Artian Source-Completion and Winding Quantization Framework

The general winding rule behind source completion Concept DOI: 10.5281/zenodo.20840233 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper abstracts the source-completion theorem behind the HVP tail-winding result. A fractional source-winding deficit cannot be patched by an arbitrary polynomial: it must be completed by legal source words, or the source packet remains incomplete. The clean closure statement is \[ \nu_\infty=1 \quad\Longrightarrow\quad \deg P_{\mathrm{Art}}=0, \qquad P_{\mathrm{Art}}(s)=1. \] For an incomplete packet, the source-completion operator must add only admissible threshold words: \[ \delta_{\mathrm{tot}}(\infty) =\delta_0(\infty)+\sum_a c_a\delta_a(\infty)=\pi. \] The theorem is useful beyond HVP because it gives a general no-knob rule for deciding when a source polynomial is legal. Core labels: Σ-SOURCE-COMPLETION-WINDING, Σ-PART-DEGREE-ZERO-CLOSURE, Σ-NO-ARBITRARY-POLYNOMIAL-KNOB.