Foundational Reasoning and Feedback Protocol (FRFP): A Formal Architecture for Long-Horizon Human–AI Collaboration

This paper investigates conditions under which AI systems in high-stakes scientific and regulatory workflows can be governed and trusted using only automated checks, and when human tacit judgment remains structurally necessary. We introduce FRFP, a categorical protocol model that separates explicit artefacts (prompts, tools, reports) from tacit states (understanding, judgment), with a single boundary and a small set of epistemic primitives, and show that this “kernel” is initial/canonical among architectures satisfying our explicit–tacit axioms. Building on this, we develop a dynamic model with finite tacit capacity, degradation, and requirement maps, and analyze stochastic pipelines via hazard profiles and safe-horizon functionals. Under the FRFP assumptions, we prove conditional inevitability theorems: along sufficiently long runs, some accepted output will fall below its grounding requirement, and no explicit-only detector, oracle, or governance operator can guarantee the absence of hallucination—i.e., can guarantee correctness across all admissible pipelines and populations. We extend the framework to collective and institutional settings and derive structural non-automation results for governance. We close with protocol templates, case sketches, and FRFP-compatible instruction sets that demonstrate how the formal architecture, given the stated assumptions on explicit–tacit separation and degradation, constrains the design of realistic human–AI workflows. Subtantially modified from earlier version. No Material change.