The ZARQA Synthetic Negentropy Core (Phase I, v2.8.3): A Unified Mathematical Framework for VFS Determinism and Autoregressive State Preservation

I present a complete, rigorously derived framework for measuring, bounding, and stabilizing the information-theoretic decay that occurs when generative models are trained recursively on their own synthetic output. Crucially, before theoretical machine-learning boundaries can be asserted, the execution environment itself must be rendered mathematically deterministic. The framework — the ZARQA Synthetic Negentropy Core (SNC) v2.8.3 — achieves this via a zero-trust Virtual File System (VFS) architecture. The framework is decomposed into eight sub-frameworks totaling 79 explicitly derived or cited statements: the information-theoretic core (SNC1–SNC10), deep-pipeline extensions (DSNC1–DSNC10), an authorized adversarial threat model (OFF_SNC1–OFF_SNC10), defensive bounds (DEF_SNC1–DEF_SNC10), observation-theoretic lower bounds (OB_SNC1–OB_SNC10), a platform-neutral hardware abstraction (PN_SNC1–PN_SNC11), certified-measurement constructions providing strict POSIX isolation (AOT_SNC1–AOT_SNC31), and economic composites (NV_SNC1–NV_SNC7). Each bound is derived from exact kernel behaviors or cited standard theorems. I do not claim any new mathematics. Every residual — the Fano floor, the Chao1 lower bound, DP-budget exhaustion, Rice-undecidable properties, and hardware-precision limits — is disclosed and its information-theoretic floor stated. The framework is falsifiable: each statement names a stated Monte Carlo, ablation, or controlled-deployment test with a sample size and a stated confidence procedure. I demonstrate that through atomic inode severance, universal polymorphic destruction, and a 5-step secure lock allocation protocol, theoretical model collapse can be bounded within a physically unhackable state machine.