Reciprocal Inference Kernel: A Normalized Stability-Pressure Control Layer for Calibrated and Cost-Aware AI Output

Large language systems can produce fluent output when supporting evidence is incomplete, conflicting, or absent. This methods paper proposes the Reciprocal Inference Kernel, an external control layer composed of two independently measured gates. Before generation, an input evidence-stability index, Xi_in, is calculated from stabilizing and destabilizing conditions. After generation, an output inverse-pressure index, Omega_out, is measured separately from the draft response. Their disagreement is represented by a consistency residual, epsilon. A locked policy routes each request to answer, retrieve more evidence, compute more, ask one clarifying question, or abstain. Both gates use normalized weighted geometric means computed in log form on a declared positive 1–5 scale. The normalization gives an all-neutral state a score of 1.0 regardless of unequal variable counts. The paper distinguishes the definitional identity Xi × Omega = 1 within a single reciprocal gate from independently measured input and output gates; the identity alone provides no evidence of correctness. The paper reports limited synthetic control evidence showing that the testing apparatus can recover an authored evidence relationship and decline to promote a candidate trajectory term supplied as noise. These findings validate mechanics only and do not establish performance on a deployed language system. The paper therefore specifies hypotheses, baselines, metrics, ablations, failure conditions, and a frozen empirical protocol. No claim of deployed-system superiority is made.