Carlos sat on his rented bed and adopted a meditative pose as he focused inward on what his introspector could sense about the state of his soul. He thought back to the inspection Lady Telrar had done. She had followed a consistent procedure for both himself and Amber, and presumably that procedure had reasons for how it was designed. She had specifically looked for soul structures from eight points around the horizontal circumference of his soul, plus one on top and one on the bottom. What might that imply? More concretely, what could his introspector detect that might be related?

Well, for one thing it suggested that soul structures were arranged in a consistent set of locations within the soul, and that the soul had a shape that supported that arrangement. What was the shape of his soul, anyway? He hadn't really given it any thought before, but his introspector found that answer with trivial ease. His soul, though intangible and immaterial, was shaped as a somewhat flattened oval disc, radially symmetric but wider across than it was tall.

The next question was what internal details that shape might have, inherent to the soul itself rather than to the structures he'd made. Now that he was looking for it, Carlos easily sensed a demarcation dividing his soul in half... And more demarcations dividing the halves into quarters, and the quarters into eighths, all arranged like slices of a pie. Each section contained a soul structure. The eight sections also tapered their vertical thickness towards the center, leaving sizable extra regions above and below, which of course were where the other two structures were located.

Carlos opened his eyes and looked over to Amber, who was also quietly sitting still on her own rented bed, contemplating something. "You said platinum rank with its eight structures gets a special boost in power, right? Think that's because of filling the circle of the soul's outer sections?"

"Outer sections? What? Wait..." Amber paused for a few second. "Huh. I never knew about that, but I can sense it too. Yes, it makes sense. Shouldn't we be focusing on why we don't have 45 synergy links, though?"

Carlos shrugged. "That's important, certainly, but there's no need to rush, and having more knowledge in general is always good. Extra pieces of knowledge can sometimes lead to surprising insights."

"I suppose." Amber shook her head slightly. "I'd rather fix the problem at hand first and indulge my curiosity later, though."

"Fair." Carlos closed his eyes again and returned to examining his soul. On the topic of synergy links, he wondered how this newly discovered layout of the soul related to synergy limitations. Newly discovered for him, anyway. Whoever designed that inspection process must have already known of it. What made it so hard to go beyond eight? Presumably there was something special about those top and bottom slots, but how did it relate to synergy constraints?

He mentally prodded his introspector, considering the question, and thought back to what Amber had explained about why synergy was necessary. She'd said synergy let soul structures be packed closer together. He had assumed that meant just a generically decreased separation distance, but that didn't mesh with the soul having discrete sections.

Carlos considered the first soul structure Lady Telrar had examined, his mana sensor, and the mana manipulator right next to it. He could sense a bond stretched between the two structures, and it truly was stretched. There was a pressure pushing the structures apart, and the link of synergy between them was resisting that pressure, holding them together in adjacent sections.

He moved part of his focus to the next structure around the circle, his spells preparer, and examined the link between it and his mana sensor. This bond was longer to cover the distance between the non adjacent structures, but it was loosely relaxed. Any pressure between those structures was negligible, diminished to nothing by distance.

Carlos turned his attention to the bottom section, and the spells activator located there. He checked that structure's various synergy links, and found that all nine of them were stretched tight. The bottom section, and the top section too, bordered all eight of the pie slice sections, and there was a small gap in the very center where the top and bottom sections touched each other like they were reaching through the hole of a donut.

"I guess that answers why going beyond eight is so rare," Carlos muttered.

"Hmm?"

Carlos looked over at Amber. "Oh, I just figured out why mythril rank is so unusual. You need a soul structure that has synergy with every single other soul structure you have."

Amber nodded. "Ah. Makes sense. On another topic, if you're done investigating curiosities, I think I've found the problem with our number of synergy links."

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"That's great! What is it?"

"Well, I was checking each pair of structures for synergy links, and when I got to the spells database and mana sensor, the link between them feels thin and weak."

Carlos frowned and checked that same link in his own soul. Sure enough, it seemed frail. There was much less mana in that connection than there should have been, so little that it felt like a bare thread that could snap at any moment. "It's the same for me. How do we fix it?" He could probably move some mana into that link with his mana redistributor, but that didn't feel right.

"Lady Telrar mentioned something about activating potential links, right? That has to be something generic that anyone can do, and we've apparently already done it without even realizing it for most of our links. Maybe it's like the final step of making a soul structure - actually use the synergy to solidify it permanently."

"Hmm." Carlos tilted his head slightly, thinking. "A lot of our synergies are so natural that we'd use them automatically just as part of using the soul structures, so that would explain the links we do have properly established. Spells database and mana sensor is one of the more dubiously contrived synergy combinations, so it makes sense that we missed it." He nodded sharply. "I think you're right, and that means finishing the remaining links will be tricky. We'll have to turn my dubiously hopeful logic for them into reality."

"Yeah. Though, I already did one more than you. Which ones are you missing?"

Rather than individually inspecting each one, Carlos posed the question to his introspector, and the answer popped into his mind a moment later. "They're all with the spells database and linker. Those two are each missing links with the mana sensor, manipulator, and reflex improver."

Amber paused for a couple seconds, then nodded. "Same for me, except that I do have the link between spells database and mana manipulator."

"You had both of those for a while before you met me, right?"

"Yeah."

"Right. I think you must have made it by casting spells directly from the database because that was all you had back then, while I missed doing that by having other structures in between in the spellcasting process. Hmm. I might be able to temporarily bypass the other structures to make that link, but it would be better to make it something that I would use regularly afterwards."

Amber nodded again. "Just having a link at all will improve how quickly and easily your soul develops, but the direct effect of the synergy has to be used to be helpful. I should see if I can change that link too, if we can manage it."

"Yeah. I think we have some more urgent things to take care of first, though. Finding someone to teach us more spells may not be possible in, what was it, Darma?"

"Dramos. But yes, mages willing to teach are scarce in frontier towns. Here in Kalor City, though, I know where to find plenty of potential teachers."

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"So this is the royal mage academy? The school you had planned to attend?" Carlos looked up, and up, at the vista of grand towers, well, towering over him. The tower in front had a glittering facade covered with innumerable lines of inlaid metals, some angular, some smoothly rounded, and all of them packed with mana. It reached towards the sky, almost rivalling some of the skyscraper buildings Carlos remembered from Earth in both height and width, and a dozen lesser but still impressive towers were arrayed behind it. Several elevated walkways stretched between towers at the lower and middle heights, but at the very top Carlos instead spotted a few people simply floating through the air from one tower to another.

Amber grinned at him. "Yep! We're actually not far off from when I was planning to be here to take the entrance exam. Ooo, will they give us a tour? I'm so excited to see the place, I just wish I could stay!" She skipped up to the front door, a massive edifice of stone and metal inlay, raised the knocker fastened to the door's center, and slammed it enthusiastically.

A complex wave of structured mana swept over her, part of it lightly tapping the surface of her soul, and a low male voice spoke in the flat droning of profound boredom and annoyance. "We're not accepting student applications right now. Come back in two months."

"We're not here to apply as students!" Amber knocked again, harder, and another wave of mana swept over her, identical to the first.

Nothing more happened for a few seconds, and then a transparent image of a disembodied head, lined with wrinkles and topped with sparse and graying hair, appeared just in front of the door. It glared at Amber, and spoke gruffly. "What do you want?"

Still almost bouncing on her feet, unfazed, Amber grinned even wider. "I am Amber Carlos, and my companion here is Carlos Founder. We are looking for a mage instructor to work with our fledging house."

The image narrowed its eyes at her. "Oh really? New nobility? What is your soul rank?"

Carlos spoke up, feeling he shouldn't be left out of such a conversation about the house he founded. "Adamantium. Tier 8. With potential to activate more synergy links."

The image turned to look at Carlos and a third wave of mana came from the door, this time sweeping through Carlos and lightly tapping his soul. "Hmph. You can't have had that for long, with how undeveloped your souls are. Surface layer compressed only once? You could get that just from making your soul structures alone with that many of them!"

Carlos raised an eyebrow. "Was that somehow not already implied by the newness of our nobility?"

The image scowled and glared at him for a few seconds before the scowl broke and released a small chuckle. "Heh. Kid, you have no idea how new nobles normally develop, do you?"

Carlos looked at Amber, and she blushed slightly and stammered. "It, um, I never really thought about it much."

The image laughed. "And yet you somehow devised an adamantium soul plan anyway. Alright you two novice geniuses, come on in!" The image faded, and a section of stone the size of a normal double door disappeared with it, revealing an old man in a blue robe standing behind it. His face looked exactly like the image had. He clapped his hands together and nodded cheerfully. "I have to say, you two aren't the craziest thing I've heard of, but you're pretty high up the list. I'm curious what other gaps you have in your education."