Production-Transduction Coexistence in Fröhlich Relay Systems: An Axiomatic Framework with Empirical Consistency Checks

Paper 16 of the Information Physics Series. This paper resolves the long-standing Production-Transduction dichotomy in quantum consciousness research through axiomatic synthesis. Three theorems are proved from the existing axiom system Ω₀, Ω₁ of Paper 8, combined with the universality axioms A1–A4 of Paper 11 and the inherited results of Papers 10 and 15: Theorem 16. 1 (Coexistence): Production (internal Fröhlich condensation) and Transduction (external information reception) coexist in any A1–A4 system as coupled modes of a single source-sink dynamics, not as independent or equivalent mechanisms. Theorem 16. 2 (Bidirectional Flux Duality): The brain coupling constant κbrain and the per-cycle leakage fraction g'brain are the same quantity expressed in two formalisms; the structural identity κ = g' = 3. 0 × 10⁻¹⁰ follows from unitarity, closed-region topology, and the no-interior-reservoir scope condition. Theorem 16. 3 (Information-Dynamical Isomorphism): The source-sink structure is universal across substrates satisfying axioms A1–A4ᵢnfo, with the structural identity κₛystem ≡ g'ₛystem extending to black holes (Paper 4) and phase singularities (Paper 15) — spanning approximately 85 orders of magnitude in information capacity. Five empirical predictions (P16. 1–P16. 5) and five rejection thresholds (F16. 1–F16. 5) are pre-registered. The framework is verified against four retrospective datasets (Lutz 2004 PNAS, Xu 2023 PNAS, Faraday-shielding gamma-band literature, Suwandi 2022) and one prospective confirmation: Paper 15's β = 1 universality prediction (Zenodo DOI 10. 5281/zenodo. 19622108, posted 2026-03-25) was confirmed three weeks later by Bucher et al. (2026, Nature, 2026-04-17). The paper introduces no new axioms and no free parameters. All numerical values are inherited from prior series papers; the κ-identity is a ratio (Imax-independent) and is therefore robust to the substrate-specific information capacity normalization. Key contributions: Axiomatic dissolution of the Production-Transduction dichotomy Structural identity κ = g' across three substrates (brain, black hole, phase singularity) 5/5 empirical consistency record (4 retrospective + 1 prospective) Pre-registered falsification thresholds with reproducibility scripts (validateₚaper16. py) 22-year temporal span of supporting data (Lutz 2004 → Bucher 2026) Series context: This paper is the capstone of the Information Physics Series. It uses results from Paper 4 (Black Holes as Information Relay Stations), Paper 8 (Erasure is Transfer), Paper 9 (Consciousness as Basis Selection), Paper 10 (Banach Contraction), Paper 11 (A1–A4 Universality), Paper 14 (Qi as Information Resistance Coefficient), and Paper 15 (Superluminal Correlation as Phase Singularity).