Topological Residue and Curvature Locking in Arc Geometry: A Dimensionless Cun-Tou Residue and Action-Valued Lift for the Reduced Planck Constant and Electron Rest Mass

This preprint develops a second-stage arc-geometric reconstruction within the framework of Arc Theory. It follows the previous single-electron double-slit reconstruction, which recovered the de Broglie relation and the double-slit interference condition from the arc-geometric constraint R = DA. The present work addresses a deeper foundational question: how the reduced Planck constant and electron rest mass may be represented within a disciplined arc-geometric ontology. The paper introduces a dimensionless Cun-Tou residue associated with forced closure of a reciprocal spacetime projection chart. In this formulation, reciprocal projected coordinates form an open structure, while a stable electronic arc configuration requires closed-loop consistency. The resulting mismatch is formalized as a dimensionless topological residue. This residue theorem does not by itself prove the numerical value of hbar. Rather, it establishes the dimensionless winding structure that later receives physical scale through an action-valued lift. The central bridge of the paper is the action-valued arc-tension lift. A dimensionless residue becomes a physical action only after being lifted through an intrinsic arc-tension modulus integrated over a residue section. In this representation, a full closure carries an action scale hA, while the unit-radian normalized residue carries hbarA = hA / (2 pi). The local action-phase relation used in the earlier double-slit reconstruction is therefore reinterpreted as the differential form of a global topological action residue. The paper also defines a phase-normalized unit-radian residue section, Sigma0. Sigma0 is not assumed at this stage to be an independently embedded physical surface. It is introduced as the unit-radian normalization of a full one-cycle Cun-Tou residue section. This distinction is intended to avoid overclaiming and to keep the mathematical status of the construction explicit. A curvature-locking representation of electron rest mass is then developed. The paper distinguishes the motion-dependent de Broglie arc-radius DA(p) from the intrinsic curvature-locking radius DC. With an intrinsic arc transfer speed cA, and under the correspondence assumption cA = c, the locking angular frequency is represented as omegaC = cA / DC. The associated curvature-locking energy leads to the rest-mass representation mA = hbarA / (c DC). When hbarA and DC are identified with the measured reduced Planck constant and reduced Compton radius, the standard electron rest-mass relation is reproduced. The work further revisits topological friction and self-decoherence. Within this extended interpretation, decoherence may contain contributions from residue slippage, projection mismatch, and environmental trace formation. The formalism preserves the measurement-localization structure of the earlier reconstruction, while suggesting a possible geometric source for coherence loss. The scope of the paper is deliberately limited. It does not claim to have independently computed the numerical SI values of hbar, electron rest mass, the locking radius DC, or the intrinsic transfer-speed correspondence cA = c from a complete first-principles arc dynamics. Nor does it claim to replace the Standard Model Higgs-Yukawa mechanism. Instead, it proposes a mathematically disciplined geometric representation and research program linking topological residue, arc-tension lift, action quantization, curvature locking, and rest mass. The paper is intended as a preprint-level contribution to Arc Theory, quantum foundations, mathematical physics, and geometric approaches to the origin of physical constants. This is a v0.2 preprint. The manuscript presents a geometric representation of the reduced Planck constant and electron rest mass within Arc Theory. It should be read as a foundational mathematical-physical reconstruction rather than as a completed replacement of quantum field theory or a fully independent numerical derivation of physical constants.