The Artian Lagrangian Framework: A Finite Action Ledger for Quantum Traction Theory, from Completed Address Events to Laboratory Least Action

A finite-event route from Lagrangians to least action Version: 2.1 Concept DOI: 10.5281/zenodo.20657182 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 Ordinary analytical mechanics begins with a smooth action functional. This framework asks what that action is the laboratory shadow of if the source object is finite, counted, and address-based. The starting object is a completed event: \[ \mathcal E\in\mathcal C_T \Longleftrightarrow Q_{\mathcal E}^{\mathrm{bundle}}=2\pi, \qquad E_{\mathcal E}\,\widetilde t_A=\hbar, \qquad \Delta V^{(4)}_{\mathcal E}=4\pi\ell_A^4. \] The source action is then a finite ledger sum over completed modular-capacity events: \[ S_{\mathrm{QTT}}^{\mathrm{src}}[\Gamma;T_0,T_1] = \sum_{\mathcal E\in\mathcal C_T(\Gamma;T_0,T_1)} \Delta S_{\mathcal E}, \qquad \Delta S_{\mathcal E}=\mathcal L_{\mathcal E}^{\mathrm{src}}\,\Delta T_{\mathcal E}. \] The familiar laboratory action appears only after access/coarse-graining: \[ S_{\mathrm{lab}}[\phi] = \int d^4x\,\sqrt{-g}\,\mathcal L_{\mathrm{lab}}(\phi,\nabla\phi,x). \] The paper's constructor order is the point: \[ \text{completed events} \longrightarrow S_{\mathrm{QTT}}^{\mathrm{src}} \longrightarrow \text{Access Law projection} \longrightarrow S_{\mathrm{lab}}. \] Stationary action is recovered as the coherent real- \(J\) dial condition of the ledger sum, \[ \delta S_{\mathrm{lab}}=0, \] while the no-retune rule for a legal sector term is \[ {\partial\mathcal L^{\mathrm{src}}\over \partial\{\text{laboratory fit parameters after projection}\}}=0. \] Read this paper as the Lagrangian grammar for QTT sector derivations: declare the completed event set, print the source Lagrangian, state capacity and closure gates, project through access, and only then compare with observation.