🔍 Resistance to Liquidity Manipulation

🔹 The core formula of SPTP signifies that the current asset price depends entirely on the quantity or shards of assets bought or sold through the protocol. New shard transactions are always created through buy actions. After the creation of a shard, subsequent sell operations within that shard continue to utilize the total amount determined at the moment of shard creation (when the shard index is identical).

🔹 When a transaction with a specific amount is completed in the Xth shard, the corresponding amount enters or leaves the liquidity pool. In subsequent opposing transactions, the transaction amount remains the same until the asset range exceeds the current shard.

🔹 Throughout the entire process, shards are created through buy actions → sell actions → re-buy actions → sell actions, and so on. The trading capital within the same shard remains 100% unchanged because, apart from transaction actions, there is no other way to alter the liquidity pool.

🔹 This effectively mitigates the problem of substantial price impact in traditional AMM DEX caused by insufficient liquidity when executing a single transaction.