「One month later.」
G?ttingen, Lower Saxony, Germany.
The Max Planck Institute for Solar System Research.
This was a place that anyone in Europe involved in solar physics had to take seriously.
The MDI magnetograph on the European Space Agency’s SOHO satellite, the PHI polarimeter on NASA’s Solar Orbiter—for the past twenty years, nearly every milestone in solar observation payloads was, in one way or another, connected to an office in this building.
And in one particular office within this building...
Professor Heinrich Richter.
Seventy years old this year.
Director of the Max Planck Institute.
The current president of Division X (Solar and Heliospheric Physics) of the International Astronomical Union (IAU).
A German National Academy of Sciences Leopoldina Member.
Winner of the American Astronomical Society’s 1998 Haier Prize, an award whose weight in the field of solar physics is roughly equivalent to a "lifetime achievement" award in other fields.
He had also authored a review article in the *Annual Review of Astronomy and Astrophysics* on the statistical laws of extreme solar particle events.
It had been sixteen years since that review was published.
To this day, it still held a firm spot in the top three most-cited papers in the field.
8:20 AM.
On Richter’s desk lay a freshly printed manuscript.
It was a manuscript pending review, forwarded to him last week by the editorial department of *Nature*.
From Huaxia. The Zijin Mountain Observatory. The Wukong Satellite collaboration.
"Direct Detection of a Break in the Cosmic-Ray Electron and Positron Spectrum at Tera-Electron-Volt Energies."
A directly detected break in the TeV electron spectrum.
Although Richter’s specialty was solar physics, he had been reading up on the cosmic-ray electron spectrum his entire life.
That TeV range was the "Holy Grail" that the high-energy astrophysics community had been chasing for over a decade.
Everyone knew there was likely something there.
But no group had been able to make the two-word claim: "direct detection."
And now... someone had.
Richter put on his reading glasses.
He had a habit of reading papers backward, starting from the methodology section at the end.
Because the beginning was always full of flashy results; if the methodology was flawed, it was all just for show.
So he first examined the full range from 25 GeV to 4.6 TeV.
The condition number evolution of the deconvolution operator at each step, the boundary settings for the anchor region, the merging method for every anomalous event, the comparison of Geant4’s hadronic models, the consistency check for P-side and N-side readouts, the absolute energy scale correction...
The more Richter read, the brighter his eyes grew. He couldn’t find a single flaw.
Every single place where he thought, ’There should be a problem here,’ the authors had not only anticipated it but had also run control experiments, which they included in the supplementary materials.
Boosted decision trees, principal component analysis, ζ-variables—three independent methods for electron/proton discrimination, and the results were all completely consistent within statistical error.
The heatmap for proton separation in Figure 1 was as clean as a textbook illustration.
Richter put down his pen and muttered to himself.
"The Huaxia people are truly rigorous."
He then flipped to the middle of the methodology, to the section on deconvolution.
When the authors wrote about the authenticity discrimination outside the anchor region, they cited a criterion.
Richter recognized it.
In the field, it was currently called the Li Criterion.
Anyone working on spectral deconvolution recently who hadn’t heard the two words "Li Criterion" was probably already retired.
Moreover, Richter had long ago come to a conclusion in his heart: in the future, anyone doing deconvolution would likely be unable to avoid this yardstick.
He was about to read on when he suddenly noticed a footnote, footnote 1, under this criterion.
He instinctively flipped to the footnote section of the page and glanced at the name.
Li Dong.
The very originator of the Li Criterion, a rising star in the world of mathematics.
The content of the footnote was not long.
[Author’s Note: The discrimination criterion cited in this section has been dubbed the "Li Criterion" in recent literature.]
[The author wishes to state that this naming is a misattribution. The method is, in its mathematical structure, a natural extension of the regularization framework established by Mr. A. N. Gikhmanov in 1963 (Gikhmanov, "Solution of Ill-Posed Problems and the Regularization Method," *Soviet Mathematics Reports*, Vol. 4, pp. 1035–1038, 1963). The author himself did not introduce any new insights at its fundamental level that go beyond the spirit of Mr. Gikhmanov’s original work.]
[The author solemnly recommends that this criterion henceforth be named after its true origin: the "Gikhmanov Criterion."]
Richter stared at the footnote for a full minute.
The Li Criterion.
Recently, was there any lab in Europe or the United States working on inverse problems that didn’t mention those two words during a meeting?
Those two words were practically synonymous with "youthful fame."
To have earned those two words meant that, at a young age, you had already embedded your surname into the textbooks of this field for the next fifty years.
How many people would fight tooth and nail for something like that?
How many people, just to attach an inch or two of credit to their own names, would insist on tacking on a "-Smith" to a minor correction in a paper that wasn’t even theirs?
He had seen far too much of it in his lifetime.
What he despised most were these kinds of people who fished for fame and reputation.
But Li Dong...
A young man who hadn’t even finished his doctorate, yet was already being watched by the entire international mathematics community.
Everyone was already getting used to calling it the Li Criterion.
And now, he himself was taking down this golden signboard.
And not in private, but publicly, in a paper that was about to shake the world, gently detaching the two words "Li Criterion" from his own surname.
And returning them to that Soviet scientist from sixty years ago.
An idea suddenly popped into Richter’s mind—
’I want to fly to Huaxia right now.’
’I want to see what this young man is like.’
’I want to have a cup of coffee with him, to become friends despite our age gap.’
His favorable impression of this paper, this group, and of Huaxia instantly rose a notch in his heart.
He flipped back to the main text and finished reading the last few pages.
The further he read, the more satisfied he felt.
Figures, tables, data, explanations.
Every connection was seamless.
He couldn’t even find a single point to question or send back for revision.
In the final column of the review form, he wrote a single line.
[Recommend for acceptance, no revisions.]
After writing it, he even let out a small laugh.
Just then, there were two knocks on his office door, and then it was pushed open.
The person who came in was his postdoctoral fellow.
Reinhard Meier.
Thirty-one years old, with a Ph.D. from Humboldt University of Berlin, he had just joined the Max Planck Institute for Solar System Research last year.
Meier was holding a piece of thermal paper, a sense of urgency on his face.
"Professor, about those few small precursor peaks from GOES-18 last time—you asked me to cross-validate with another dataset to see if it was an instrument issue."
"The results from ERNE on SOHO are in, too."
Richter’s hand, holding his coffee cup, paused.
SOHO is a solar satellite from a joint European Space Agency and NASA mission, permanently stationed at the L1 Lagrange point between the Sun and Earth.
ERNE is its high-energy particle detector, and it’s in a completely separate orbit from GOES-18.
"Put it down."
Meier placed the paper on the desk, took half a step back, but didn’t leave.
Richter pulled the ERNE plot in front of him.
He scanned the axes and the background counts, confirmed the channel gain hadn’t expired, and only then did he look at the curve.
ERNE’s high-energy proton channel also showed a few small peaks in the same time window.
Their positions were identical to the ones from GOES.
Richter glanced at the somewhat excited Meier, then began drawing red circles on both plots. With each circle, he mentally ran through a checklist of possibilities.
’Instrument drift? The last calibrations for the two instruments were two weeks apart; their drift directions wouldn’t simultaneously skew the same way... Ruled out.’
’Cosmic ray background? I checked the neutron monitor records for the same period. They’re flat. Ruled out.’
’Solar activity itself, channel crosstalk...’
’All ruled out.’
Finally, he put down his red pen. On the two plots, the red circles connected to form a clear upward trend.
"It’s the same old story."
Meier had expected his professor to discuss it with him, but Richter just took a sip of his black coffee.
"Professor?"
Meier asked cautiously.
Richter waved his hand dismissively.
"Reinhard, you’re thirty-one. I’ve been in this field longer than you’ve been alive."
"I’ve seen small peaks like these no fewer than fifty times, and every single time, it’s the same script."
"Young Ph.D.s take data they can’t yet explain, pair it with a flashy theoretical framework, give it a fancy name, and throw it on arXiv. Then the media hypes it up for a while."
"Six months later, when data with a longer baseline comes out, these small peaks either get swallowed by the new background noise or turn out to be nothing more than normal bumps in cosmic ray statistical fluctuations."
Richter looked at his student seriously and said.
"I hope you won’t be like them."
A conflicted look appeared on Meier’s face.
"...Professor, but the energy band matches this time."
"Matches what?"
"It matches the shape predicted by the precursor hypothesis."
Richter looked up at him, a hint of resignation in his voice.
"Which precursor hypothesis are you talking about?"
"Mekaridi’s 2015 paper."
"That paper reported on the isotopic signal left by the ancient event in 774–775 AD," Richter said. "What it tells you is the energy magnitude of the event itself—roughly one to two orders of magnitude higher than the 1859 Carrington Event. It doesn’t tell you what the precursor energy band looks like."
"The precursor energy band was an extrapolation hypothesis proposed by Kleiver and Dietrich in 2013."
"The parent distribution for that hypothesis was based on only two real samples: the one in 774–775 AD and the one in 993–994 AD."
"Two samples, extrapolated to the TeV energy band... the error bars would be large enough to cover the entire Milky Way."
Meier lowered his head.
Richter’s voice wasn’t loud, but his words dismantled the burst of enthusiasm Meier had brought in with him.
Richter picked up his fountain pen and wrote a short line in the bottom-right corner of the ERNE plot—
[To be filed, not for publication.]
After writing, he looked up at Meier.
"Meier."
"When you look at these small peaks, what you see is a flashy paper."
"What I see are all those precursor-identification papers from the past few years on arXiv that you can’t even avoid if you tried."
"Every single one of them takes data of this quality to push for some high-profile prediction window."
"Every single one leaves a headline-worthy keyword for the media."
"This kind of thing..."
Richter paused.
"A true scholar doesn’t do it."
Finally, Richter looked at the somewhat dejected Meier and said.
"If, after six months, these small peaks actually hold up, then we will write a rigorous Letter."
Meier looked up, the light that had vanished from his eyes now rekindled.
Richter glanced at the manuscript on the right side of his desk and said.
"Meier, you should learn from Li Dong."
Meier froze for a moment, not immediately registering who this "Li Dong" his professor was talking about was.
Richter paid him no mind, simply muttering to himself.
"I have never seen someone so pure."
"A person like that... if you asked him to chase the hype and write a paper on precursor identification..."
"He absolutely wouldn’t do it."
「Meanwhile.」
Jinling, Huaxia. A certain apartment.
The "pure" Li Dong was staring at a new posterior distribution on his computer screen.
[Main Peak Arrival Window: T?+ 17.1 months (± 1.3 months)]
[Magnitude: Carrington Level]
[Posterior Confidence: 88.4%]

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