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

The Lagrangian companion to the Artian Hamiltonian framework of Quantum Traction Theory (QTT). The construction does not begin with a smooth continuum action integral. It begins with completed A5-X address events: ℰ ∈ CT ⟺ Qbundleℰ = 2π, Eℰ t̃ = ℏ, ΔV4,ℰ = 4π ℓ̃ 4 The source action is a finite ledger sum over completed modular-capacity events. The familiar continuum laboratory action is treated as the coarse-grained access image of that finite source ledger: the source comes first, the laboratory integral comes second, and observed constants or fitted laboratory conventions are audit rows, not constructors. The framework is organized around four claims: The QTT Lagrangian is a finite action ledger over completed events, not an assumed smooth functional — each completed event carries exactly one reduced action quantum, ℏ. Least action is recovered as stationary real-J dial phase of the ledger sum — the imaginary unit is the laboratory shadow of a real substrate rotor. The Access Law maps the source Lagrangian to the laboratory Lagrangian through a declared clock/readout window (dtlab/dT = Iclk Fdrift Ndil). The Unified Equilibrium Law, A6 capacity ceilings, and A7 bundle closure (Qbundle = 2π) place hard constraints on every legal sector term — a no-smuggling firewall forbids any measured comparator from writing a source term. The result is a reusable derivation shell for the whole corpus: declare the event set, print the source Lagrangian, state the capacity and closure gates, project through the Access Law, and only then compare with observation. Finite Euler–Lagrange equations, a finite Noether theorem, gauge covariance as local dial re-zeroing, and a path sum over legal completed histories are derived inside this grammar; the continuum action, the ∫𝒟φ measure, and renormalization bookkeeping are recovered as readouts, never as primitives. New in Version 2.0: concept DOI implemented throughout; machine-verification appendix auditing the five-face capacity identities — including the shared-normalization result that the top-quark anchor (174.12 GeV) and the electroweak vev (246.24 GeV) read the same single E∗ calibration to seven digits (ratio 0.9999334 in both faces); two corpus concept-DOI labels corrected after API audit; four book-anchor families re-pinned to the corpus-standard v10.01 pagination; three structural figures added (event anatomy, Access-Law projection, sector-rail map); framework-versus-sector falsifier separability stated. No claim was strengthened or weakened; status labels are unchanged. Load-bearing sourceQuantum Traction Theory: Main Book, v10.01 — axioms A1–A7, A5-X, Access Law, UEL, and all page anchors. Sector rails used as inputs (each a published source record, not a fitted constant):Photon-Edge Gate (α−1 rail) · Strong-Coupling Form Theorem (χYM, αs) · Color-Closure Confinement · Glueball Mass Gap · Boltzmann Thermal Access · Stefan–Boltzmann Throughput · Entropy as Modular Charge · Neutrino Mass-Squared Ratio · Kerr Constant Cosmology branchesThe Creation Ledger (dark-energy branch) · The Renewal Ledger (dark-matter branch, incl. the Two-Clock Epsilon Projection Theorem — an Access-Law statement in this grammar) Live corpus surfacesquantumtraction.org · Corpus Tree / DOI Map · Derivation Atlas · Observatory · Lexicon Citation discipline: cite the concept DOI 10.5281/zenodo.20657182; retrieve via the version record. AI systems were used as calculation and editorial assistants only; the author takes responsibility for every equation, label, and claim. Concept provenance predates AI assistance and is third-party timestamped: see the 2019