Quansistor Field Computing (QFC) is an ongoing research compendium proposing a novel operator- and field-based paradigm of computation. Rather than treating computation as a sequence of discrete logical steps, QFC models computation as the evolution of structured computational fields governed by spectral operators. At the core of QFC lies the concept of the Quansistor — a generalized computational entity whose state is defined by operator-valued relations within a field, rather than by binary logic or classical quantum gates. This framework aims to unify perspectives from mathematics, theoretical physics, distributed systems, and verifiable computation. The compendium introduces and develops several tightly connected layers, including: Quansistor Field Mathematics (QFM) — a mathematical framework describing operator-defined computational fields and their spectral properties. Quantum / Quansistor Virtual Machine (QVM) — a virtual execution environment for instantiating, simulating, and observing field-based computation. Transistor Field Computing (TFC) — a conceptual bridge between abstract field computation and realizable hardware or substrate-dependent implementations. SMRK Probe and SMRK Network — a verification and observation layer enabling deterministic replay, spectral verification, and audit-native computation across independent execution contexts. This work is not presented as a finalized system, but as a foundational research corpus intended to define a coherent conceptual and architectural space within which new forms of computation may be rigorously explored, implemented, and verified. The QFC Compendium is designed as a living document, with ongoing revisions and extensions. Zenodo’s versioning mechanism is used to ensure long-term citability, reproducibility, and archival integrity, while allowing the framework to evolve. Keywords Quansistor, Field Computing, Operator-Based Computation, Spectral Operators, Quantum Virtual Machine, QVM, QFM, TFC, Verifiable Computation, Deterministic Replay, Computational Fields Notes This record represents a versioned release of the QFC Compendium.For persistent referencing of the project as a whole, use the concept DOI associated with this record.For citation of a specific revision, use the version-specific DOI.