Quasiperiodic Wang Tiling zk-STARK Signatures (QWTSS): A Post-Quantum Signature Scheme Anchored in the Topologically Frustrated Glassy Phase

The emergence of quantum computing threatens classical public-key cryptography, necessitating the development of robust post-quantum alternatives built upon structurally diverse hardness assumptions. We introduce Quasiperiodic Wang Tiling zk-STARK Signatures (QWTSS), a novel digital signature scheme grounded in the NP-hard combinatorial optimization of bounded aperiodic Wang tile sets. Through stochastic sampling of secret keys within the thermodynamic glassy phase of the configuration space, QWTSS inherently avoids the planted distribution vulnerabilities common to constructive combinatorial primitives. We empirically demonstrate that this critically constrained regime undergoes solution-space shattering and exhibits the Overlap Gap Property (OGP), fracturing into isolated, multifractal solution clusters. The resulting critically constrained operational regime provides extensive combinatorial backtracking against exact classical solvers, while the OGP inhibits heuristic local-search traversal. Furthermore, we model how the phase-space anisotropy of these clusters significantly suppresses the quantum overlap integral. By coupling this structural hardness with a zk-STARK, QWTSS enables a prover to demonstrate knowledge of a specific geometric configuration without leaking the underlying witness. This yields a non-algebraic post-quantum primitive computationally bound to simulated thermodynamic work.