It was done. The final equations had been calculated. He had referenced all available magical theory limitless times. All indications had confirmed his hypothesis that what he was trying to do and would be successful at was feasible. He had checked over the contents of the final steps several hundred times. The hundreds of books he had read since committing to this line of magecraft had been absorbed of all knowledge in order to complete this Formula. He had the tools now. Shirou Emiya would definitely succeed.
Magical Formulas were the established methods made through calculations of complex mathematics, science and astrology as well as magical theory that would create a system that would take over the responsibility from the Magus in casting the spell. They were a common part of magecraft but were also not often created.
To create a Magical Formula is to effectively create a new realm of magecraft. It was to act as a foundation for the spells that would be involved within that magecraft. Most commonly used Magical Formulae had been there for centuries, refined and perfected. To create a new Magical Formula would normally be a century long project. The spells supported by this new foundation would be too weak otherwise. Only the most ambitious of Magi even harbored the thought of creating a Magical Formula. None with the same intentions of Shirou.
While all Magi had their own version of personal magecraft different from the mainstream, they mostly adapted them using current Thaumaturgical foundations for use. Others stopped pursuing that line of magecraft and pursued something more practical, like elements. Others created Mystic Codes to manifest their Magecraft. It would be too absurd a thought for most Magi to even undergo the effort of specifically creating a new Magical Formula just to actualize their own personal magecraft. Shirou was not most Magi.
Through using a Magical Formula in casting a spell, the Magus need not dedicate any mental nor physical resources towards it. There were no caveats on concentration, calculation or anything required to carry out the spell. There were no physical sacrifices needed as in rituals. All that was needed was an adequate amount of magical energy.
A requirement to using a Magical Formula to cast a spell was to use an Aria. This was not an exception that Shirou had been able to avoid. His Magical Formula had required an Aria as well. This was not a problem for there was no real harms to having to chant the Aria in his goal. The Aria required for the incantation had only required one sentence and count anyway.
Arias or incantations were a type self-hypnosis cast on the Magus. The regular use of an Aria is to place a mind of a Magus in a state in which the control on the Magical Circuits is greater than ever before. Allowing for more magical energy to be produced in both input and output. A greater advantage was to be able to shape the Magical Energy produce by a Magus to unprecedented extents, allowing them to actualize the spells that were supported by the complex Thaumaturgical theory.
What an Aria did, was place the mind of a Magus in a more passive and controllable state, allowing for the Magus in that instant, to be able to use the complete resources of the human brain beyond the constraints of mortality in order to be able to actualize more complex effects by bringing out temporarily, a higher potential from the soul of the Magus to compensate for the mind being too weak to comprehend the basic aspects of the complex Magical Formulae.
Shirou's Magical Formula was no different. In order to make his spells stronger, he had to bring out a stronger and purer version of the concept he was using. It would normally require him to mentally comprehend all aspects and the implications of using the concept. This took up massive mental resources and would be impossible once Shirou used a concept with greater potential behind it.
As such, Shirou wasn't currently able to use higher level concepts. The creation of this Magical formula for his spell would solve this issue. This would allow him to be able to use higher concepts at a greater power level while using a low amount of Magical Energy. This would also ensure the success of the spell as long as he had enough Magical Energy.
Creating a Magical Formula for his spells also served an unintended effect to his spell. While spells were typically of fixed power unless more magical energy was provided, Shirou's ability was as a result of his Origin. The link of his soul to the Root. Through using of an Aria to draw out more potential from his Soul, in theory, the greater strength of his soul and thus greater connection to the Root at the time of casting would greatly enhance the power and limits of his spell.
This was the key reason why his Spell was able to be actualized using the Magical Formula with only a one count incantation. Spells had an inherent stability based on their Magical Formula and Thaumaturgical Foundation.
Powerful spells were less stable and required many counts and phrases in order to be able to stabilize the mystery and carry it out smoothly and successfully every time.
Less powerful spells or Spells with a more stabilized Thaumaturgical process and Magical Formula were very stable and thus could be actualized easily just with minimal phrases and a quick shaping of magical energy.
Shirou's spell would normally be extremely unstable due to his Magical Formula being a new and untested, optimized system. It would also be weaker due to its lack of inherent mystery behind it, with its only user using it to actualize his personal magecraft. Using this new Magical Formula would normally require an absurd length of time in order to chant the phrases in order to carry out the spell. However, due to his Spell requiring the drawing of concepts from the Root, by bringing out the greater potential of his soul for the moment of chanting the Aria, he was able to widen the connection of his soul to the Root and thus actualize the concept he was using more easily. This allowed the spell to be extremely simple and stable thus only requiring the basic minimum count in order to hypnotise himself to draw out the power from his Soul.
Now that he was about to try the spell with the Magical Formula for the first time, he felt that his mind had gone blank. He was unable to think of an Aria of enough significance to power a hypnosis powerful enough for what he wanted to do.
Arias or incantations were not normally chanted towards the outer World, for the environment to allow its effects. Rather, Arias are chanted towards one's inner World, the soul of the Magus. Due to this, in order to the Aria to be of sufficient power to hypnotise the individual's soul they must be full of meaning and importance to one's Soul. They must reflect the nature of the individual's spell or Soul in order for them to be effective.
This was what Shirou had been caught in. He had to choose an Aria of personal significance to him in order to actualize his soul. Shirou stood there thinking, pondering. He had already stood still for half an hour and yet he was still lost. He couldn't stand here forever. What use would the creation of a Magical Formula be if he couldn't use its effects due to his incompetence? As he got more and more desperate, like always, the instincts ingrained in his Soul provided him with an answer. His lips instinctively revealed its deepest facts from his Soul.
"May the Truth foist its burden of significance upon me"
The Aria was not a command. Most Magus tended to prefer to activate their spells with a command as an Aria. Shirou was different. This was not an Aria. This was a desperate plea. It was a plea from his empty Soul. Lacking of significance even with a cause to pursue. It was fitting. A concept was a meaning. A reason of existence. It fit that the only way he would be able to activate his spell would be to borrow a meaning that filled his lacking Soul, giving his Soul true significance.
The entire shed that was the Magical Workshop in the Emiya Residence lit up. It was currently dead silent in the middle of the night but there was an intense white light that shined out from the few openings of the shed. Six white Magical Circles manifested from both his arms. Three at each side. They were of a pearly silvery color that had a pretentious brightness.
The Magical Circles were atypical in which they were not enclosed around his hands nor at the tips of them. They were instead around his hands, rotating, revolving and not in any way connected to his limbs. The Magical Circles were a pearly silvery white but were also translucent with square patterns within the circles orbiting around his hands.
The system was activated. Now if everything had gone well, he could impose whatever concept onto a foreign object and have it take effect without a smidgen of thought. Shirou looked around the shed. There were no objects of note. If he wanted to test his success, he would need to impose a sufficiently powerful concept to know the degree of his supposed new limits.
He wasn't quite sure what he would test his new system on. That was the problem with devoting every part of his life to a goal. He didn't quite know what to do with it once he had reached a part of it. Sure, he knew perfectly what he wanted to do. He wanted to immediately use a concept counter to the Curse and nullify his father's condition and have the spell be effective.
If only it was that straightforward. He could only revisit what he knew. He had new limits. They were unknown. Were they powerful? Supposedly so. Were they powerful enough to defeat something backed with the legend of a Heroic Spirit? He didn't know. He had to work his way there though.
An idea drifted through his mind expecting to be dismissed. He had almost done so as well. He had kept the idea though. It might be absolutely stupid and foolish for him to carry out, but if his spell worked, there would be no issues. All it came down to was the degree of trust he had in himself.
Did he trust his own Magical Formula to work? An untested Formula made by a Magus with no official Magical education? Even if he failed, did the effects of the idea even matter if he had already failed in his goal?
Trusting in himself, he projected a nameless steel sword from his journey to the museum several years back. The sword was not anything special but it would do what he required. With no further hesitation, Shirou Emiya ran himself through with the sword. As Shirou was thrusting the sword into himself, he activated the spell that was now supported by this new system.
What he felt was his Soul or mind leaving the current reality into a hazy and misty dark place of nothingness. The environment was empty but it was somehow also full of meaning at the same time. What this new environment projected was the feeling that there were infinite possibilities now available to him. By instinct, he drew a portion of the mist towards himself. It was a mental representation that his mind had provided him with in order to be able to activate what he wanted.
In that hazy misty place that his mind had took him, the Mist was the representation of the limitless concepts that existed within reality. He took the concept he required in the world and dragged it away from the main body of the Mist. He was drawn out of that place and in his disorientation, Shirou found that he was still where he left off in the midst of what could be considered a suicidal move.
The sword was a plain double-edged straight sword able to thrust and slash with equal effectiveness. It was of average sharpness for a typical sword and it had pierced through him as he expected. The sword came out from the back of his back. There was minimal resistance as it speared through him. That did not matter.
The sword currently stuck through Shirou did not matter. What mattered was that he was successful. The sword was within him and if there were ten more of the same swords that pierced him, he would look like a pincushion. He would still be fine then.
There was no blood. The sword had gone through the center of his body under his rib cage. It had gone through his liver. Where was the copious amount of blood that was supposed to be flowing out of him like a fountain? Where was the pain that Shirou was supposed to be feeling? Where was the weakness that would strike him at any moment as the consequences from the wound?
What had happened before Shirou had considered stabbing himself was that he had recalled his research on mythological feats and thought up of an experiment sufficiently demanding enough to prove what he wanted.
Some Heroes across history were said to have been invulnerable to weapons. Invulnerability. That was a powerful concept. Invulnerability itself would be impossible to utilize as a concept before. It was simply too hard to comprehend. Agelessness and being impervious to harm was the maximum what most people assumed and comprehended. There was more to this concept than most individuals thought.
There was still the mind of the Individual. While that might be invulnerable from the outside, what about mental issues? Would they still take effect? What about the Soul? Would that be invulnerable too? Invulnerability was not a simple concept to comprehend. It did not even matter the inherent power of such a concept. It would be impossible to actualize if one did not comprehend the implications. Not all concepts were equal.
This was why invulnerability was nigh impossible to achieve with magecraft. Resistance from harm and extension of life was possible. No one ever got as far as invulnerability. Even the most ancient and powerful Thaumaturgical Theory did not currently provide the possibility to actualize invulnerability to any degree.
What Shirou did was to cast the concept of 'invulnerability against bladed weapons' onto himself. What his new system did was to utilize his own comprehension of the concept. If he were to attempt to utilize this concept without his system, it would be impossible from the mental strain alone. He would have to comprehend all possible interpretations of both the concept of invulnerability itself and all possible interpretations of bladed weapons. Even with the strain, the spell would not succeed before and he would now be bleeding and dying on the floor of the shed.
Such a difficulty from trying to impose a concept was unneeded. He only needed to achieve specific and general effects from the concepts. He need not need to know all the conceivable possibilities. He only needed the spell to utilize the inherent essence and spirit of his motives that was his personal perception of the concept.
His spell was successful. He pulled the sword out. His sword exited his body cleanly as the area took away by the sword rearranged themselves to their original places and configuration. Upon the complete exit of the sword, he observed that there was no difference to his body at all. There were no scars nor scratches. He was invulnerable to the sword. For all purposes, he was just another sheath for the sword.
The energy that the spell took was significant but not extreme nor was it crippling. That was expected. He had not provided Magical Energy beyond the minimum required for the concept to manifest. A sword that contained even basic reinforcement would be able to draw blood and penetrate his organs.
This was due to the inherent basic mystery of Magic within the Magical Energy inside a reinforced sword. It countered his concept which was also based on Mystery. He could scale its effectiveness up however. With his current level of Magical Energy, if he used his maximum output, the spell would scale to extreme levels of high Thaumaturgy and anything short of a true Noble Phantasm would not be able to hurt him.
This was what he wanted to achieve. Would he be able to defeat a Curse currently? No. Even with his complete output, he still couldn't overcome a curse with the mystery of a Heroic Spirit behind it. Especially a Curse that was likely some sort of Noble Phantasm. This was no big deal. He was past his greatest hurdle currently. With more practice he would be able to reach the level he needed within the year.
If he repeatedly practiced the spell to grant him the 'invulnerability against bladed weapons' currently, through the continuous practice and activation of the concept, he would naturally gain a better perception and comprehension of the concept. This would allow him to impose greater parts of the complete concept in its entirety every instance he used the concept and with its greater purity be able to achieve the same effect with less and less Magical Energy provided every time. In reverse, if he continued to provide the same amount of Magical Energy, the spell and concept would be more and more powerful each time he used it.
What mattered was practice. He was over his greatest hurdle now. His goal was within sight. There were no other factors limiting him. He had finished his Magical Formula. He had overcome the problems so far. Now the only limit was time. He had enough time. He was optimistic. What could go wrong now?
He did not have enough time. Shirou was currently in school. It was a currently a few months after the start of the year. As this was their second year as students, the teachers had decided that they should challenge them with a different assignment instead of just regular exams. What the teachers had decided was to give them a major project to accomplish that would settle their grades for the year.
It was a combined project that involved aspects of all the subjects they took. It was a massive project that was not to be done in school. It was supposed to be done in pairs outside of curriculum time. Predictably, he had partnered up with Rin for this project.
This project had not come at the best time. He was currently making good progress through his goal. While this wouldn't be a major setback that would hinder his goal such that he failed it, Shirou would prefer there not to be any setbacks at all. Rin was excited about this project. If it didn't hinder him, he would say he had some interest in it as well. It was also an interesting project by itself, ignoring the harm to Shirou's progress to his objective.
As he looked to the side to who was now also his project partner, he recalled a promise he had made years ago. A promise that had almost slipped his mind. Since this was a project they had to do after school, this was also an opportunity to finally make good on his promise.
"Rin, you should come over to my home."
"What? What! Shirou! You can't just phrase things like that." Her face reddened as she looked around quickly to spot if anyone had heard the improper words that had came out from the mouth of her project partner.
"What? I just wanted to introduce you to my parent." he replied confusingly, clarifying his intention to invite her over to the Emiya Residence for the first time.
"Shirou, shouldn't you invite a girl for a date or something before reaching that stage? It is a bit fast isn't it?" Rin now assured that no one was listening in or paying attention to them, had decided to change her tactics to tease Shirou.
"What? Oh. No! No! No! You know what I mean!" He had finally realized what was wrong about the way he had phrased his invite. Trust her to reverse the situation to her amusement with his ineptness in such situations.
"Of course, I know what you mean. I am not sure the rest of the school will though if anyone had heard your question." Rin looked at him more strictly this time. It was a warning to be more aware next time before he blurted out something that could be interpreted in the wrong way.
"It's just that I have been over so often so it would only be appropriate to do this project at a different place this time." He sighed as he tried to phrase his thoughts in an appropriate manner. They were friends now. Friends went over to each other's places.
"If it is fine at your side, we should start as early as possible, after school would be the best." She inquired, not sure about how comfortable her friend was with the situation being in reverse. She herself had just gotten too used to him being at her home.
They would leave school early. Shirou had handed in his book review and had 'completed' his club activities for the day while as long as Rin had finished her responsibility as part of the student council, she would be free to leave. She normally stayed in school longer for other aspects of her role but she knew her friend had wanted to make optimal use of their time.
They made their usual way out of the school. The route to the Fuyuki Bridge was the same from the school. As opposed to the perils of traveling to school in the morning, the streets were quiet and there were less cars on the road. Everyone was currently at work. It would be a few hours yet before the earliest of office workers would leave work and populate the roads.
While the Miyama District was more of a housing district, there were still some office buildings after the bridge crossing from the Shinto side of the city. With the offices there were also other high-rise residential districts.
They were currently walking on the same main road that led to Fuyuki bridge through the Miyama District. Normally, they would get to the Tohsaka Mansion by turning left into a smaller street just as they passed the high-rise portion of the city and the structures gradually became shorter. It was a different story to lead to the Emiya Residence. Shirou had found that it was faster to pass through the Shopping district of Miyama before turning right into a smaller but long stretch of the street that led to the intersection that connected the Emiya Residence to the rest of the city.
As they walked through the street, Rin observed the surroundings gradually changing in architecture to suit a more traditional Japanese style of building instead of the European style of her side of the district or the modern high-rises that populated the center of Fuyuki. Walking further along the street provided the same pattern but the styling of the houses had gotten older and older. Just as they were about to reach the intersection, Rin noticed that most of the modern indications of the current age on the styling of the houses had completely disappeared. If it wasn't for the modern roads they were walking on or the clothing they were wearing, Rin would have thought she was in the nineteenth century.
As they crossed the intersection, they turned right. Shirou could already see his home in the distance. It was still some way however. The two sides of the street were different. On his right, there would be walls surrounding older Japanese residences much like the ones he lived in. On his left, there was a grove of trees too small to be even called a forest or wood. They were natural. A part of the city that has never been touched for centuries since their development. There were no paths inside for any type of park or navigation. They were just a natural part of the environment, untouched in the city planning thus far.
The Emiya Residence was surrounded by a thick wall made with stone, wood and bricks. The wall was of a decent height, half a dozen meters tall. They were topped off with brick tiles. There were trees that surrounded the actual property within the walls. The tips of the trees were peaking over the walls.
The wooden door that granted access outside the walls was unlocked. Shirou pushed the door open, walking through while Rin followed his lead. The door had made a creaky loud noise as it opened. As Rin stepped in, she was greeted with a large open space with a concrete path that led to the main building.
The property was vast. Even just the main building alone had dwarfed the entire Tohsaka Mansion and Matou Mansion combined in land area. It was a traditional Japanese property that could not be truly called a mansion but fulfilled its definition by its vastness. The property had only a single level with all its rooms spread out across the large property.
The front door of the main building was made of wood and paper. Shirou opened it by sliding it to the left. The entrance of the Emiya Residence was a narrow hallway made out of wood and plain white wall paper. There were two doors to the left that were used as storage and four different cabinets to the right that served as more storage.
The only direction beyond the hallway was towards the right. Before they walked down the hallway, they removed their shoes and place it in a wooden cabinet towards the right of the front door. They turned right and Shirou knocked on a wooden sliding door before sliding it open and gesturing for both of them to enter.
The room that they entered was the living room of the Emiya Residence that also doubled as a dining room. There was a Kitchen at the back of the room. It was smaller than the kitchen in the Tohsaka Mansion but it was still of average size. There was a single cabinet at the side of the room. In the centre of the room was a short legged wooden table. Sitting by the table was a figure in white robes reading from a scroll. There was a cup of tea on the table in front of him.
The figure was skinny and looked a bit haggard, He had black spiky hair that was left unstyled. He had a small stubble of black hair on his chin. His eyes were a vacant empty black and his face was blank with stress lines.
He put down the scroll he was reading and his body seemed to change entirely in demeanor once he heard the door opening. He looked more alert and less stressed. He raised his head to look at Shirou with a kindly and affectionate expression at odds to his previously blank one before his eyebrows seemed to raise slightly upon spotting Rin.
"Oh, Shirou you are back. Who is this young lady with you?"
"Kiritsugu, Rin is a friend and classmate from school. As we have to do a major project for the year results, I suggested she come over."
"Mr Emiya, it is a pleasure to meet you. You may just call me Rin."
"It is a pleasure to meet you too Rin, you may make yourself at home."
"Kiritsugu, we will be in the dojo to do our project. Is it fine if she leaves after having dinner later?"
Kiritsugu nodded. With the permission granted by his father, the pair exited the room on the way to the dojo. The Dojo was down the hallway after several rooms where the hallway was no longer surrounded by wooden walls but rather with clear glass panels. Walking alongside the panels, they came to a spot overlooking the yard.
Shirou brought her to a door that led to the yard. As they crossed the yard to get to the dojo, a large building at the back of the Emiya Residence, Rin felt a faint trace of magical energy in the direction of what looked like a rickety old shed made with concrete walls. What Rin felt was not energy from the bounded field which was a foreign magical energy, presumably the work of the elder Emiya. It was an energy more familiar to Rin. It was Shirou's magical energy.
Rin thought that the shed must have been the place which her friend had used as a Magical Workshop. It was the only area that was suitable for one. The rest of the house was too open which allowed the natural magical energy in the world to flow too freely and uncontrollably. Only the Shed which was a made with a more rigid type of construction would be fit for such a use.
They entered the dojo. It was a large building with ample space for any type of physical activity. It was a plain room with wooden panelling throughout the vast length of the room. There were several kendo sticks at the side of the room. As both of them got into the room and left their bags at the side, Shirou activated his magical circuits and created a bounded field on the entrance of the room.
Rin could easily recognize what type of bounded field it was just by its energy signature alone. It was a warning type bounded field which would warn Shirou when the door was about to open. It was suitable for their conversation they were about to have. While it was unlikely they would be barged in on, it was best to be cautious. As Shirou finished setting up the bounded field, they looked at each other. They were both silent. Rin decided that she would start first.
"He couldn't sense that I am a Magus."
Shirou nodded. It was why he felt fine with inviting Rin over. His father would have known something was up if he knew Rin was a Magus. That was why he had not provided Rin's family name in her introduction. Without his Magical senses, there was no way he would know Rin was a Magus if he had not provided her name. It was not overly suspicious to not give her families name. The only thing it indicated was that Shirou and Rin had a closer relationship which was true.
"He has an extremely faint trace of magical energy; it was of the same type that made up the bounded field of the house. His magical circuits must have not been in use for a long time for me only being able to sense him from several meters away."
Shirou nodded again. "He hasn't done magecraft for a while now. I think his magical circuits have been too dilapidated to work. A couple more years and I think that his magical signature would fade away entirely."
"He had quit his job several months back. He said that he felt that it was time to retire but I don't think he was in any state for a job anymore. He is still just currently in his thirties." As he said this, she saw that Shirou was looking down and was clenching his fists. While she had believed him and placed her faith in him for two years now, this had proven his motivations. It was her responsibility as a friend to spare him from this subject. Before it had a resolution, it would continue to hit him hard.
"I suppose you have already kept your promise and proven your words... Lets not dwell on this matter any longer... Let's start our project, shall we? I don't suppose anyone else would be able to do better than us."
Rin had said this to give both of them a way out of the conversation. Shirou had already proven himself, not that she needed him to after knowing him for a while now but it was also better to get out of this conversation and gloomy atmosphere. She was sure that Shirou would take her cue as he would prefer to finish the project as fast as possible anyway.
It took several hours to work on their project. They had stopped working on it when it was about time for dinner. They would still have to work on the school project for at least a week yet before they would be able to complete it. They both led themselves to the living room where Shirou walked towards the back area of the room to prepare dinner. Rin had tried to volunteer but Kiritsugu had refused and forbidden Shirou from allowing her to help by stating that it was discourteous for her to help cook on only her first visit.
While Kiritsugu was not a talkative individual, he had still made idle conversation with Rin. The conversation was surprisingly normal. He asked her about their school and their experiences. He had also questioned her about her friendship with Shirou in which she invented an alternate possibility as to how they met in school. It was surprisingly domestic for three individuals who currently was or had been active Magi. Shirou had even chimed in the conversations once in a while.
Kiritsugu was relieved. Contrary to what he knew of his son's social skills, his son had managed to make a friend in normal circumstances. It was the one positive of the situation in his life. He was glad for his son. As much as Kiritsugu would tell himself he didn't mind it, he would acknowledge that loneliness was a terrible sensation to wish on any human being, Magus or not.
His son had a support system now. Taiga would always spare her time for Shirou if he had needed it, Shirou was currently in school and in regular contact with his similar aged peers and Kiritsugu now had definite proof that his son had managed to make friends. From what he had observed from their interactions, they were rather close friends even. Such would be individuals whom Shirou would be able to rely on. While Kiritsugu had made some arrangements, it was better and more organic this way.
His life had gone terribly thus far. Every action and cause in his life had somehow gone wrong. Not everything about his existence was pointless however. The boy he had saved and adopted as his son after the fire was proof of that. He was proof that whatever had gone wrong with his life, all the sins he had accrued, there was a single individual that he had saved and that was enough. That was all the hope was needed.
He had abandoned so many things in his life. He had abandoned a life with his father even with his sins, he had abandoned a different life with his mother figure even with the potential consequences and he had abandoned his heart in order to try to obtain salvation for the world. He had abandoned everything he had or could possibly have enjoyed so far. It had not been for nothing. If nothing else, Shirou Emiya would be his legacy. It was the best possible one he could have left...
Authors Notes:
We Start the chapter off with Shirou Emiya finally finishing the Magical Formula that would allow him to save Kiritsugu. Most of this part is just lore about the detailed Magical system that this story follows as well as what a feat it is for Shirou to create a Magical Formula.
About the Aria. I wasn't quite sure what would not sound terrible but I just decided to go for something vaguely meaningful. Basically it is the meaning of the process of the spell as well as Shirou at this current moment. What the spell does is basically use Shirou's connection from the Root to draw forth the concept. He draws from the Root or 'truth' in the Aria the shell or 'significance' of the concept and he uses his own magical energy to actualize the shell of the concept. Basically, Aria kinda describes his life right now as the Root/truth provides him with concepts/meaning for existence while he is also actively trying to find meaning in life at the same time.
After succeeding in the spell now with a Magical Formula behind it, he needs something to test it on. Whatever he is trying to test on needs to have two requirements. He needs the concept to be complicated to see if it has the same limitations and he also needs the concept to be powerful to some degree to see if he can achieve more with effectively the same magical energy as before. I could have him do something else to test the results but I think this strangely fit him as it is not being actively suicidal but rather his confidence in his own abilities and determination for his goal to succeed.
More lore and justification on why Shirou does what he does as well as the Magical Theory involved within. We also now know how close to the goal he is and what he needs to be able to complete his goal successfully.
Immediately something goes wrong as he is suddenly limited on time. This is the troubles of being in school for Shirou. He already knows most school material from having to learn it for magecraft but now he has to do an assignment that will take up lots of his time. Fortunately, he is doing it with Rin but still it is quite troublesome for him.
He remembers his promise and attempts to make good on it. He is still rather socially inept in communication so Rin takes the opportunity to tease him on it. Rin knows the rumors in school about them and she doesn't really care but she does want the current state to be the extent of those rumors so she warns Shirou to be careful.
Rin travels to the Emiya Residence for the first time and has a brief meeting with Kiritsugu and we learn about his current state just as Shirou complete his Magical Formula to hopefully defeat the curse when he masters it to a sufficient level. Rin delivers her observations on the situation and then we finish the chapter by seeing what Kiritsugu thinks of his son actually having friends now.
This portion is actually not the resolution of Rin's trips to the Emiya Residence but it was getting too long so I decided to split this portion of the chapter and continue it on the next chapter. It doesn't really effect the flow since the other parts of this chapter will flow slightly better if it is separated anyway but just a heads up that there will be some more of this.