[@Fisticuffs]
[sub]There are a few things that can happen, depending on which set of laws of physics you are basing the summoning/conjuration on: the physical laws or the magical laws.

In the physical laws, mass is conserved. Therefore, the sword can either be created using nearby matter(manipulation/creation) or summoned(transported from one location to the other).

Creating the sword via manipulation can work by drawing out the carbon and/or other metals from the surroundings and condensing them into a single mass. The "Creation" method would likely use Earth magic, but may require background knowledge on the periodic elements.

Summoning the sword will likely be more difficult, as it would require the sword to be broken down into energy, transferred, and rearranged into its previous state without any loss; the existence of magic will likely help in achieving this. Alternatively: the distance between point A, where the object currently is, and point B, where the object is being summoned to, can be shortened by manipulating space until the points meet, making the transfer instant. The "Transference" method likely uses Aether magic, as it can manipulate pure energy(like light)and move it along a path. The "Blink" method likely uses Void magic, as it requires space itself to be manipulated. Both are(in my opinion) significantly more difficult to achieve than the "Creation" method.

If we assume that summoning/conjuration follows magic's laws, then the sword "does not exist"; mana does not have matter, and is merely used to imitate the properties of matter.

Therefore, in order to use the "Conjuration" method, one must have an exact understanding of the properties of the object being summoned; living creatures are much harder to summon, as the ego is not so easily imitated.[/sub]
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[sub]Mana exists in two states, "Law" and "Chaos". Mana in the Law state is usually bound to physical objects(gems, people, etc), and will often cause atmospheric mana to shift towards Law. As a result, beings with sensitivity towards changes in mana can detect when a presence with a high Law characteristics(in other words, objects with large amounts of stored mana) are nearby. Atmospheric mana will always be in the Chaos state. However, there are exceptions to these rules that result in certain phenomenon.

In order to cast magic, Law mana inside the body must be agitated into the Chaos state. The Chaos mana is then expelled from the body, centered around a Law "core". However, the Law mana that makes up the core is unstable due to not being bound to anything physical, and thus the "image" of the spell becomes necessary for the magic to travel any significant distance. One's ability to visualize the core often determines their aptitude towards certain types of magic.

(Summoning is unique in that summoned objects or creatures are separate from the image of the caster--they themselves are the concept used to shape the mana. Summoned creatures' self-conscious existences are similar to that of the Deorum--concepts with egos, albeit less powerful.)

Normally it is impossible to bind Chaos mana to an object. However, there are two exceptions:

By engraving certain symbols on an object, it is given increased Law characteristics that forcibly anchors Chaos mana to it. The symbols also provides "imagery" to the mana, similarly to how reading a description can invoke an image in one's mind. Should any of the symbols be damaged, the stored mana will explode(Summoning circles must be perfect, or else the summoning will fail).

The existence of monsters are the second exception to the rule. Chaos mana will shift violently while confined to a vessel; if the vessel is living, the mana will cause rapid growth, creating a monster. For this reason, engraving symbols onto a living being is considered a forbidden magic.[/sub]
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[sub]well, it goes something like that
(I guess)[/sub][/sub]