Amortization collapse for reference stabilized geometric Rényi superchannel divergences

Preprint, version 1 For every real order 1 < α ≤ 2, we prove that the reference-stabilized geometric Rényi divergence of two finite-dimensional deterministic physical superchannels equals its nested amortized extension. Joint inserted channels A R → B R and the external state references in the inner channel divergences range over all positive finite dimensions. The proof combines a supported matrix perspective transformer inequality with a comb contraction, a completion of positive testers, and a physical realization of positive definite testers. It includes singular supported operators and gives value +∞ for unsupported comb pairs. In the supported case, the ordinary supremum already has the same value at reference dimension |C||A||B|. A conventional proof is presented alongside a correspondence with a Lean 4 theorem and a reproducible source artifact. The result concerns the nested quantity of Hirche's Eq. (39); it does not establish collapse of the larger fully amortized quantity in Eq. (40). AI contribution and provenance. This work was developed through an AI-assisted research process initiated and directed by Vinícius Mohr. GPT-6.1-Sol and Claude Opus 5.5 agents carried out the mathematical exploration, Lean formalization, proof development, critical review, and literature searches. GPT-6.1-Sol wrote the manuscript, including the conventional proof exposition reconstructed from the formal sources. Vinícius Mohr initiated the research by directing the agents to investigate open problems from the Quantum Information and Quantum Computation Open Problem Zoo using a lean-orchestrator framework, and subsequently requested verification and manuscript preparation. A detailed account of the respective human and AI roles, proof provenance, and verification procedure is provided in the manuscript and accompanying repository.