for all of them were within the anchor interval.

All nine of them were hits.

Beneath the table, Sutton added only a single sentence.

"Professor Hartwig, regarding ’physical realizability,’ please first explain these nine papers of your own."

The takedown Rasko received was even more brutal.

The private message he had sent to the editors-in-chief of several journals was screenshotted by one of them and posted on their X account.

That editor-in-chief added only one sentence.

"Our journal’s self-review found a forty-two percent rate. I’m afraid I cannot follow Professor Rasko’s suggestion."

As for Lindgren...

This time, he didn’t even get a chance to speak for himself.

That very afternoon, a young associate professor from his own research group, just over thirty years old, quietly posted a preprint on arXiv.

In the preprint, the associate professor went through every paper Lindgren’s group had published over the past eight years that used the cyclic weight trick.

The conclusion was stated in the last line of the abstract.

Out of five papers, three fell within the anchor interval.

The night the preprint was posted, Lindgren’s assistant quietly deleted the blog post that shared Hartwig’s article.

By this point, most people in the inverse problems field understood what was going on.

The defiance of the three senior scholars was less about defending academic truth...

...and more about protecting the résumés they had spent the last fifteen years building up.

Once the Li Criterion was truly established and widely accepted, those résumés would have to undergo a complete re-evaluation.

After the re-evaluation, what remained to be listed on their résumés would likely be cut in half.

It wasn’t that they didn’t believe in the Li Criterion.

It was because they believed in it too much that they were so defiant.

And just as the three senior scholars were beaten into silence by one self-review report after another...

...the editorial department of *Inverse Problems* finally caved.

...

London, IOP Publishing Group Headquarters.

Editorial office of *Inverse Problems*, Office of the Deputy Editor-in-Chief.

Maria Torres slammed the final internal self-review report onto her desk.

Over the past ten years, the journal had published a total of 147 papers that used the cyclic weight trick.

Of those, sixty-two had Li Criterion coefficients that fell within the anchor interval.

A rate of forty-two percent.

With this number laid out on the table, Torres was speechless.

She silently flipped the report to the last page, her eyes fixed on the most conspicuous line of red text.

[It is recommended to immediately retract the paper by Engelhardt et al., published in the 4th issue of 2023, and to issue an apology to the academic community for the oversight in the review process.]

The next morning, *Inverse Problems* posted an editorial announcement on its official website’s homepage.

It was signed by Deputy Editor-in-Chief Maria Torres.

The announcement was short, but every paragraph carried immense weight.

First paragraph: The editorial board has received multiple letters from readers and replication reports.

Second paragraph: The editorial board, in conjunction with two independent external reviewers, has conducted a complete internal review of the "pseudo-convergence anchor" criterion proposed in Li Dong’s Comment and fully recognizes its validity.

Third paragraph: We officially announce the retraction of the paper "A Hybrid Tikhonov-Variational Regularization Scheme for Ill-Posed Spectral Inverse Problems—Residual Phase Coupling with Cyclic Weights" by Mueller Engelhardt et al., published in the 4th issue of 2023.

And the fourth paragraph was the most explosive one.

[In light of the significant methodological contribution this criterion provides to the field of inverse problems, the editorial board of this journal now publicly and sincerely invites Dr. Li Dong of Yan University to organize his work into a full paper for submission. The journal will handle the review process with the highest priority and guarantees acceptance upon first submission.]