206: Chapter 206 Why does it feel like he's fishing?

[P-094: The decomposition conditions of the last group of marked primes cannot be reproduced from the public attachments.]

The public tower construction attachments require that the final set of local decomposition conditions be jointly covered by three mutually independent certificates, but the public index only provides two mutually distinct objects among them.

After opening the third row link, the page still returns the second certificate.

If the third local position lacks a certificate, external readers will be unable to independently reproduce this set of conditions along the public materials, and the subsequent tower lemmas can no longer be invoked in public verification.

Note: Please have the author confirm whether the third certificate actually exists and provide its generation records prior to publication.

...

In the public inquiry directory at the bottom right of the computer screen, a new prompt popped up.

The latest submitter came from Princeton, and the inquiry text was very short, citing only the theorem page, parameter page, and two local decomposition certificates.

Seeing this, Jiang Lin, who was just about to take the trash downstairs, put the trash bag back by the door and retraced the path provided by the other party.

The first certificate responded normally, and the second certificate could be opened.

When clicking the link marked as the third, the page indeed instantly looped back to the second one.

He brought up the underlying hash values for comparison, and the SHA-256 strings of the two were identical.

At the lecture this morning, the Instructor had just told more than six hundred people that whoever could make the public materials unable to be independently reproduced could hang the red card back on the verification portal.

Now, the card had arrived.

Jiang Lin smiled slightly, opened the public status page, and changed the yellow banner above the verification portal to red.

[Real-time update of the public status page]

[Public reproduction status: Temporarily blocked]

[Main theorem status: Controlled verification completed / External review continues]

[Reason for block: The third local decomposition certificate required by P-094 cannot be independently obtained via the public index.]

[Currently pending confirmation: Missing underlying object or erroneous public version mapping.]

After submitting the modification, conspicuous red banners appeared simultaneously on the personal homepage, preprint attachment page, and attack directory.

The download count, which had just crossed one hundred thousand, was still soaring rapidly, but the most eye-catching content on the page had changed from normal to temporarily blocked.

The Instructor's phone call came in less than a minute.

"You've already flagged the public reproduction red?"

"Readers can't reach the third object following the existing index, and the reproduction chain is broken."

"Have you checked the original directory?"

"I'm checking it now. But the status page states what others can verify right now, not what we have done in the past."

The sound of paper being rapidly turned came from the other end of the phone, and the Instructor made a decisive decision: "I'll contact the two groups in the tower direction. You freeze the release package, and don't add any certificates to the existing version to avoid disturbing the scene."

"Already frozen."

"What about the statement on the school's official website?"

"Add the current status, retain the original text, and don't cover anything up."

After the phone call was hung up, the original review team's work group lit up again. The people who were standing in the auditorium receiving applause this morning were now quickly returning to their computers one by one.

Liang Zhixia's message popped up right after, her words revealing the urgency of public relations.

[Seventeen media outlets are asking whether it's a retraction.]

Jiang Lin sent her the complete screenshot of the red status page.

[Forward uniformly; do not explain it as a retraction, nor explain it as having been ruled out.]

Liang Zhixia took half a minute to reply.

[You just made the news this morning, and this afternoon you personally hung a red banner on yourself. It's hard for the media to maintain the precision you demand.]

[That's why we give them the original text.]

[Understood, I'll make sure the words 'fatal flaw' are followed by at least a question mark.]

Liang Zhixia subsequently forwarded three screenshots of news that had already begun to spread.

The fermentation speed of public opinion far exceeded imagination.

The first self-media article appeared at 1:31, claiming that Jiang Lin's counterexample had been breached by overseas scholars a few hours after its release, but the accompanying picture was still the five-hundred-dollar problem list from the auditorium this morning.

The second article pieced Q-001 and P-094 together, with the title reading that problems arose once again in the place experts had just verified.

The third one was even simpler, directly announcing that the seventy-six-year-old conjecture was safe and sound.

On the contrary, the public challenger himself maintained a scholar's rigor in the comment section, reminding: "Currently, we can only confirm that the attachments cannot be reproduced, and it has not yet been proven that the third local object is truly missing."

But the spread speed of this sentence could not catch up with those dazzling red screenshots at all.

At 1:46, the door of Room 402 was knocked three times from the outside.

Gu Mingche walked in with his computer in his arms, half a section of rolled-up printing paper still sticking out of his backpack's side pocket.

"Walking from the cafeteria to Building 17, I received messages from twelve people in total, eight of whom asked if the external verification had stopped, and four of whom asked if my work-related injury certificate should also be flagged in red."

Jiang Lin turned the P-094 interface on the screen to him.

"The third row link is duplicated."

Gu Mingche put the computer on the other side of the desk, sitting in the exact same spot as last night.

"This column belongs to me."

"The decomposition conditions belong to the tower verification group."

"They are responsible for judging whether the third lock can lock the door, and I am responsible for checking whether the key has the wrong number hanging on it."

Gu Mingche's fingers flew across the keyboard, opening the hash list of the release package and filtering out the object corresponding to the final set of marked primes.

There were three different hashes in total in the list, and their generation times were all in the early morning of November 4th, earlier than the public submission on November 6th.

However, the second and third rows of the public directory cited the exact same hash.

The third object quietly remained in the list, with no entries pointing to it in the text, directory, or webpage.

Gu Mingche dragged the two sets of numbering side by side onto the screen.

The original calculation files used zero, one, and two for numbering, which were changed to one, two, and three in the review manuscript for readability. The display name of the third row had been changed, but the link field still copied the address of the previous row.

"The third file is here."

Gu Mingche circled that lonely hash.

"As for whether it's the third lock you're looking for, I won't sign on behalf of mathematicians."

Jiang Lin retrieved the corresponding object from the frozen directory.

He was extremely cautious, reading only the content and generation records while keeping the release package as it was.

The certificate statement indeed corresponded to the third local position, the parameter seed also belonged to the same group as the first two, and the complete calculation log had been overwritten by the total hash of November 4th.

This at least ruled out the possibility of temporarily making a new file to impersonate old evidence.

Jiang Lin wrote the finding under P-094 while retaining the red status.

[Latest feedback: A candidate certificate generated prior to publication but not referenced by the public index has been located. Public reproduction continues to be temporarily blocked, the main theorem status remains unchanged, and we await independent verification of whether this object satisfies all conditions of the third local position.]

Gu Mingche looked at the red banner still remaining at the very top of the homepage: "The files have been found, why not take it down yet?"

"Finding doesn't equal checking."

"Very well." Gu Mingche pulled out the paper rolled up in his backpack's side pocket and flattened it out—it was precisely the five-hundred-dollar problem list from this morning. "Then I won't ask you to reimburse me for the soybean milk for now."

The two independent verification groups subsequently took away the candidate certificate from different portals and acted separately.

Group 1: Recalculate the decomposition type of the third local position.

Group 2: Bypass the original script, reconstruct the local extension directly from the parameter seed, and then rigorously check its correspondence with the marked set required by the tower lemma.

Jiang Lin was only responsible for providing the object numbers already existing in the frozen version, and absolutely did not answer what any intermediate value should be, so as to ensure the independence of the verification.

During the wait, more than two hundred comments flooded in under P-094.

Some used fierce language to demand an immediate retraction, some rationally argued that a wrong link did not affect the mathematical conclusion, and others attempted to conspiratorially deduce from the file generation time that Jiang Lin had known there was a problem here all along.

Gu Mingche left all comments without proposition numbers and page numbers in the public discussion area, and the seven inquiries that genuinely pointed out verifiable conditions were compiled into the attack directory.

Last night he was still worried about whose fault it would be if others discovered that the letter D was used twice, and now the answer was clearly laid out on the table.

The link pointed to the wrong place—his fault.

"After N-017, I only checked the page number jumps in the main text and attachment directory; the hash index was generated by the publishing script." Gu Mingche tapped on the keyboard, writing halfway through the index errata, paused for a moment, and deleted this sentence of explanation. "Forget it, write the scope of responsibilities and missed inspection locations in the public record, don't write defenses."

"Agreed."

"Can't you be polite and say this isn't entirely my responsibility?"

"It's not solely your responsibility."

"That sounds more like you're preparing to add a few more people to take the blame together."

Gu Mingche listed the release script maintainer and himself into the error responsibility field, and listed Jiang Lin separately as the handling person in charge.

Who was responsible for modifying the index, who was responsible for re-verifying the mathematical objects, and who was responsible for repackaging—each occupied a row, clear and distinct.

At 3:00 PM, the first verification group sent back their results.

The third object indeed corresponded to the missing local position in the index, and the decomposition type was consistent with the statement in the main text.

After quotienting out the corresponding Frobenius element, the lower bound of the generator rank remained unchanged.

But they still refused to take down the card, because Group 2's reconstruction starting from the parameter seed was still lacking the final class group calculation.

At 3:52 PM, the school's official website added a temporary update at the very top of the original statement, fully quoting the P-094 status, and changed the morning's sentence "no blocking items have been found as of the current time" to "there is currently a public reproduction block."

At 4:56 PM, the last grid changed from gray to green.

Group 2's independent reconstruction yielded the same decomposition type, confirming that the candidate certificate matched the complete conjugate orbit, and all three local conditions were fully satisfied.

The submitter of P-094 personally re-verified the records of both groups and solemnly added a conclusion beneath the original inquiry.

[Verification conclusion: The mathematical objects have existed since before publication; the issue stems from the third row of the public index repeatedly pointing to the second certificate. The current inquiry no longer blocks public reproduction.]

Jiang Lin still waited until the verifiers from both groups had all signed off on their respective scopes before actually opening the frozen release directory.

The repair action was minimal, modifying only a single index.

Changing the third row link from the hash of the second certificate to that pre-existing third hash, the main text, parameters, proof objects, and calculation logs were left completely untouched.

The new version number changed from v1.0 to v1.0.1.

Index errata R-003 remained permanently on the home page of the attachments as part of the academic record.

[R-003 permanently established: The third row of the local decomposition table erroneously and repeatedly cited the second certificate, causing the third local position to be un-reproducible independently via the public directory.]

[Scope of impact: Consistency between public index and versions.]

[Impact on main theorem: Through two groups of independent reconstruction, currently none found.]

At 5:06 PM, Jiang Lin restored the public reproduction status from a temporary block to independently readable, while the main theorem column still maintained controlled verification passed and external review continuing.

That red banner had only stayed at the verification portal for three hours and forty-three minutes.

But it was captured in screenshots into news, forums, and countless chat groups, and was faithfully recorded in the paper's version history.

From now on, anyone who opened R-003 could clearly see that a wrong link had once brought the entire public reproduction path to a standstill for over three hours.

After finishing the modification of the last directory jump, Gu Mingche let out a long sigh of relief and leaned back against the back of his chair.

"Can I now apply to upgrade my work-related injury certificate into an accident report?"

"Your name is in R-003."

"Thanks, your comfort can always be filed away directly."

The trash bag by the door was still in its original place; Jiang Lin picked it up to head downstairs, but a new email came into the public mailbox.

The sender was the combinatorial mathematician responsible for maintaining an electronic archive of Erdős problems.

The other party had attached Jiang Lin's preprint, public attack directory, and this red card record under the unit distance problem entry. The status still hadn't been changed to resolved; it only changed from a standalone open problem to a pending-verification problem with a candidate counterexample.

The email attachment was a page of the updated problem list.

Beneath that original line of the $n^(1+o(1))$ conjecture, an extra line of small text added on November 7th appeared.

[L. Jiang, claimed counterexample, verification in progress.]

The five hundred dollars at the end was still marked in its original place, and the bonus status remained unpaid.

Gu Mingche pulled out the old version printed in the morning from the desk and looked at it side by side with the new version.

"Should I throw away the old one?"

"Put it into the version history." Jiang Lin didn't even turn his head.

"I knew it."

Gu Mingche picked up the stapler, and with a 'click', stapled the old version, the new version, and the R-003 report that bore witness to the three-hour-and-forty-three-minute storm together, stuffing them back into the increasingly thick public verification instructions on Jiang Lin's desk.

The five hundred dollars was clipped in the very last page, continuing to await the next round of inquiries.