Arithmetic Expression Spaces: Expansion, Motion, Ripple Duals, Commutativization, and Tearing

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-26
DOI
https://doi.org/10.5281/zenodo.23660191
Primary Topic
Mathematics and Applications
Type
preprint
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preprint

Arithmetic Expression Spaces: Expansion, Motion, Ripple Duals, Commutativization, and Tearing

Mingli Yuan
Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
preprint

Arithmetic Expression Spaces: Expansion, Motion, Ripple Duals, Commutativization, and Tearing

Mingli Yuan
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Mathematics and Applications
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