The Klein bottle was not truly a “bottle.” It was a visual representation of spatial curvature. Xiao Yu’s plan was to distort three-dimensional space into the shape of a Klein bottle and use its unique characteristic, having no distinction between inside and outside, to pass through the Four-Dimensional Barrier without destroying it.

In Xiao Yu’s design, the bottle’s body would exist within three-dimensional space, while the junction of the bottle’s mouth and body would lie within the Four-Dimensional Barrier. In this way, the connection between the mouth and the base of the bottle would occur via the fourth dimension. Once constructed, in theory, all Xiao Yu needed to do was enter the bottle from either the mouth or the base and travel a set distance. After restoring space to its original flat form, he would have emerged on the other side of the Four-Dimensional Barrier. It was that simple.

The principle was simple, but construction was incredibly difficult. Building a Klein bottle required massive amounts of calculation and energy: space curvature, required energy, precision of travel, alignment with the Four-Dimensional Barrier, any mistake in any of these aspects could result in catastrophic consequences. At best, the mission would fail; at worst, the ship could become stuck on the barrier, half of it having crossed through while the other half remained inside. Given the properties of the Four-Dimensional Barrier, if such a situation occurred, the part of the ship that remained inside would be randomly teleported back into the system, meaning the vessel would be torn in two. Naturally, any ship caught in such a state would be destroyed.

It wouldn’t matter as much if it were some irrelevant ship, but if the Hebei were split in two, Xiao Yu would be doomed. Even if it were just a City-Class ship destroyed, it would still represent a major loss for Xiao Yu.

Under his command, thousands of Luka scientists launched into action, and Xiao Yu himself fully dedicated his mind to the calculations.

Xiao Yu planned to first build a small-scale Klein bottle as a test.

He began by constructing a series of instruments powered by elemental decay. With this energy, the instruments could distort space under Xiao Yu’s direction to the necessary degree.

Building the instruments themselves wasn’t difficult. Xiao Yu had already gained sufficient experience and technology from developing Faster-Than-Light starships.

Calculating space curvature and assembling the instruments consumed a full year. Even with his personal experience of Four-Dimensional Space and a deep reservoir of related knowledge, calculating such models drained tremendous computational capacity. This was the cost of a three-dimensional being attempting to glimpse the secrets of the fourth dimension.

But Xiao Yu’s efforts were eventually rewarded. After one year, all the calculations were complete, and the instruments were fully constructed. Then came the most critical step of the entire operation.

How to construct the most important structure of the Klein bottle inside the Four-Dimensional Barrier, how to connect the mouth to the base without passing through the body.

One of the properties of the Four-Dimensional Barrier was that any matter in contact with it would be randomly teleported back inside the star system. This meant Xiao Yu couldn’t place any physical instruments inside the barrier. But he found another way: using the gravitational influence of Gravitational Bombs to shape this key structure.

Through two previous large-scale Gravitational Bomb tests, Xiao Yu confirmed that the Four-Dimensional Barrier could still be affected by gravity, or more accurately, by space curvature, since gravity’s essence was the curvature of space. With a method to influence it now available, everything else followed. Through precise calculations, Xiao Yu manufactured a large number of miniature Gravitational Bombs. He would use these bombs to exert influence on the Four-Dimensional Barrier and carve out a passage inside it through which the bottle’s mouth could pass.

Once all preparations were complete, Xiao Yu began the critical phase of the project.

“Bombs Three, Sixteen, Nineteen, and Eighty-Five, detonate… good. Bomb Seventy-One, detonate. Next is Bomb Fifty-Six and Bomb Three Thousand Five Hundred and Three…”

Muttering as he worked, Xiao Yu manipulated tens of thousands of miniature Gravitational Bombs to detonate with millisecond-level precision.

As the bombs exploded, slight bulges appeared on the formerly smooth surface of the Four-Dimensional Barrier. Within those bulges, a passageway was gradually being formed.

Simultaneously, the space curvature instruments began their operation. They needed to connect with the Four-Dimensional passage as soon as it was open. A moment too late or too early would result in failure.

Fortunately, Xiao Yu’s astonishing precision and speed of calculation ensured the experiment’s success. Amid the cheers of more than two thousand Luka scientists, Xiao Yu allowed himself a small sigh of relief.

A small-scale Klein bottle had finally been constructed. Its mouth, through four-dimensional restructuring, had connected with the interior of the bottle—its base—without passing through the body.

In front of the instruments Xiao Yu had set up, a pitch-black opening had appeared. The reason it was so dark was because the Klein bottle’s entrance and exit were one and the same, forming a loop. Any light that entered could never exit again. And since it produced no light inside, it appeared utterly black.

The gaping darkness looked like the mouth of a ravenous beast. Whether what lay ahead was rebirth or destruction, Xiao Yu did not know. But there was no turning back.

Under his control, a specially constructed satellite drifted forward and, under the gaze of thousands, entered the opening.

The moment it crossed the threshold, it vanished from Xiao Yu’s view, because it had entered a twisted space. This twisted space absorbed all light, similar in nature to a black hole.

From that point on, everything depended on calculations and the satellite’s onboard autonomous systems.

“Flight time: three seconds,” Xiao Yu murmured. “Three… two… one… zero. Alright, shut down the space curvature instruments. Restore spatial flatness.”

The instruments powered down. Without the immense energy sustaining it, the curved three-dimensional space instantly returned to normal. When it did, Xiao Yu found that the satellite had vanished without a trace.

That left two possibilities: either the satellite had successfully passed beyond the Four-Dimensional Barrier, or it had been randomly teleported somewhere inside the star system.

Xiao Yu had long anticipated this outcome, so he remained calm and simply waited.

Inside the satellite was a preset program. Thirty seconds after entering the Klein bottle, it would automatically broadcast a message. This signal would allow Xiao Yu to determine its position.

If it remained within the star system, Xiao Yu could locate it through that broadcast. And if it had made it past the Four-Dimensional Barrier, the barrier’s property of allowing signals to exit would still permit him to receive the message.

The moment drew near. Those thirty seconds felt like divine judgment on doomsday, placing everyone who knew the truth on edge.

When the thirty seconds had passed, Xiao Yu’s instruments deployed in space received the signal exactly on schedule. He immediately began analysis.

Over two thousand Luka scientists waited, breath held, for Xiao Yu’s verdict, a message that would determine their fate.

This entire project had consumed three years of effort. Xiao Yu had only ten years left. His fuel reserves could only last another five. That meant if this attempt failed, neither he nor the Luka people would get another chance.

Xiao Yu’s four-dimensional interface trembled as he fed the data into the analysis program, awaiting the final judgment.

After just one ten-thousandth of a second, he received the result.

“This satellite is currently located… seven billion, six hundred and forty million, three thousand two hundred kilometers from the central stellar mass!”

“Whew.” Xiao Yu exhaled gently.

At this moment, the distance between the Four-Dimensional Barrier and the central stellar mass was seven billion, six hundred and forty million, three thousand one hundred kilometers.

The satellite’s distance was greater than that of the barrier.

The result was clear, the satellite was now outside the Four-Dimensional Barrier.

In the great hall, Xiao Yu’s projected figure slowly turned. His face expressionless, he opened his mouth.

“The result is in. We… have succeeded! The satellite has successfully reached the other side of the Four-Dimensional Barrier!”

His words exploded through the hall like a thunderclap. For a moment, there was terrifying silence, full seconds passed before any sound returned.

But those first sounds weren’t cheers, they were sobs.

Luka Three and Luka Four, the two most brilliant scientists, collapsed to the floor, as if all strength had left them. Their faces were covered in tears. Gazing up at the ceiling, they murmured, “We did it… we really did it…”

Sixty years of struggle! Countless efforts, sacrifices, and sleepless nights had finally yielded the reward they had dreamed of.

“We did it! We really did it!”

In that moment, the grand hall became an ocean of joy. After the initial shock passed, thousands of Luka scientists jumped up cheering. Their voices were still choked with emotion, their faces still wet with tears, but their expressions were those of joy, joyful laughter.

They jumped, laughed, and embraced one another. Xiao Yu, too, couldn’t help but smile.

This was a celebration of rebirth, a celebration of relentless effort finally being rewarded.