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July 23, 2026Open Access

Anonymous Equal-Amplitude Composite-Wave Model: Basic Axiom System v6

NKNoriaki KiharaSystem Equipment (China)

Key Points

This paper defines Basic Axiom System v6 of the Anonymous Equal-Amplitude Composite-Wave Model, adding important axioms and consequences.
Introduced one working axiom and three derived consequences between Axiom 16 and Axiom 17.
Validated axiom through computer-assisted proofs with conditions on N and provided dimensional analyses.
Derived normal uniqueness conditions relevant to the new axiom.
Proved that rotation modes grow linearly while relational waves grow quadratically.
Established a generic-position rank equality with dimensions N(N-5)/2 for N >= 5.
Identified specific conditions for sign-free uniqueness in three dimensions.

Abstract

A pure definition paper for Basic Axiom System v6 of the Anonymous Equal-Amplitude Composite-Wave Model, preserving the concept DOI of v3-v5. Version v6 adds, between Axiom 16 and Axiom 17, one working axiom and three derived consequences that ground the adoption conditions of Axiom 16: Working Axiom I states the phase-difference sine relational update rule as an explicit working hypothesis satisfying the antisymmetry condition; Consequence 16. 1 (under Working Axiom I) gives the vertex decomposition K = sumₖ (cₖ sₖT - sₖ cₖT) and the linear rank bound rank K = 5, while equality for all N remains a new hypothesis; Consequence 16. 3 states normal uniqueness — the normal-candidate space has dimension d-2 and sign-free uniqueness holds only for d = 3 — as the basis of the second adoption condition of Axiom 16. Proofs are given in Paper 3 of the Dimensional Generation Structure series (Concept DOI: 10. 5281/zenodo. 21465898).

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