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While high-level examples are not common, mana constructs in general are far from rare. In the series alone, we have several examples. Jackets and Barrier Jackets are the most obvious and wide-spread, but Familiars, Summons, shapeshifting lineages and the Wolkenritter also qualify. The basic definition of a mana construct is a physical object or entity whose form is comprised out of condensed mana given physical definition. Certain Devices have mana construct parts, the most obvious being Bardiche's blade, though they also use extradimensional elements in their construction - a Device is generally considerably larger than its storage form appears to be. Low level mana-construct "objects" of this form are sometimes vulnerable to AMFs, though the closer to their power source they are, the more resistant they will be. Jackets, for example, are very difficult to disrupt with an AMF, as they are tied directly to the Linker Core and almost flush with the body, and thus benefit from the mage's natural resistance to adverse magics. This goes double for Barrier Jackets, which are hardened against this sort of chicanery.
The "material" of mana constructs is condensed mana, shaped and constrained by a program-pattern that describes them. This allows for effects and properties virtually unknown to Terran materials science, as they can be used to create objects that are strong, light and resilient, or which consist of mana patterns that guide electricity to make them highly conductive at easily accessible temperatures. Miracles are not possible, and more outlandish physical properties tend to require prohibitive amounts of power, but even with limited ranges, this quality of mana constructs allows for great breadth and variability in mechanical and aesthetic designs. Texture, colour, rigidity, conductivity... all these things and more can be adjusted with relative ease, given the right underlying structure. Much of the advanced technology that the TSAB uses includes mana-construct components which play a vital role in the functioning of the item in question. Forcefields are an obvious example, but the solid-state data storage they use includes internal mana-construct elements in the read/write apparatus, and the holographic windows used for data access and long-distance communication are mana constructs as well.
However, mana constructs are perhaps most impressive when they host an intelligence of some kind. The forms this can take are so many and varied as to be impossible to list. True Summons are mana constructs created from Lost Logia templates written into their summoner's Linker Core. Shapeshifting lineages, most originating from the Dawn States era, have in common the engineered ability to put their human form in an extradimensional pocket and assume a mana construct form of some sort - Yuuno, for example, who can turn into a ferret. The human and war forms of Familiars are mana constructs, as are the bodies of those rare surviving Belkan Unison Devices that still exist. The Wolkenritter of the Book of Darkness are yet another example, programs externalised from their progenitor-tome in mana construct bodies. Finally, and perhaps most impressively, the invincible War Form of the Sankt Kaiser lineage was a mana construct, shifting their human form into extradimensional storage and replacing it with a human-form mana construct matching their own adult body.
Whatever their source, mana construct bodies have several things in common. First, and most crucially, they are not biological. Their flesh, such as it is, is a convincing simulacrum formed from condensed mana. While many will have "organs" fitting the internal physiology of their form, they are non-crucial, and generally serve a role of acclimatisation or camouflage rather than vital processes. The War Form of the Sankt Kaisers is a notable exception to this rule, though by no means the only one - it was "solid mana" throughout, one of the reasons for its extraordinary resilience. The default appearance of a mana construct, as with Arf's chains, Yuuno's barriers or Fate's scythe-blade, is a glowing form of condensed light. More complex ones can alter this to look like normal materials.
There are multiple forms of form-generation. Some of the power-hungry types recreate the form from scratch each time, such as summons or the Sankt Kaiser War Form. These allow for instant repair simply by dismissing and resummoning the form, but it makes for an extremely mana-intensive process. Others, like Familiars and shapeshifters, simply compress superfluous forms into extradimensional space when not in use. This slows healing, as they must recover and repair themselves, but only requires a single enormous power surge at the initial moment of their creation.
The most noticeable element of mana construct bodies is the upshot of their lack of biology. Mana constructs are inhumanly tough. Their organs are superfluous, their consciousness delocalised. Wounds and trauma will damage their structure and the program-pattern that describes their form, eventually leading to dissolution, but this is nowhere near as fragile a balance as a living organism. Stabbing a mana construct through the lung will accomplish nothing more than to hurt them, they will not suffocate or go into shock, nor will they grow weak from blood loss or trauma. While enough accumulated damage will begin to slow and hinder a mana construct, this will not begin to occur until they have accrued significant damage to their structure unless their specific injuries prevent them from moving (for instance, a broken arm preventing them from wielding a weapon effectively). Mana constructs can, given sufficient time and energy input, recover from almost any would that does not kill them - a severed arm or a hole punched through them will eventually heal. They will not suffer a concussion from harsh impacts, as the damage from their brain hitting the inside of their skull does not affect their consciousness. Nor can they be winded, and while exhaustion will eventually set in, it takes much longer than it does for entities constrained by biology. A Sankt Kaiser's War Form was incredibly tough even before this came into play, their very skin acting like Barrier Jacket armour.
There are still limits, of course. No force of might or magic in recorded history has ever been invincible, and Olivie Segbrecht herself fell in battle. Apex summons can be destroyed, Familiars killed, and Barrier Jackets rent asunder if sufficient power and skill is devoted to the task. Here, then, are some of the limitations by which mana constructs are still constrained. Mana constructs are still bound by natural laws. Gravity, electromagnetism, inertia and mass - all these things apply to them, and they cannot escape the limits such laws impose. While a mana construct's physical properties may be variable, they are only so within limits, and that only if they are programmed to be. They can still be damaged, and enough damage will destroy them. They still need energy to repair their structure, either sourced from a Linker Core or from food.
The latter is an option for those with internal organs, which chemically break down food not for its sugars and proteins, but rather to extract mana as a byproduct of the reactions. For shapeshifters, damage will not carry across forms, but nor will it revert instantly on changing back and forth - the structure of their injured form must be repaired or healed at normal speed. Vesta's bruised ribs, or the injuries to Yuuno's human form, encourage them to spend time in a different form and eat large amounts while they heal. Mana constructs still feel pain, though many can dull or even entirely disassociate this sensation. They are also energy-expensive. An awful lot of condensed mana is packed into their forms, and creating and maintaining one is a difficult task, especially for something as high-level as a Familiar or an apex summon.
Overall, then, mana constructs are a potent and useful tool, and a sapient one is no small thing to dismiss in battle or labour. They have drawbacks, and are far from a solve-all tool, but they are ubiquitous for a reason.