Empirical insights into Rina's magic: a comprehensive examination.

As Rina is likely to remain by my side for a long time, I shall document everything I learn about her. These entries will cover the results of experiments I will perform on Rina, as well as my conclusions and hypotheses.
The scientific rigor may vary, and my thoughts might occasionally digress a bit. Still, I shall try my best. I ask of you, my future self, that you select the most pertinent parts and that you write an updated version later on.

I must admit, the manner in which I forced her to abandon her home to accompany Cyne and me makes me feel as though I have abducted a child. She is still only twelve years old, after all.
Most branches of the Guild will consider her an adult because the consensus holds that mental maturity aligns fairly well with outward appearance regardless of the species, but it still does not feel right to me.
Rina may be treated as mature, but she lacks the life experience of a real adult. It is not even as though her perception of time is any different from mine. 
I wanted to talk to her parents but, from what I understand, she has been living alone for quite some time. Before she was considered to be of age in this kingdom, even. As she made it clear that she does not wish to talk much about her past, I shall refrain for now from asking her directly. Whether Rina's parents have passed away or she ran away from them, this subject appears to be taboo. I do not want to make her uncomfortable after I forced her to follow me.

In any case, I shall study the different aspects of Rina day after day. By putting them on paper, my goal is to understand what her magic is truly about and to discover a solution for her life-threatening condition.
It goes without saying that I will prioritize understanding the latter.

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Nolcya the 9th, 1257

Mana leak

So, Rina suffers from an odd condition similar to mine - she passively loses mana from her body at a constant rate. Though her loss occurs significantly slower than my own, her mana recovery rate is abysmally low. It is to the point that Rina loses mana a bit faster than she can recover it. By my estimations, she would fall into a state of mana deprivation after approximately four days without aid.
It should be noted that this duration only applies in the case she does not actively use magic. Otherwise, she might die in just a day because of her low mana pool.
A regular mana potion per day appears to keep her condition in check. Fortunately, Serena has agreed to provide extra potions, as those we produce are of such high quality that Rina would require only a portion of a vial daily.
I intend to deliver Rina's mana injection myself every day while I stockpile excess potions so that she can survive even when I am away as per my noble duties. To that end, I have finished preparing a spell adapted to her peculiar mana-neutralizing property. This will have to wait until I have confirmed we are dealing with neutralization, however.

While I do not have any evidence yet, my hypothesis is that this mana leak is related to that strange property.
This is the next aspect I shall analyze.

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Nolcya the 10th, 1257

Neutralization

One of the goals of this empirical study is to analyze the neutralization ability exhibited by Rina.
In order to do this, the first thing I had to do was confirm this is really what this phenomenon is.
To that end, I estimated the half-life of three different groups of mana with the same density that I trapped into my pendant.
I do not have the absolute certitude that we are truly dealing with perfect neutralization, but I have yet to see any decay from my mana after a full day within this cramped space after it was affected by Rina. In comparison, the chemically-induced neutralization made my mana decay by 15% in the same time period which suggests a half-life of about four days, while my regular mana degraded almost entirely in only a few hours within the empty artifact. Its half-life appears to be only a few dozen minutes.
Although these results will need to be affined in the following days, they heavily corroborate the perfect neutralization hypothesis for the time being.

This phenomenon, which I will call neutralization for now given the evidence I have, does not actually happen in contact with Rina: it comes from her mana. It only seems like this property arises from her skin because of the constant leak.
This confirms that she had been emitting a bit of mana even before I activated her veins. What other explanation would there be for her use of my mana to protect herself from a sword if she was not emitting anything in the first place?
In any case, the neutralization propagates through mana at an astonishing rate. The most notable thing is that this property is contagious. When it has been neutralized, even my mana gets the ability to neutralize foreign mana.

Therefore I surmise that it would be quite unwise for any mage to assimilate this neutral mana, as it would contaminate their mana veins. Afterward, any mana that leaves their hands would be perpetually neutralizing itself, becoming uncontrollable.
Fortunately, the lack of control when mana loses a mage's signature would make it near-impossible for someone to accidentally absorb the neutralized mana.
No, there is actually a way for a mage to inadvertently contaminate themselves. Since spells are still active even after mana has been neutralized, this means that mages who use for instance some sort of mind-reading magic would be affected. They would emit their mana normally, have it pass through Rina's mana barrier and get it neutralized as a result, enter Rina's brain, exit it, and then come back inside the mage's brain, therefore contaminating their own mana circuitry.
Well, I suppose it is not that big of a deal if their mind-reading spell is still working in the same way even with neutral mana; it is not like they need to manually manipulate it in the air.
No, that would actually be a problem... This would even be absurdly bad. With their mana that now perpetually neutralizes itself, mind-reading mages would afterward contaminate all their targets by making their contagious mana enter their bodies and brains, spreading this neutralization epidemic wildly.

I might need to address this issue alongside the mana leak.

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Nolcya the 11th, 1257

Momentum Lock

What would happen if an unstoppable force met an immovable object? That scenario is a famous paradox and anyone defending one side or the other does not truly understand the situation. Logic permits only one possibility: that the two cannot coexist at all.
An object that remains unmoved regardless of the forces exerted upon it must possess infinite inertia, which is the resistance of a system to change in motion. Infinite inertia in turn requires infinite mass.
Meanwhile, an object incapable of being halted by any obstacle must also boast infinite inertia. It is easy to understand that it leaves no further mass to allocate. Thus, the two cannot exist concurrently.
However, if an object could be granted infinite inertia, it could fulfill both roles. I believe this illustrates the crux of Rina's abilities. Naturally, her measly mana pool cannot possibly provide the energy to create an infinite resistance to change in motion. Increasing her inertia would necessitate generating inertial mass, which would require unimaginable quantities of mana.

Rather, my hypothesis is that her spell acts on what is sometimes called inertia in motion: the momentum. That value is a vector with both a direction and a magnitude. It can be seen as a quantity of motion. To alter momentum, a force must be applied over a certain period of time, which is called an impulse. This comes from the impulse-momentum theorem that can be derived from Newton's Second Law of Motion.

Therefore, my theory is that her magic counterbalances impulses trying to put her in motion when she is motionless. On the other hand, if Rina is already in motion when her spell activates, it will oppose any impulse attempting to make her accelerate, decelerate, or simply change her trajectory.
In this manner, she embodies both the immovable object while at rest and the unstoppable force while in motion.

I suggest the name 'Momentum Lock' for this spell as it appears to analyze the net force of the targetted system at the instant of the spell's activation before proceeding to protect the system's momentum from any external interference.
Besides the constant emission of mana, 'Momentum Lock' expends mana only in proportion to the impulses it must negate, rendering it remarkably efficient energy-wise. This is especially true when compared to my own costly kinetic armor which needs a constant recast of a kinetic-to-mana conversion.
Moreover, since the main goal of Rina's magic is to forbid any perceivable change in motion, the counter-impulses are applied so fast that the process is seemingly instantaneous, without any delay. I believe my magic has much to learn from Rina's.

While this purely classical model appears to successfully explain Rina's magic, I am omitting an important detail. Although no external force should be able to alter Rina's motion as long as she has mana, it appears gravity has an effect.
In particular, if Rina gathers enough mana on her hand to activate 'Momentum Lock' while she is punching the air, her hand will inevitably follow a parabola toward the ground, even though it is opposing both air friction and the drag of her body, forced to follow after the punch. Her hand will even oppose the forceful impulse applied by the ground trying to slow her down, to the point that her hand starts to penetrate the surface. Of course, Rina's hand cannot travel deep into the ground because she cannot mobilize too much mana in her hand.

I am fully aware that gravity is typically considered to be a non-impulsive force, meaning it is not associated with an impulse. After all, the force of gravity is constantly applied and would mess with calculations.
However, gravity being ignored for simplicity does not tell us much about why Rina's magic is neglecting it. 

I have to acknowledge the possibility the spell is overlooking this force in order to save up mana. To begin with, it seems optimized for short activations.
However, and this might very well be my obsession with this branch of physics, I cannot help but think that 'Momentum Lock' might not consider gravity as just any standard force. In this certain branch, it really is not.
 
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Nolcya the 12th, 1257

It appears Rina has taken a particular liking to flowers. Just today, she gazed at the ones in front of the Guild for an hour straight. Perhaps it provides her solace in these difficult times. I shall buy her the biggest bouquet in town.
If she has to stay close to me even when I quit being an adventurer in the future, maybe I could employ her as my servant and let her take care of the garden.

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Nolcya the 13th, 1257

It appears I will go back to the capital sooner than I expected.
As I thought, piling up mana potions for this kind of unforeseen circumstance is a good idea.

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Nolcya the 14th, 1257
 
Four-momentum Lock?

When Rina shuts her eyes, she perceives straight lines. This is consistent with a magic type that lets her retain her trajectory through space regardless of the obstacles in her way. However, as was previously discussed, gravity curves her trajectory. There appears to be a divergence.
Or, does it? What if, instead of being lines in space, they were lines in spacetime instead? What if the model that best describes Rina's magic was not found in classical physics but in General Relativity?

What is gravitation? In Einstein's theory, it is defined as the curvature of spacetime caused by the presence of mass and energy. This means that a satellite orbiting a planet is not actually moving in a circle in the traditional sense. In the curved spacetime, the satellite is following what is known as a geodesic — the closest thing to a straight line. To us, this path appears curved because spacetime itself is distorted.

This relativistic framework suggests that Rina's magic follows the geodesics, i.e.— straight lines curved by the very geometry of spacetime. If we use the same example as in one of the previous entries, her punch does follow a straight line, which just happens to be distorted by the mass of an entire planet.
In addition to elucidating the trajectory discrepancy, it also resolves the energy issue. As Rina's punch gradually strays from its initial path, the magnitude of its momentum changes, and the kinetic energy increases. If we introduce the concept of four-momentum, the relativistic version of the momentum, it works out.

This is to me the most elegant explanation for Rina's magic. Anything that tries to make her diverge from the geodesic her spell expected will be opposed as long as there is mana. That includes any weapon hitting her, or any obstacle meeting her path. Whether 'Momentum Lock' counterbalances four-forces or forcefully reapplies her registered four-momentum as soon as her trajectory starts deviating by a few microns, I cannot tell. It could even be that I am looking too much into it and the impulse generation is sufficient to explain everything.

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Nolcya the 15th, 1257

The cons of Rina's magic

While this spell has a lot of potential, it is proving harder for Rina to master her magic than I expected. For one thing, her spell activates whenever a sufficient amount of mana comes into contact with her epiderm. By that, I of course mean any mana since it gets neutralized.

While this might sound like a good thing, as with that time I saved her life by chance, it can be an enormous disadvantage in combat.
Anyone who knows the conditions for the activation of Momentum Lock can mess with her. If she's motionless, enveloping her with mana will freeze her in place, whereas doing it while she's moving will force her to continue her trajectory until she eventually crashes on the ground depending on the area affected by the mana.
As I have tested it, I can say this is not just an assumption. She was utterly unable to touch me, even though I was not enhancing my movements in any way.
Moreover, since she is constantly emitting mana, she eventually reaches the threshold herself and just freezes if she is immobile for too long.
She can of course break through her spell considering the low amount of energy involved, but she still panics when it happens. This is probably the reason why, out of nowhere, she would move from one side of the table to another in the middle of a meal.

As far as I understand it, the only way to cast a spell is to, well, actively cast mana with a spell. This does not explain much but I at least have never heard of spells that are cast automatically when a condition, in this case having enough mana density on the epiderm, is verified.
Investigating this "condition" for the activation of the spell reminded me of those I usually put in the spells I develop myself, which led me to the following hypothesis: perhaps this activation is not actually one. Perhaps this condition is already part of the 'Momentum Lock' spell that is constantly being cast.
If this hypothesis is correct, I would be inclined to think her constant mana emission is also part of that spell.

This implication is concerning regarding the nature of my own condition. If Rina's mana leak is part of a spell that needs a certain amount to reach the next step and perform magic, how does it relate to me?
... Did I unknowingly cast a dormant spell that has been waiting for sufficient energy, forcing me to ceaselessly emit every day the equivalent of several times Rina's mana pool? What sort of unfathomable spell would necessitate so much mana that even 'Ortu Solis' does not reach the threshold when I conjure it? 
On reflection, I am not sure I want to know. As long as I periodically reclaim my emitted mana and halt 'Ortu Solis' before that terrifying condition is verified, all should be well. 

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Nolcya the 16th, 1257

Spells and extraneous mana operations

As of today, a spell is described as the implementation of a magic type and is the lowest-level action a mage can perform with the assistance of its magic type. If it is 'Fireball Creation', then the corresponding spell will perform mana operations in such a way that the emerging result, called magic, is the generation of a fireball. Since this is an example of a restricted spell, such a mage can base more complex and unassisted workflows only on top of that spell. They will never be able to gently light a candle because the fundamental spell is hidden within a multitude of mana operations.

Spells tend to keep their implementation simple, with only operations that contribute to the end result. The reason is likely to be the minimization of mana consumption because every operation has a cost.
However, there is no immutable law that prevents the inclusion of extraneous mana operations in a spell, such as having the mana shape itself into the Aphrodite of Milos before turning back into a sphere and then resuming the fireball spell's normal execution.
I suppose that, in an analogous way to how entropy statistically disfavors ordered combinations without necessarily prohibiting them from occurring spontaneously, spells tend to go right to the point with the simplest mana operations.

The implication of this conjecture is that a spell can - theoretically - exhibit properties that do not seem related to the magic type upon initial examination.

I know for a fact that it goes beyond mere conjecture, though, because I can integrate any mana operation I want into a spell. This includes autonomously displacing mana, condensing it, or even applying conditional operations.
Well, I am not capable of asserting that those "algorithms" I implement are identical in nature to innate spells. Though it would appear they are at least similar if we go by the usual definition of magic being the reality-bending phenomenon brought upon by a spell.

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Nolcya the 17th, 1257

I realize that my initial assessment of Rina's personality was not accurate. I thought she was quite introverted, almost more than me, but it appears I misjudged her. Yesterday, as I walked with her in the city, every single child we met knew her. It is not even that she stands out in the streets, because she usually hides her ears. If anything, I stand out much more... In the end, I ended up standing like a houseplant while she was leisurely talking with kids and even remembering their names. Even the vendors called out her name. Is she in reality a complete extrovert? Why is she not like this when she is with me? Is she adapting her behavior depending on who she is with? Is she... an ambivert?
Why did I even document this particular observation again?

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Nolcya the 18th, 1257

A first conclusion

I shall summarize the important points I have thus far learned about Rina.
- Her spell, 'Momentum Lock', locks the momentum of the body parts she targets.
- This magical effect occurs when sufficient mana contacts her skin.
- Due to a condition similar to my own, she passively emits mana from her body at a constant rate.
- Her mana possesses the ability to completely neutralize other mana on contact. It has now been more than ten days since I started experimenting on my mana after it was touched by Rina, and I have not measured any decay since then. Its half-life may very well be a few months, years, decades, or centuries. It might even be greater than the age of the universe for all I know.

I am about to propose a tentative hypothesis that connects these disparate attributes.
I spent hours in the library, both in the city and in the manor, to find some clues that would back my hypothesis up but I unfortunately found nothing. Maybe Serena would know more about this subject, but I am afraid she would lose her sanity over Rina's neutralization ability.
In any case, here is my hypothesis: some people, maybe only beastfolks, might possess a talent that lets their original spell gradually evolve over their lifespan while retaining its fundamental nature. If it concerns only beastfolks, it would make sense that this ability remains undocumented, because few individuals bother spellcasting within their lifespan due to their lack of mana.

In a similar way to how more restricted magic types develop spells that envelop themselves with more mana operations than with a versatile magic type, Rina's spell might have adapted over time by adding different layers of mana operations. It would have made her spell more restricted than initially, but it would also have made it easier to use.

Perhaps the earliest iteration of Rina's spell simply locked the momentum of any system, or maybe it was already restricted to her epiderm. Over time, it might have adapted to be constantly active, primed to shield her as soon as she mobilized her mana, with minimal delay.

Without any consequent flow of mana from Rina, the spell may have mutated once again to tap into her internal reserves and have some mana at the ready.
Realizing even this was inadequate because there was not enough mana to reach the activation threshold, it may have progressed even further by harvesting mana from external mages. To bypass compatibility issues, it likely mimicked the mana veins' passive neutralization. By neutralizing exterior mana and using it as its own, the spell therefore guarantees optimal chances for the magic to occur without relying too much on the caster.
At last, I activated her mana veins, which made the mana emission strong enough to freeze Rina in her sleep.

It should be noted that if such gradual evolution really occurred because of Rina's lack of mana and her veins not being activated, her spell might eventually return to its original form by removing some of the additional mana operations like the troublesome mana leak and potentially even the neutralization property. After all, now that she is able to quickly mobilize her own mana on her epiderm, the only useful feature of her spell is the constant casting that makes it extremely reactive.

I do hope the leak comes to pass so that she may freely determine her own future, unburdened by her spell.
When I told Rina about the possibility of her being able to leave Phesiora within a few years, however, she snapped at me and ran to her room. 
After thoroughly replaying the scene in my head, I believe she thought I was trying to get rid of her. We only met about ten days ago, so I have difficulty thinking she is already attached to me. Maybe it is something akin to Stockholm syndrome and she has developed some sort of psychological bond with me, her captor. That Destiny talk might have made things even worse by implanting in her mind the idea that there is a grand reason for everything that is happening to her. Or maybe it is her canine-like instincts that prompted her to choose me as a master to remain loyal to.
I am not interested in having a slave at my service, though. I want her to choose her own path.

This concludes the first phase of my analysis concerning Rina's magic, which also provides some insights into her as a person.
I shall continue documenting everything I learn about her.

Alice R.