Artian Source-Completion and Winding Quantization Framework

Artian Source-Completion and Winding Quantization Framework Version: 1.02 Concept DOI: 10.5281/zenodo.20840233 Version DOI: 10.5281/zenodo.20840234 Author: Ali Attar Website: quantumtraction.org Corpus category: Supporting QTT records This paper develops a standalone Quantum Traction Theory source-completion framework. It extracts the general theorem behind the HVP v26.01 tail-winding result: a fractional source-winding deficit cannot be repaired by a fitted front polynomial. The missing source winding must be carried by source-owned completion faces with integer ledger weights and fixed threshold-opening blocks. The v1.02 clarification is methodological and important. Once a completion ansatz is chosen, endpoint closure is algebraic. The scientific content is therefore not the endpoint identity by itself, but the provenance of the legal source faces \(\mathcal A_{\rm legal}\), the integer weights \(N_a\), and the profile blocks \(B_a(s)\). The central source-completion equation is \[ \delta_{\rm comp}(s) = \Delta_{\rm miss} \frac{\sum_{a\in\mathcal A_{\rm legal}}N_a B_a(s)} {\sum_{a\in\mathcal A_{\rm legal}}N_a}, \qquad \Delta_{\rm miss} = \pi\nu_{\rm req}-\delta_{\rm base}(\infty). \] The endpoint condition is \[ \frac{\delta_{\rm base}(\infty)+\delta_{\rm comp}(\infty)}{\pi} = \nu_{\rm req}\in\mathbb Z. \] The paper also proves the polynomial obstruction on the physical cut: a finite real source polynomial can change endpoint phase only by integer multiples of \(\pi\). Therefore it cannot supply a fractional deficit such as \[ \Delta_{\rm miss} = \arctan\!\left(\frac{3}{4\pi}\right). \] For the pion vector source, the degree lock gives \[ \deg P_{\rm Art} = \nu_{\rm req}-r_{\rm src}. \] With \(r_{\rm src}=1\) and \(\nu_{\rm req}=1\), \[ P_{\rm Art}(s)=1. \] The HVP v26.01 worked example uses the minimal legal tail family \[ \mathcal A_{\rm tail}^{26.01} = \{\omega\pi,\ K\bar K\}, \qquad N_{\omega\pi}:N_{K\bar K}=1:2. \] The resulting tail profile is \[ \delta_{\rm tail}^{26.01}(s) = \frac{\Delta_{\rm miss}}{3} \left[B_{\omega\pi}(s)+2B_{K\bar K}(s)\right]. \] This gives the endpoint closure \[ \delta_{\rm base}(\infty)+\delta_{\rm tail}^{26.01}(\infty)=\pi, \] and the source-side diagnostic values \[ \langle r_\pi^2\rangle_{\rm cont}^{26.01} = 0.423121001647522\,{\rm fm}^2, \] \[ a_{\mu,2\pi}^{\rm cont,26.01} = 341.695899284104\times10^{-10}. \] These are profile-dependent source diagnostics, not observation-green row verdicts. Main status labels: GREEN: Σ-SOURCE-COMPLETION-WINDING-GATE-CLOSED GREEN: Σ-HVP-MINIMAL-TWO-FACE-TAIL-PROFILE-EXECUTED-AS-SOURCE-DIAGNOSTIC GREEN: Σ-HVP-PART-IDENTITY-POLYNOMIAL-OBSTRUCTION-CLOSED YELLOW: Σ-HVP-FULL-GLOBAL-FPI-PAYLOAD-PENDING YELLOW: Σ-HVP-SOURCE-COVARIANCE-PENDING YELLOW: Σ-HVP-ABSOLUTE-2PI-SCALAR-ADJUDICATION-PENDING Audit and claim scope: Concept DOI is the stable citation target for this research family. Version DOI and Zenodo record ID identify this exact public release for reconstruction. This description is a record-level guide; the paper itself controls theorem status, assumptions, and falsifiers. Related QTT anchors: Main book concept DOI: 10.5281/zenodo.17527179 Corpus Tree row: quantumtraction.org/doi-map/#record-20840234 Blog Map row: quantumtraction.org/blog-map/#corpus-record-20840234 Derivation Atlas: quantumtraction.org/derivation-atlas/ Lexicon: quantumtraction.org/lexicon/ Related QTT DOI (isSupplementTo): 10.5281/zenodo.17527179 Related QTT DOI (isSupplementTo): 10.5281/zenodo.20732034 Related QTT DOI (references): 10.5281/zenodo.20744161 Related QTT DOI (references): 10.5281/zenodo.20625550 Included files: source_completion_winding_v1_02_certificate.json zenodo_metadata_v1_02.md source_completion_winding_v1_02_check.py SHA256SUMS qtt_source_completion_winding_framework_v1_02.pdf source_completion_winding_v1_02_release_package.zip README.md qtt_source_completion_winding_framework_v1_02.tex render_audit_v1_02.md