> For the complete documentation index, see [llms.txt](https://doc.cryptostone.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://doc.cryptostone.org/crypto-stone/crypto-stone-wp-cn/wa-kuang-xi-tong/24-jian-ban-ji-zhi-yu-scarcitymultiplier.md).

# 24. 减半与 Scarcity Multiplier

CryptoStone 的减半机制并不是以整体集合为基准，而是按各宝石独立适用。\
当宝石 j 的最大发行量为 N\_j，当前已挖掘数量为 n\_j，挖矿进度为 q\_j 时，计算如下。

$$
q\_j = n\_j \div N\_j
$$

例如，Diamond 的最大发行量为 110,000 个，当前已挖掘 55,000 个时：

$$
q\_{\text{Diamond}} = 55,000 \div 110,000 = 0.5
$$

也就是说，Diamond Pool 已达到 50% 的挖矿区间。

各宝石的稀缺性倍率 S\_j 会根据挖矿进度 q\_j 上升。

| Mined Supply Ratio | Remaining Supply | Scarcity Multiplier |
| ------------------ | ---------------: | ------------------: |
| 0% \~ 50%          |      100% \~ 50% |                  1x |
| 50% \~ 75%         |       50% \~ 25% |                  2x |
| 75% \~ 87.5%       |     25% \~ 12.5% |                  4x |
| 87.5% \~ 93.75%    |   12.5% \~ 6.25% |                  8x |
| 93.75% \~ 96.875%  |  6.25% \~ 3.125% |                 16x |
| 96.875% 以上         |        3.125% 以下 |                 32x |

将其一般化后，可表达如下。

$$
S\_j(q\_j) = 2^{\min(5, \lfloor \log\_2(1 \div (1 - q\_j)) \rfloor)}
$$

不过，当 q\_j 属于初期区间时，S\_j(q\_j) 至少保持为 1x。实际智能合约中，可以不直接计算上述公式，而是基于预先公开的区间表进行实现。

该公式表达了各宝石剩余供应量减少时，挖矿难度会呈几何级数上升的结构。这是将现实矿山中储量减少时挖矿成本和难度上升的结构，转移到数字环境中的设计。


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