The Item levels for Elven and Mithral Chain do not seem to mesh between the description for special materials, and the treasure tables.
The Mithral Chain and Elven Chain under special non magic treasures table list item levels 7, and 15 for the Master and Legendary qualities on page 356. The Treasure List table on 352 lists item level 12, and 353 shows item level 19.
The raw costs seem to imply level 12 and 19, not 7 and 15.
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The levels on the the and on page 356 for the other items don't match either. The cost of mithral chain shirt also doesn't match the formula for mithral items. It's listed as 1,800 gp when it should be 1,200 gp based on the description of mithral on page 355. The other items have matching prices. And considering the special materials rules don't mention any level increases, I'd assume the levels given on page 356 are the correct ones and not the ones on the treasure table. It looks like the chart, page 356 and the special materials rules were based on different versions of the rules. I'm defaulting to the assumption that the special material rules on pages 354 and 355 are the correct ones because they're the most in depth and most consistent.
Mithral chain shirt is also kind of pointless now considering master chain shirts already have no armor check penalty and only cost 360 gp (even expert chain shirts have no penalty and are even cheaper at 35 gp). The hardness of 9 is also lower than the hardness of a steel master chain shirt, 12. The armor check bonuses from mithral only come into play with medium (except scale) and heavy armors.
Special materials in general need some work. Darkwood compared to normal wood is similar to mithral compared to steel, except it doesn't have the bonus of dealing with resistances/weaknesses. Both need to at least have their hardness raised to be at least equal to and preferably better than steel or wood of the same quality that they'd replace. As it is now, a darkwood shield is the same hardness of one made from cloth or glass of the same quality! Cold Iron has 1 lower hardness than steel of the same quality, but that might at least make some sense, while mithral and darkwood were suposed to be superior materials. Adamantine probably needs some benefit for armor, because as it is there isn't any at all unless there are sunder rules, which don't exist currently. Silver and orichalcum seem fine though.
I'm also unsure why elven chain was changed to being a chain shirt instead of full chainmail. It makes more sense as the later than the former. The current benefit is also pretty weak for the price.
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I bet they meant it to be chainmail and someone screwed up. Like bulk 8 on the snare kit.
Yeah Elven Chain has historically been the Medium Armor Chainmail, not Chain Shirt.