ZFCρ Paper LXIII: Increment Second-Order Orthogonality and the SAE Axiom Intersection — From Deterministic Pairing to Zero-Mode Pinning
ZFCρ 第LXIII篇：余项增量二阶正交性与SAE公理的交汇——从确定性配对到零模Pinning
Paper LXIII introduces the concept of increment second-order orthogonality: the key structural property that characterizes the interaction between deterministic ZFCρ pairings and arithmetic correlations at the second-order level. The paper identifies the precise intersection between this orthogonality condition and the SAE axiom (remainder conservation), showing that zero-mode pinning — the mechanism by which the spectral zero mode is structurally constrained — emerges from deterministic pairing via the SAE axiom. This positions increment second-order orthogonality as the structural bridge between pure spectral analysis and the SAE foundational framework.
Full content available in the PDF on Zenodo. This paper is part of the ZFCρ series pursuing H’ — a spectral-density reformulation of Hilbert’s H problem. Paper LXIII builds directly on Papers LXI and LXII.