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

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-13
DOI
https://doi.org/10.5281/zenodo.20674606
Primary Topic
Model Reduction and Neural Networks
Type
article
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article

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

Takashi Ito
Zenodo (CERN European Organization for Nuclear Research)
Model Reduction and Neural Networks
article

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

Takashi Ito
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 5%
Model Reduction and Neural Networks
DOIOpen Access PDFOpenAlex
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Re-Phase Vol.3.5: Dual and Inner-Product Compatibility — Adjoints, Gram Geometry, and Feature-Relevant Ambiguity — Takashi Ito · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS