Artian Constitutive Mechanics

Abstract

A QTT Source-Work Framework for Stiffness, Oscillation, Damping and Noise Artian Constitutive Mechanics, version 1.0, joins restoring force, mechanical response and equilibrium fluctuations through one independently selected QTT source-work packet. \[ \boxed{\begin{gathered} \mathcal P_A\longmapsto \left(u_A,\mathsf B,\mathscr J_A\right) \longmapsto \left(\mathsf D_A,\gamma_A,S_f^{\rm sym}\right),\\ \mathsf D_A=\mathsf B^{-1/2}\nabla_q^2u_A\,\mathsf B^{-1/2}, \qquad S_f^{\rm sym}(\nu) =\coth\!\left(\frac{\nu}{2\Theta}\right)\mathscr J_A(\nu),\\ \nu=\omega\widetilde t_A>0,\qquad \Theta=\frac{k_BT_\gamma}{E_*},\qquad \partial_{\mathbf y_{\rm target}}\mathcal P_A=0 . \end{gathered}} \] The packet determines supported work, inertial source counts and retained environmental transitions. Work curvature fixes stiffness and oscillation. The same retarded force spectrum fixes loss and equilibrium noise; the target response is not used to choose their coefficients. Worked system: a confined electron pair. An exact finite spherical Dirichlet Green function supplies applied quadrupole work and self/mutual image charges. A selected near-center equilibrium determines both axial stiffnesses, local radial stability and classical/quantum nonlinear corrections. For the declared 2 mV quadrupole setting and 1 mm guard radius and field scale, the predicted axial stiffnesses are \(3.19970927\times10^{-16}\) and \(9.61291270\times10^{-16}\,\mathrm{N/m}\). Their harmonic frequencies are 2.982846421 and 5.170149874 MHz. These are calculations for the specified apparatus class, not measurements. One electrode-work map also fixes damping and noise. A specified outgoing vacuum coaxial port has geometry-derived impedance 41.5600594 ohm for radius ratio two. The derived interior capacitance and a separate extra-capacitance bound give a linear stretch energy-decay interval of 0.0074670261 to 0.0074670400 per second. The same voltage operator determines thermal force noise, two-quantum transitions and correlated dephasing. The nominally dark common mode has zero linear port coupling but nonzero quadratic heating. \[ \gamma_{-,1}^{(0)}= \frac{\alpha_A\hbar d^2}{m_AB_e d_{\mathrm{el}}^4} \log\!\left(\frac{b_c}{a_c}\right), \qquad S_{F,-}^{\mathrm{sym}}(\omega)= g_-^2\hbar\omega\coth\!\left(\frac{\hbar\omega}{2k_BT_p}\right) \operatorname{Re}Z_p(\omega). \] The framework includes a static-relaxation Schur complement, exact classical finite-bath memory elimination, a finite spectral thermal proof, causal and truncation qualifications, and separately labeled free-space bright/dark radiation reference cases. The latter are not substituted for the finite metallic chamber. Construction and evidence. No stiffness, oscillator frequency, linewidth, resistance or noise amplitude is fitted to a target response. Geometry, controls, bath temperature and preparation are explicit physical inputs; photon and electron values are frozen QTT dependencies with provenance. The release reports a source-native ideal-system construction and mathematical verification, not an observed significance or QTT-exclusive empirical selection. A matched microscopic electrodynamics account supplied with the same inputs shares the leading laboratory formulas without target fitting. The full reconstruction package contains the Markdown manuscript, standalone LaTeX, input packet, executable checks, numerical tables, figures, source provenance, laboratory execution card and SHA-256 manifest. Concept DOI: 10.5281/zenodo.23438104. Reader anchors. QTT main book v10.01: pp. 48-51, 236-266, 695-704, 742-744 and 857-860; stable book concept DOI. Also see the Lexicon and Two Universes. Same-author corpus references are dependencies, not independent empirical confirmations.