The memory wall -- the widening gap between processor throughput and memory bandwidth -- has become the defining hardware constraint of the artificial intelligence era, now compounded by a structural NAND flash supply crisis driven by AI demand. We propose a post-transistor, pre-quantum memory architecture built on single-layer fluorographane (CF), in which the bistable covalent orientation of each fluorine atom relative to the sp3-hybridized carbon scaffold constitutes an intrinsic, radiation-hard binary degree of freedom. The C-F inversion barrier of ~4.6 eV (B3LYP-D3BJ/def2-TZVP, this work; verified transition state with one imaginary frequency; confirmed at 4.8 eV by DLPNO-CCSD(T)/def2-TZVP; rigorous lower bound from the fluorophenalane molecular model) yields a thermal bit-flip rate of ~10^{-65} s^{-1} and a quantum tunneling rate of ~10^{-76} s^{-1} at 300 K, simultaneously eliminating both spontaneous bit-loss mechanisms. The barrier lies below the C-F bond dissociation energy (5.6 eV) at both levels of theory, so the covalent bond remains intact throughout the inversion. A single 1 cm^2 sheet encodes 447 TB of non-volatile information at zero retention energy. Volumetric nanotape architectures extend this to 0.4-9 ZB/cm^3. We present a tiered read-write architecture progressing from scanning-probe validation (Tier 1, achievable with existing instrumentation) through near-field mid-infrared arrays (Tier 2) to a dual-face parallel configuration governed by a central controller, with a projected aggregate throughput of 25 PB/s at full Tier 2 array scale. A scanning-probe prototype already constitutes a functional non-volatile memory device with areal density exceeding all existing technologies by more than five orders of magnitude.