An extensive mathemagical evaluation of our attempts at permanent conjuration revealed that they were perpetually acting against a force to remove them. This much was somewhat obvious, but the important discovery was the nature of this force. Specifically, it was an 'imbalance' in the world. Essentially, we are making too many things exist, and that is inherently unstable. The solution to this, is obvious. We have found ways to have the conjuration 'replace' rather than 'impose'. As such, if we have something cease to exist as we perform a conjuration, the conjuration will naturally replace that 'sacrifice' with the conjured item, thus using the 'right to exist' of the sacrifice and allowing the conjured object to persist in our world without further effort nor instability.
There, however, some rules that seem important. These can, generally, be overcome by applying more magic, but the cost can escalate at a very extreme rate so it is best to remain close to these rules.
It seems that, uh, 'ownership' is important. If you cant' forcefully control something then it is difficult to sacrifice it. We experimented with marbles, replacing them with conjured marbles of different colours... We found that it was easy to get hired merchants to attain the appropriate 'possessiveness' that we required. A marble in the hand was easy, one spotted on the ground that was abandoned or lost required some great effort, one being offered by someone else was easy, one being held by someone else was extremely difficult, requiring a team of wizards to perform a long and involved ceremony in an extensively prepared location at close range to replace a mere marble bead, and even then we suspect that it only worked because the assembled wizards could have taken it by force. On the other hand, we found that we could mark possession into a pattern that can be inscribed in magically-conducive material and then empowered to form a magical identification zone which rapidly transfers possession to the owner of the zone. Essentially, whatever remains within the centre of a mostly-circular design with certain important embellishments will, in a matter of seconds, attain absolutely no resistance to being sacrificed. So far we have found powdered off-cuts from cut quartz or diamond(but any magically-attuned material should suffice) to work as a medium, and have had success making portable Sacrificial Summoning Circle(tm)(S.S.C.)s by encasing the powders in other materials. The prototype was made by building the S.S.C. in a pre-prepared clay sculpture of the design, covering the powder with more clay, firing the clay and then dipping it in molten metal. It is now extremely durable and, while there was some resistance to magic(Which we would like to research further) over an exposed line of dust, once attuned to a conjurer it remains attuned to them until broken or attuned to someone else, so this does not represent an ongoing cost, which is preferable to trying to build expensive dust patterns with a mobile force. Fixed facilities should not require such methods, so civil production should be simpler...
'Weight' seems, err, well, worrying. It is actually quite easy to overcome a weight difference, while volume is much more difficult, but there are, umm, 'echoes' through magic that occur when weight is shifted. We suspect that the world has a very specific weight and that changing that could have, well, there was more than one reference made to Ragnarok when consequences were discussed. We have included a passage into the incantation to preserve the weight no matter what, and suggest that it not be tampered with. Volume differences will cause great difficulty, so the Sacrifice and Summon should have similar weight and volume.
There is also an intrinsic 'nature' to all things, as far as the magic is concerned. With most dusts and fluids, that is 'flow'. Metals tend to be 'bend'. Fibres and fabrics seem to veer towards 'tear'. Crystals, gems, and wood seems to be 'structure'. Stone is, uhh, well we are using the term 'crush' for now... Life seems to be 'longevity' but there are some quirks that could fill an entire report by themselves and we have barely even scratched the surface there, there even seems to be some weird patterns where a summoned being could make up the difference from 'outside' somehow and... well, it is an involved topic for another project, we believe that we can replace certain insects with firewasps but are having some control issues... Of course, there are many more natures and too many exceptions already found to list and many more yet undiscovered. Typically, overcoming one nature to attain another is impractically difficult, replacing a speck of water with quicksilver broke some things, and people... Within a 'nature' things are easier, but it still helps if they match. Sand to water is difficult, but viable. Soil, ironically, needs to be dried out before being replaced with water, but it is then almost as viable as sand. Perhaps the most practical measure is replacing soiled water with pure water, which is easy, but still a noticeable drain of a wizard's time and effort. It seems that wood has a very different structure to crystals, quartz is much heavier than our crystal weapons, and precious gems are difficult to acquire in significant quantities. We did make a single caltrop from a small lump of quartz, but the expenditure to increase the volume made it seem impractical for production. According to some of our specialists, the mathemagical signature of a crystal weapon's signature is that of many hollow boxes of innumerable sizes made up of rigid strings, except completely different and all one thing... We tried to get a carpenter to make a lump of wood that somewhat matched that description, well, several carpenters actually, they found it... tedious... but eventually produced something that was, indeed easier to convert into our crystal weapons, but still impractically difficult for distribution and the production of the complex wood sculpture was enough to make the expense impractical too. For now, permanent crystal weapons would require significant usage of our limited quartz supplies combined with a large drain on our magical forces. We could look into plant manipulation to produce wood with a similar structure, or growing gems, or growing weapon crystals from a small seed...
'Value' seems to have no mathemagical basis. We believe it to be a purely mental artefact and that the wizards are effectively restraining themselves, though we have yet t find any way to entirely remove its influence. essentially a wizard who thinks that they are getting a good deal, probably won't... There does seems to be an advantage to familiarity, so all we can suggest is that wizards keep doing it and it will get easier...