The first blockchain secured by hyperbolic geometry and Falcon-512. Hybrid post-quantum signatures — 128-bit PQ security from NIST FIPS 206 lattice cryptography, layered with SL(3,p) Schnorr-Γ (~189-bit classical hardness via 3×3 matrices). Both must verify. Not bolted on — built in.
QTCL is a quantum-classical hybrid blockchain with a hybrid post-quantum signature scheme. Every wallet uses Falcon-512 (NIST FIPS 206, 128-bit PQ security) alongside SL(3,p) Schnorr-Γ (~189-bit classical DLP security via 3×3 matrices over a 255-bit prime). Both signatures must verify — a quantum attacker breaks neither Falcon's lattice hardness nor a classical attacker bypasses the hyperbolic geometry.
Blocks are edge primitives in a depth-8 {8,3} Poincaré disk tessellation spanning 106,496 pseudoqubits. Consensus integrates W-state tripartite quantum entanglement via a 5-oracle Byzantine system, with fidelity scores that must exceed threshold for block validity. QTCL-PoW (SHA3-256 + SHAKE-256 scratchpad) binds classical mining effort to the quantum oracle state.
QTCL uses a hybrid signature scheme — every transaction and block requires two independent signatures that both must verify. Falcon-512 (NIST FIPS 206, finalized 2024) provides 128-bit post-quantum security based on lattice assumptions resistant to Shor's algorithm. Schnorr-Γ over SL(3,p) provides ~189-bit classical security from the discrete logarithm problem in the special linear group SL(3, 2255−31) — 3×3 matrices with determinant 1.
SL(3,p) alone is Shor-vulnerable in its cyclic subgroups — quantum algorithms attack the DLP. Falcon-512 alone lacks the geometric hardness properties unique to non-abelian group cryptography. The hybrid scheme means a forger must break both: lattice problems for quantum resistance, and the 189-bit DLP for classical security. The v4 upgrade from SL(2,p) to SL(3,p) tripled the classical security bits. The encryption layer — GeodesicLWE — is a hyperbolic analogue of Learning With Errors, with LDPC error coupling over the {8,3} tessellation.