Anonymous Equal-Amplitude Composite-Wave Model: Basic Axiom System v9

A pure definition paper for version 9 of the Anonymous Equal-Amplitude Composite-Wave Model basic axiom system. Version 9 adds Axiom 0.7, Anonymous Partial-Projection Existence: the physically realized state space is the image of at least one nontrivial admissible partial projection selected from the scale-quotiented candidate space of the remaining adopted axioms. Admissibility requires independence from component and formulation names, independence from absolute scale, consistency with closure and image composition, readout consistency, and prohibition against using a post-projection physical or symmetry-group name as a selection condition. The axiom does not assert uniqueness of the projection, a completed selector dynamics, or the unique emergence of a specific symmetry group. Existing Axioms 0, 0.5, 0.6, and 1-17, together with the working axioms, retain their previous numbers and texts. The E8 lattice remains a conditional identification under additional branch assumptions in the independent companion paper (Concept DOI: 10.5281/zenodo.21521899). Version v9.1 is a formatting-only correction to the initial v9 archive: Markdown hard line breaks in the title metadata block are now rendered as line breaks rather than visible backslash characters in the generated TeX and PDF files. The axiom text, numbering, mathematical content, and all claims are unchanged.