Sharpen is a very special enchantment, gained by certain items that kill a Spikagi.
Wait, certain items? What items? Sharpen only affects solid items, and then only organic objects (like bone, wood, or enamel), or objects made of or containing organic carbon (coal, bone steel). However, Sharpen most strongly affects paper and diamonds.
Enough already, what does it do? The Sharpen enchantment causes any straight lines, edges, or points on an object (let's say a wood, coal, or bone object) to become as sharp as a steel razor. Those same areas on a steel item will be twice as sharp, but if those areas were already sharp, they will be four times as sharp. A Sharpened steel battleax or sword will therefore be four times as sharp as a steel razor.
Paper, however, becomes ridiculously sharp under the effect of Sharpen, becoming four times as sharp as an obsidian scalpel. In my estimation, a Sharpened origami katana should be able to cut through a cement slab, even a modern car, like it's melted butter. Diamonds, however? Once Sharpened, a cut diamond will become like a plasma sword or lightsaber, cutting through objects with the same ease and precision.
This sharpness does not go away; Sharpened items stay sharp, you can't blunt, dull, chip or file down (erode away) their points or edges. If an object is too soft or brittle to hold and keep an edge (or sharp point), Sharpen nullifies that, giving it the same strength (hardness, tensile strength) and flexibility as tempered steel, while retaining the benefits of the Sharpen enchantment (so there's no blunting, dulling, chipping or filing a Sharpened object). (So the aforementioned katana will have all of that but with the addition of ridiculous sharpness, while the diamond will retain its incredible hardness but gain the tensile strength and flexibility of tempered steel, making it much less likely to shatter).
So, my question is, What Benefits Would The Sharpen Enchantment Have On Items?
The best answer should start with a shortlist (summary) of what items or kinds of items would be benefited by this Enchantment and why. Remember, items can only be added if they can be used to kill a Spikagi. (Paper should be able to do that, right? I mean, stab a Spikagi's eye with a paper blade, choke it with a crumpled piece of paper....)
The best answer should have categories or groups of items that would be benefited by this Enchantment, for #3 below.
Each category of item that would be Benefited by this Enchantment should be thoroughly analyzed to determine how much this Enchantment would benefit them overall.
The best answer should, preferably, also account for whether the Sharpen enchantment really benefits paper, or rather, paper armor, and diamonds. I wanted to make paper and diamond viable for military use through this Enchantment, so those who find out about this Enchantment's effect upon paper and diamonds can use them to their advantage.
Firstly, my understanding of blades is limited, but I do appreciate knowing that a blade can only cut so far depending on how thick it is.
As for evaluating how much sharper an item becomes due to Sharpening, I suppose a crude scale, akin to Moh's Scale of hardness for minerals, could be constructed, determining an object's sharpness by the hardest materials it can cut.
As for balancing durability and sharpness, I believe that is pretty well covered by the Enchantment itself. Steel is pretty durable, and Sharpened objects don't blunt or file down....