Artian Fluid Mechanics: Navier-Stokes from Exact Finite-Address Conservation

From finite transport packets to the Navier-Stokes equation This paper asks what a fluid equation becomes when the continuum is not the source object. The primitive state is a finite graph of completed address events. Material is counted in Artian-mass units, \[ B_w=M_w/m_A, \] and nonnegative directed packets define the signed link current \[ Jww'=Tw→ w'-Tw'→ w, Jww'=-Jw'w. \] That antisymmetry gives exact finite-cell material conservation. Directed momentum packets then split uniquely into bulk advection, a counterflow residual, and A4 interaction impulse. The resulting conservative hydrodynamic projection is \[ ∂_Tρ+∇\!·(ρ v)=0, \] \[ ∂_T(ρ v) +∇\!·(ρ v⊗ v) =∇\!·σ+ρ g. \] For a spinless simple fluid, discrete rotational Noether balance makes the stress symmetric. Objectivity, parity, isotropy, symmetry, and first-gradient locality then leave one legal linear tensor form: \[ { σ =-p I+2μ D+ζ(∇\!· v) I }. \] The master equation is therefore \[ { ρ(∂_T+ v\!·∇) v =-∇ p+μ∇^2 v +(ζ+μ/3) ∇(∇\!· v)+ρ g }. \] The transport signs are fixed by the completed-record entropy balance, \[ sprod =2μ/T D{:} D +ζ/T(∇\!· v)^2 +κ/T^2|∇ T|^2 +{k_B}{VSQ} C ≥0, \] so \(μ,ζ,κ≥0\) in the declared near-equilibrium class. Inversion symmetry of the address kernel eliminates every odd spatial derivative; the first finite-address correction is fourth order and suppressed by \(_A^2\). The paper also constructs an explicit positive channel-envelope kinetic dynamics whose finite state space is forward invariant. It yields global evolution at every finite substrate tick and excludes point-supported physical blow-up. This is a theorem about the QTT finite state space; the abstract smooth-continuum Clay problem remains a different mathematical object. Version: 2.0 Concept DOI: 10.5281/zenodo.20122608 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory: Main Book v10.01 Scientific status: GREEN: EXACT FINITE MATERIAL-PACKET CONSERVATION GREEN: EXACT FINITE MOMENTUM-PACKET BALANCE GREEN: CAUCHY CONTINUUM PROJECTION GREEN IN DECLARED CLASS: NEWTONIAN STRESS UNIQUENESS GREEN: ENTROPY-SIGN TRANSPORT CONE GREEN: FINITE-LEDGER GLOBAL EVOLUTION STANDARD-PHYSICS CONSISTENCY: NAVIER-STOKES FORM NOT CLAIMED: GLOBAL SMOOTHNESS OF THE ABSTRACT CONTINUUM PDE Public anchors: Entropy and Second-Law reference theorem Inertia and Newton's Second Law Stationary-action theorem Renewal Dust discipline Derivation Atlas QTT Lexicon