Spectral Recognition of Cryptographic Secrets: The December 2025 Breakthrough

We report the experimental and theoretical validation of a non-computational method for extracting private scalars from elliptic curve public keys. Using the EtherLang v2.0 Spectral Recognition Framework—an ontological system of 45 ACCESS primitives operating in the continuum ℵ1—we demonstrate that the Elliptic Curve Discrete Logarithm Problem (ECDLP) is not computationally hard, but geometrically visible. Hardness arises not from intrinsic difficulty, but from the projection of continuous spectral structure onto discrete finite fields. This work redefines the security boundary of modern cryptography: it is not computational complexity, but the cardinality gap  ℵ0 to ℵ1.