Maybe HD Manip for Hajime?
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(Kouki is a 5D Isekai magnet)According to the explanation, hero referred to someone with the qualification to become the protector of the “World Tree’s Branch”.
In other words it was the same existence like the avatar of “World Tree’s Branch” like Aularodde, but in case of avatar, they also functioned as the last fortress, so they fundamentally were unable to separate from the “Branch”.
When the world’s balance was starting to go out of order due to internal or external calamity or due to conflict and the like among the lives of that world, the “hero” would shoulder the role of balancer as the hands and feet of the avatar.
That was why, when the avatar sought help and carried out a summoning, it would definitely get connected to the hero. Also, it was because the hero was an existence with the quality that the World Tree recognized, the hero was able to pass through the gap between worlds. Though as the side effect of that, when a hole was drilled open in the gap between worlds, most of the time it would also get connected to the hero. Ch 386
This abandoned capital didn’t actually exist anywhere within the real world. It had once stood where the sea they’d come from was, but the seal had transported it into a gap between dimensions. Basically, this whole space was a city-sized Treasure Trove.
And because the whale was also the product of that ancient civilization, it too possessed the power to transcend space and time. However, its power had been greatly weakened, so it could only transport people here once, and only people who visited the particular stretch of sea the capital had once been on. Meaning this was the only chance anyone would ever have to repair this seal. Restoration magic wouldn’t be enough to do it because a lot of the damage to the seal was too old to be realistically recovered. It would take more mana than anyone in the world possessed. Which was why the whale had needed to bring in people who could analyze the seal and rebuild it from the ground up, namely Synergists who could use creation magic. Not only that, Synergists with more skill and mana than either Hajime or Oscar possessed individually.
“So it brought you and Oscar-oniisan together even though you’re from different times, Daddy! It made a miracle!” p259
While they’d been traveling to Hajime, it had told them the gist of the situation. Apparently, the whale was the guardian of this destroyed city. Long ago, this city had been brought to ruin by the same monsters that were flooding out of the castle. Those monsters had actually been created by human hands, and the strongest of them made the nigh-immortal Hell Eater Hajime and the others had just recently fought look cute.
But, as it always went in stories like this, the people had been unable to control the monsters they’d created, and brought their empire to ruin. However, they’d at least had the tenacity and the good sense to seal away the monsters they’d created. But to do so, they’d needed to use the whale as a cornerstone.
Now, centuries or perhaps millennia later, the seal had been weakened to the point where it was nearly gone. If the lynchpin of the seal, the tower that the whale was fused with, broke, then the ancient evil horrors would regain their full strength and would start terrorizing people across all worlds and all times. p259
The fog rolled over the submarine, engulfing it. It was thick enough that people standing on opposite sides of the deck wouldn’t be able to see each other. It reminded Hajime of the fog in the Haltina Woods. Everyone quickly formed a protective circle around Myu and Remia. p212
Of course, Myu had no idea what the creature was, either. But it seemed she was sensing something from it. Something inside her was telling Myu that they couldn’t hurt it, and Hajime could tell from the earnest look in her eyes that she sincerely believed that. She just couldn’t express it in words. While Hajime was hesitating, their surroundings continued to transform. The whirlwind of mist sped up until they were surrounded by a wall of fog, making it look like they were in the eye of a storm. But the sky above them wasn’t clear, like it would be in a normal storm. It, too, was covered in swirling dense fog. But instead of sucking up the surrounding water, the fog hurricane was pushing it away, creating a crater in the ocean.“Does it mean to drag us down to the bottom of the ocean?”
“It’s strange... I can sense mana from everything around us, both the fog and the water.”
"Hajime-san, I think we’ll be okay! I’m not seeing any future where we die, at least!” p214
Looking down at his watch, he noticed almost no time had passed since the last thing he remembered. Hajime slowly got to a sitting position, careful not to push Remia or Myu off. p273
More energy=range
The interval is mentioned again
Shaking=weakened
The condition to travelling the realms is weakning the interval, but this is not the case for Hajime. Which is why a lot of characters who could travel them were surprised by this feat.