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Re-Phase Vol.3.5: Dual and Inner-Product Compatibility — Adjoints, Gram Geometry, and Feature-Relevant Ambiguity

Year: 2026

Type: article

Abstract: This volume develops a static linear dual and inner-product enrichment of the Re-Phase compatibility framework. It studies how observation-compatible candidates can still differ in target features, and explains why observation-invisible directions need not be feature-invisible. The note introduces dual pullbacks, adjoints, Gram operators, orthogonal projections, weak observation directions, and Rayleigh quotient comparisons as non-primitive inner-product enrichments.

Source: Zenodo (CERN European Organization for Nuclear Research)

Author: Ito, Takashi

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7164657789

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