LemniCoin Ecosystem: Pioneering Quantum-Resistant Cryptography with Lemniscate-AGM Isogeny Encryption

Abstract

This paper unveils the LemniCoin ecosystem, advancing from a Binance Smart Chain (BSC) foundation to a quantum-resistant paradigm through the Lemniscate-AGM Isogeny (LAI) cryptosystem.Building on security audits conducted on March 27, 2025, and April 13, 2025, we introduce LemniCoin-QR (April 2025), a quantumhardened token; a secure wallet (May 2025); and LemniChain (December 2025), a Proof-of-Stake (PoS) blockchain.The Lemniscate-AGM Isogeny Problem (LAIP) underpins LAI, offering unparalleled resistance to quantum threats, surpassing Bitcoin (BTC) and Ethereum (ETH).We provide detailed proofs, audit insights, and implementation strategies, demonstrating superior security, transaction efficiency, and environmental sustainability-positioning LemniCoin as a premier investment in the post-quantum era.