What question did this study set out to answer?

To explore the organization of curvature-correction candidates through square maps and linear simplexification.

June 23, 2026Open Access

Linear Simplexification by Square-Quantity Readout and a Dimension-wise Organization of Curvature-Correction Candidates

Key Points

To explore the organization of curvature-correction candidates through square maps and linear simplexification.
Observational analysis of square-quantity readout
Study of linear simplexification of sum-of-squares constraints
Dimension-wise organization of curvature-correction candidates.
Identified the relationship between square maps and linear constraints
Juxtaposed new readout methods with existing geodesic area coefficients
Provided insight into dimensional organization of curvature candidates.

Abstract

An observational and organizing paper on the positive square map Xᵢ=xᵢ², linear simplexification of sum-of-squares constraints, elementary motion-form readouts, and the dimension-wise appearance of curvature-correction candidates. The paper does not claim to derive physical laws; it juxtaposes square-quantity readout with the geodesic unit-cell area coefficient from the self-referenced Paper 0.

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