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.20674605
Primary Topic
Model Reduction and Neural Networks
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
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
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

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