Quantum-Resistant Ed25519 (PQ-Ed25519)

Canon² — Trust Layer Research Archive. Ed25519 is the cryptographic foundation of the Lume ecosystem. Every certificate in the Trust Layer's Certificate Fabric, every signal in the Synthetic Organism Runtime's Signal Bus, every state commitment in the deterministic transition graph, and every governance authorization in the GUPAS framework is signed with an Ed25519 key and verified through Ed25519 signature validation [16]. The security of the entire ecosystem—identity anchoring, provenance auditing, governance enforcement, and autonomous organism certification—depends on the computational infeasibility of forging Ed25519 signatures. A sufficiently powerful quantum computer running Shor's algorithm [20] would reduce this computational infeasibility to polynomial-time tractability, rendering every certificate, every identity, and every governance authorization in the ecosystem forgeable. I present a complete quantum-resistant cryptographic architecture for the Lume ecosystem that preserves deterministic semantics, certificate continuity, identity persistence, and governance validity throughout the transition from classical Ed25519 to post-quantum signature schemes. The architecture proceeds through three phases: Phase I (Hybrid), in which every signature operation produces a dual signature combining Ed25519 with a NIST-standardized post-quantum scheme (CRYSTALS-Dilithium [17], Falcon [18], or SPHINCS+ [19]); Phase II (PQ-Primary), in which the post-quantum signature becomes the primary verification target and the Ed25519 signature becomes a backward-compatibility fallback; and Phase III (PQ-Native), in which all new certificates, identities, and governance authorizations are issued exclusively under post-quantum signatures. The architecture integrates with Lume [1] through AST-level cryptographic operation canonicalization, with the Trust Layer [3] through certificate fabric upgrades and identity migration protocols, with Lume-V [4] through envelope-constrained cryptographic transitions, with DAIGS [5] through cognitive substrate extensions for cryptographic reasoning, with LDIR [12] through multilingual cryptographic semantic normalization, with SOR [13] through organism identity preservation, and with GUPAS [2] through governance-safe transition policies. I identify and formalize six failure modes specific to cryptographic transition—identity fragmentation, certificate invalidation, hybrid mismatch, PQ signature drift, governance misalignment, and intent inversion—each with defined detection mechanisms and corrective responses. To my knowledge, this paper presents the first complete quantum-resistant cryptographic architecture for a deterministic, certificate-bound natural-language programming ecosystem.