Quantum Error-Correcting Code Structure of Holographic Entropy Bounds in Cyclic Cosmology

We demonstrate that the holographic entropy bound across cosmological bounces has the structure of a quantum error-correcting code (QECC). The accessible entropy is protected by a stabiliser code with bond dimension χ, yielding Cᵤniv = 0. 24 ± 0. 07 from the code rate. We derive the HΣΔ filtering mechanism — a Sigma-Delta modulator that performs noise-shaped entropy reset at each bounce, preserving coherent modes while pushing thermal entropy into inaccessible (hidden sector) degrees of freedom. The QECC structure provides the microscopic foundation for the phenomenological observations of Papers I–II. Part III of VII.