“There you are!” Carter Walsh excitedly yelped as he wrenched open the second to last door of the hallway. He’d had to wait three and half hours to finally reach this door, and before that almost four years in addition. Obviously he couldn’t hold himself back even if he did care about the strict rules of the Graduation Expo’s protocol.

Sprinting carelessly across the short room Carter wrapped his daughter into a tight hug, “Look at you, you look so grown up. We missed you so much.”

“I missed you too dad.” Katie laughed patting her father’s back a few times before forcible dislodging him in order to restore the proper order.

“This is silly, but fine,” Carter said with a shake of his head as he pulled a business card from his pocket. “Hello, I am Carter Walsh and I represent Walsh Complex Array Foundry as Chairman as well as the Bureau of Magical Usage and Ethics as a Chief Inspector.”

“That’s better,” Katie said with a huff, righting her clothes as she took another glance at her father. “You’re serious?”

“Hmm?” Carter grunted curiously as he glanced between himself and his daughter. “What’s wrong?”

He couldn’t quiet understand what his daughter was asking about, but she had a strangely doubtful expression on her face.

“So, what do you think of my creation?” Katie again prompted with a raised eyebrow. “You’ve been looking at examples of it for almost two hours and you couldn’t notice once? That can’t be…”

Carter was struck with a further confusion as he hadn’t seen even a single array in any of the previous rooms, yet she made it seem like he’d been struck in the face by her handy work since the very first room. “Was it the glowing cloth? But that’s— I suppose if there’s multiple stacked layers with pathways in-between then a—”

“No… Dad,” Katie said, shaking her head as if she too shared his guilt. “We were doing it wrong.”

“Excuse me?” Carter questioned, subtly shaking of his head as if he’d heard her wrong. “I understand since I once stood in your position, but it’d be wise to learn to reign in your ego.”

“It’s not my words.” Katie sighed with an understanding nod. “It’s not something I can explain in fifteen minutes obviously, but trust me, not as your daughter, but as a fellow graduate, our overreliance on two dimensions is a limitation to the possible power of complex arrays.”

“You’re quoting to the speaker.” Carter responded as he heard his own words come from his daughter’s mouth.

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“But you didn’t solve the problem. You just started adding band-aids.” Katie responded, again with words that hadn’t been her own original realizations, but something she’d become convinced of by another. “Real three dimensional arrays are possible. And they don’t require array stacking or transposition. We were hobbled by the crutch. Rafael’s wands use skewed arrays that work almost identically to their flattened equivalents, Haruto’s robes use a flexible array that can block anything under a sixth level mage, Ana used a multi-tiered array imprinted along lengths of silver tube to minimize the size and complexity of her projector lenses, and I helped in the recasting of Jun’s furnace to better transmit heat. Also, it’s entirely etched with a concave array that uses narrowing capillary lines as a heat shunt th…”

“I get it…” Carter nodded, stunned, but not so unwilling to admit when he’d been proven wrong. He hadn’t noticed even a single array, yet every single project had been using them, it was incredibly embarrassing in a sense, but simultaneously a part of him was madly curious about how such arrays could be designed. “You’re a genius.”

“No.” Katie reiterated impulsively as she glanced to the left-hand wall. “You didn’t forget what I said earlier right?”

Carter detected the hidden meaning, so even if he wanted to continue hearing about the usages she’d found for her new array format, he was given no choice.

“I do remember,” Carter said, thinking back to the previous six people he’d spoken to in the hallway before her. All of them were clearly forces of nature that would have huge effects on the world, but he couldn’t spot a one that jumped out to him as to fit the message.

“You’ll know.” Katie said, revealing enough, but not outright saying that he’d yet to meet him. “I doubt anyone will bite, but just in case, please look carefully. And hopefully you’ll thank me later.”

“Ok—” Carter blankly said, still a bit confused about what his daughter was trying to do by going so far for another student.

“I knew you’d be unsatisfied, so take a look at this real quick while we still have a couple minutes left.” Katie said while pulling a few diagrams of arrays out for her father to consider.

“It’s just like our puzzles…” Carter laughed while retrieving the worksheet from his daughter. Quickly however the reminiscence departed as he became entranced in the strangely formed arrays that, in his mind, should not even be possible.

The first was rectangular and clearly ended with unfinished capillaries, the longer Carter considered it the more that dawned on him, it must have been the tiered array designed for the lenses Katie had mentioned. Wrapped around a silver tube the arcs would align, completing the flow, but this only drew more concerns to Carter.

With no constriction, it wasn’t possible to force an effect, it’s a fundamental rule of array design. There must always exist a smaller shape, which acts as a constrictor allowing an effect to take place.

That’s when Carter spotted the designs drawn beneath the first one, he’d thought it was simply a variation, but this had to be the inner-surface array that acted as a three-dimensional constrictor.

“Incredible,” Carter grunted in amazement as he flipped to the next blueprint which explained basics of ‘array skewing’. There was no way to describe it other than an entire new level of array design. It didn’t simply build on the fundamentals that Carter had set as the basics of three-dimensional arrays, it shattered them in exchange for a far better solution.

“You have no idea…” Katie laughed with a hint of sympathy.