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Zenodo
2026
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| Online-Zugang: | https://doi.org/10.5281/zenodo.19978542 |
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- <p>This is Paper 5 in the Reset Dynamics series.</p> <p>**Title:** Welding Between Structured Zeros — From Rupture to Reconnection</p> <p>**Abstract:**<br>Following the structured zero and rupture framework (Paper 4), we introduce welding as a structural operation that connects distinct contexts at their structured zeros. We show that classical notions such as continuity and smoothness emerge from welding regularity. Furthermore, we introduce welding strength and welding residual as intrinsic measures of structural compatibility. This framework reinterprets smoothness and singularities as properties of structural connections rather than intrinsic properties of functions.</p> <p>**Key contributions:**<br>- Welding defined as structural identification between structured zeros: 0[π₁] ∼ 0[π₂]<br>- Welding classification by regularity (smooth, continuous, discontinuous)<br>- Welding strength: measure of structural compatibility<br>- Welding residual: structural discrepancy that remains after welding<br>- Reinterpretation of continuity and differentiability via welding</p> <p>**Reset Dynamics Series Overview:**<br>- Paper 1: Γ-Constrained Realizability and the Structural Inevitability of Non-Composability<br>- Paper 2: Structural Closure and Generative Rupture<br>- Paper 3: Division by Zero as Structural Rupture<br>- Paper 4: Zero Is Not Atomic — Structured Zero and the Inevitability of Rupture<br>- Paper 5 (this work): Welding Between Structured Zeros — From Rupture to Reconnection<br>- Paper 6: Selection and Control in Rupture Dynamics<br>- Paper 7: Structure Space and Addressable Memory</p> <p>**Related Zenodo records:**<br>- Paper 1: https://zenodo.org/records/19373151<br>- Paper 2: https://zenodo.org/records/19609968<br>- Paper 3: https://zenodo.org/records/19861236<br>- Paper 4: https://zenodo.org/records/19923360</p>