Foundational Reasoning and Feedback Protocol (FRFP): An Updated Formal Specification

The Foundational Reasoning and Feedback Protocol (FRFP) is a formal framework for structuring
reasoning and evaluation in long-horizon human–AI workflows. It distinguishes between explicit
processes, which operate on representations and are mechanically reproducible, and tacit processes,
which determine correctness, validity, and acceptance. The framework enforces a one-way boundary
between these domains, under which explicit computation produces artifacts that must be evaluated
through tacit judgment. This paper presents the FRFP theory in the form established by complete
machine-checked formalization in Lean 4. The formalization yields four refinements to the published
theory: (1) Basis reduction: the original 11 premises reduce to 7 independent axioms, with four (ETS,
RB, AE, MD)nowderivable theorems; (2) Precision corrections: six definitions required strengthen
ing, notably explicit credence bounds, clamped degradation, and normal-form uniqueness modulo
navigation equivalence; (3) New formal structures: three types implicit in the original paper are
made explicit — the runToOmega bijection, the CorrectnessJudgment type, and lifted-action commu
tativity; (4) Novel theorems: three non-trivial results emerge from proof obligations — a canonical
first-unresolved-witness theorem, a governance-safe trace-extension theorem, and a protocol normal
form decomposition theorem. Where the published paper and Lean code diverge, the Lean version is
stated explicitly and documented