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[Clarification of an XY Problem]

I am currently developing a world with a hard magic system based entirely on manipulating the natural order of reality in accordance with physical possibility. As long as the ultimate end-state of a magical act results in a universe that continues to follow physical law, and the intermediate states are well-defined enough to be abstractly formalized, the only barrier to magic is how much energy is expended in the process.

Naturally, simple alchemical processes like the spontaneous synthesis and transmutation of matter is possible in this system, so material currency, especially metal coins, wouldn't be impossible to create from scrap material to a sufficiently powerful mage. The shape and design of such coins could also be flawlessly reproduced for someone who has dedicated enough effort into analyzing, memorizing, and codifying the design as an arcane formula.

My question isn't exactly how to deter, prevent, or detect counterfeiting of currency, but rather a sold-state physical/material question:

What physical material would be the hardest to synthetically reproduce at an atomic level through physics-based magic

The factors at play:

  • It is physically impossible to create an object through arcana if its composition is not sufficiently well-understood to be codified into a magic formula
  • The amount of 'energy' consumed to perform a magic act is linked to the difference of inherent energy levels of a closed system before and after the magical effect is produced: he amount of 'energy' consumed to perform a magic act is linked to the difference of inherent energy levels of a closed system before and after the magical effect is produced: warming a glass of room-temperature water is less costly than boiling it
  • If a process is possible without any arcane intervention, the arcane energy consumed by short-cutting the process via arcana is generally lower than trying to produce a non-mundane effect: combining carbon and iron into steel with magic is easier than turning lead into gold, even when the composition of steel and gold are both equally well understood

Given these parameters, what material would be the most difficult to create a facsimile of via arcana, either based on energy requirements or on complexity-based analysis-proofing?

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    $\begingroup$ "It is physically impossible to create an object through arcana if its composition is not sufficiently well-understood to be codified into a magic formula"... so anything biological is right out. Opalescent shell might work? $\endgroup$ – Matthew Mar 24 at 22:38
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Organic objects

These are things like wood, ivory, shells, bone. The first stated rule is: "It is physically impossible to create an object through arcana if its composition is not sufficiently well-understood to be codified into a magic formula." And the composition for organic objects isn't well understood at all. I'd imagine that, in addition to knowing the raw percentages of each element, you'd also need a vague idea of how the construction went on. Else you'd run the risk of creating coal when trying to create diamonds.

And when it comes to object complexity, nothing can beat the complexity of an organic substance, artificially made from nature by complex organic processes, made up from organic components that have traces of a few uncommon elements and arranges in unique patterns.

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    $\begingroup$ This answer is better than my transuranium nuclear currency answer, but I still think mine leads to more exciting times in the marketplace. $\endgroup$ – CaptainSkyfish Mar 25 at 21:45
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    $\begingroup$ "Hi, I'd like to buy fifty coins worth of your produ- NO, WAIT DON'T PUT ALL THOSE COINS TOGETHER IN THE SAME PILE!" $\endgroup$ – Halfthawed Mar 25 at 22:23
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    $\begingroup$ This is actually a really compelling idea. The government maintains a secret arboretum comprised of a species of tree found nowhere else. It is a naturally sustainable but incredibly scarce material that cannot be sourced except by treasonous trespassing, and cannot be alchemized without far more investment of time and resources than would justify the minimal payoff. $\endgroup$ – archaephyrryx Mar 28 at 4:47
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Could you draw some inspiration from computer science, particularly public key cryptography?

Public key cryptographic methods involve some asymmetry - if you have the public key, it is relatively simple to encrypt a message, but decrypting it is computationally prohibitive (at least relative to the encryption process). If you have the private key, then decryption is roughly as easy as encryption.

Suppose your world's governments have access to some kind of "private key" (which forms the basis of the currency-making formula) that makes a pattern that gets woven into their coins as part of the atomic structure. The pattern is sufficiently complex that trying to reverse engineer its shape is possible, but incredibly difficult. However, the public gets access to the "public key", which is something that reacts to the pattern, meaning you can always verify the legitimacy of the currency you have. Maybe there's a simple alchemical pattern that, when applied to a real coin, will make it glow, but if applied to a counterfeit will have no effect.

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    $\begingroup$ Was going to post something like this as well, except add even more security. If all the coins have their own serial number, which is hashed with the public key and that hash is encoded into the structure of the material, like artificial DNA, even if someone understands the whole structure, they won't be able to create new serial numbers without the private key, only copy existing ones, which is much easier to discover and track. That's without even getting into magic methods of securing. $\endgroup$ – Curiosity Mar 25 at 9:09
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Composite materials.

As far as I can tell these spells create uniform materials. You can combine aluminum and copper for construction aluminium of a certain %, but it is harder to make the top a different % mixture than the bottom and let these differences flow into each other naturally.

So you introduce a composite material. Like bank notes you keep the exact formula and composition of the paper and ink secret, or as much a secret as possible. The material of the coins is smelted in such a way that the bottom is a different composition than the top. They also all have a specific weight and some features like ribs and edges that increase the time and effort of copy attempts through magic, making it more worth it to try and mint them yourself than to create them.

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    $\begingroup$ Uniform materials are certainly easier to synthesize, but composite materials are by no means impossible. There is no fixed "list" of all spells, and novel arcana are fairly common. This is certainly a compelling idea, though. $\endgroup$ – archaephyrryx Mar 25 at 3:02
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Given that alchemy is a bit like chemistry, the answer to what is hardest to create might be the same as it is in chemistry.

Which is heavy elements. To make those crazy transuranium elements down at the very end of the periodic table, they have to bust through the electromagnetic barrier surrounding the nucleus of an atom, which takes a ton of energy and a heck of a shot. We're talking shooting million of pool balls at a target on Mars.

Course, then all your currency is radioactive and explodes instantly. But in theory, the heavier the element, the more complicated it is at the nuclear level and the more energy needed to make it. So you might consider something like Plutonium surrounded by a protective barrier of lead. No one is going to be shaving the edges of THAT coin to make a few extra bucks...

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