Translation Remainder Clause and Lean 4 Architecture

This repository contains the Translation Remainder Clause (TRC) v5 meta-analysis protocol and its accompanying machine-checked Lean 4 formal architecture. The TRC provides a domain-neutral audit grammar for tracking how information, uncertainty, boundary conditions, and alternative mechanisms are systematically discarded as observations move through institutional translation chains (Measurement → Raw Data → Processed Data → Consensus). The publication includes two primary components: 1. The Methodological Protocol and Cross-Domain Registry (TRC v5) A rigorously structured diagnostic methodology requiring an 8-field audit record for any consensus claim: the translation chain, the explicitly discarded remainder, a counterfactual relevance test, formal predicates, blocked obligations, a corrected scoped verdict, and a resolution condition. The document includes a 13-case exploratory registry demonstrating the framework's representational capacity across physics, biology, and computational domains. 2. Lean 4 Formal Architecture A machine-verified proof of the audit grammar's internal consistency, compiling with zero sorry placeholders and no non-standard axioms. The Lean 4 formalization enforces strict epistemic hygiene by: · Mandating Tier 0 Measurement Semantics: Empirical comparisons are restricted to tolerance-window overlap and band-disjointness, structurally forbidding the use of exact real-number equality for continuous measurements. · Treating Witnesses as Data: The architecture rejects Classical.arbitrary placeholders, forcing unmodeled remainders and blocked obligations to be carried as explicit, computable data within the type system. · Executing a Recursive Negative Control: The formalization includes a self-audit where the TRC protocol evaluates its own translation chain, mathematically proving that the framework's downgrade operations are idempotent and do not result in infinite regress or logical contradiction. Epistemic Scope and Boundary This artifact is an uncertainty-bearing research infrastructure, not a claim of universal physical law or institutional conspiracy. The Lean 4 formalization establishes the type correctness and formal coherence of the audit grammar; it does not establish the empirical adequacy of the underlying domain claims. The target quality of this methodology is remainder visibility: ensuring that the unverified boundaries of a scientific claim are explicitly carried forward into subsequent research.