The verification of transactions in blockchain networks presents a bifurcation in protocol implementation: one pathway aligns with complete state replication through full nodes, while the alternative, as outlined in Nakamoto's seminal whitepaper [1], advocates simplified payment verification (SPV) wherein clients validate transactions via header-only proofs. This paper formalises and mathematically models the latter, extending it beyond its conceptual origin into a fully specified, implementable, and security-provable protocol. In doing so, we consolidate foundational concepts from the original whitepaper, correct widespread misinterpretations, and construct a complete formal model using automata theory, game-theoretic reasoning, and complexity-theoretic metrics. This treatise employs a layered structure: beginning with an exegesis of the SPV concept as it appears in the original protocol specification, we examine the trajectory of mis-implementations, diverging threat models, and false economic assumptions. Subsequent sections provide a rigorous formalisation of SPV in a low-bandwidth adversarial context. This includes the introduction of protocol optimisations that conform to the Bitcoin protocol as defined in 2008, with proofs grounded in computational and information-theoretic primitives. Later sections analyse game-theoretic cost models for misbehaviour, followed by a discussion of implementation artefacts and evaluation in simulated hostile environments. The final structure includes appendices detailing code listings, mathematical proofs, and graphical models that substantiate the proposed design.

Research into methods for improving the performance of large language models (LLMs) through fine-tuning, retrieval-augmented generation (RAG) and soft-prompting has tended to focus on the use of highly technical or high-cost techniques, making many of the newly discovered approaches comparatively inaccessible to non-technical users. In this paper we tested an unmodified version of GPT 3.5, a fine-tuned version, and the same unmodified model when given access to a vectorised RAG database, both in isolation and in combination with a basic, non-algorithmic soft prompt. In each case we tested the model's ability to answer a set of 100 questions relating primarily to events that occurred after September 2021 (the point at which GPT 3.5's training data set ends). We found that if commercial platforms are used and default settings are applied with no iteration in order to establish a baseline set of outputs, a fine-tuned model outperforms GPT 3.5 Turbo, while the RAG approach out-performed both. The application of a soft prompt significantly improved the performance of each approach.