Paper 0 — Arithmetic Expression Spaces.** Arithmetic expansions under explicit operand-slot conventions, the distributive law as the rewrite relating distinct expansions, arithmetic expression spaces and the four operations as motions, the models `E_0` and `E_1`, the continuous arithmetic motion, the dual reading called ripple geometry, affine cocycles, the accumulative commutative space with its weighted torsion--Stokes theorem, tearing, the contact structure of that defect, two obstructions to linear language, punctured spaces with a register of computed witnesses, finite-type compactification, arbitrary positive puncture counts and full-collar three-ended reconstruction. Paper 0 is the geometric foundation of the series; it does not revise Paper I's marked-history formalism.
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Mingli Yuan (2026) studied this question.
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