Artian's Source-Work and Ion-Escape Framework

Why a heating spectrum cannot determine an ion's escape history A trapped ion can heat slowly near the bottom of its well and still disappear quickly. What must a physical theory specify to predict both observations with one construction? This framework joins source work, finite environmental forces, retained memory and the actual survival detector in one packet: \[ \boxed{ \begin{gathered} \Pi_{\rm src}\longmapsto \left(u_{\rm src},\mathcal T_{\rm surv},\rho_0,\mathcal A_{\rm det}\right) \longmapsto \left\{\dot{\bar n},\ S_n,\ \delta r,\ \omega_{\rm eff}\right\},\\ f_j=-\partial_{q_j}u_{\rm src},\qquad S_n=\operatorname{Tr}\!\left[\mathcal T_{\rm surv}^{\,n}(\rho_0)\right],\\ \frac{\partial\Pi_{\rm src}}{\partial\mathbf y_{\rm validation}}=0. \end{gathered}} \] The packet fixes the work, contacts, initial preparation and detector before the validation outcomes are judged. Its force, heating, survival and mechanical response are different projections of the same process. A stationary surviving transfer gives the displayed power; changing controls require a time-ordered product. A sharp source-work force bound In a qualified positive quadratic loading chart, a finite environmental allocation constrains the force rather than supplying an arbitrary noise amplitude: \[ u=q^{\mathsf T}Aq+2q^{\mathsf T}C\xi+\xi^{\mathsf T}B_e\xi, \qquad f_e=-2C\xi, \qquad \xi^{\mathsf T}B_e\xi\le\chi. \] \[ \boxed{(v^{\mathsf T}f_e)^2\le4\chi\,v^{\mathsf T}Av.} \] The work metric and allocation are physically qualified inputs. The coefficient four follows from differentiating quadratic work and the Gram inequality. The same bound limits the integrated covariance of a stationary classical force. Same spectrum, different escape An exact bounded-force counterexample makes the information gap concrete. Two declared synthetic force processes have identical means and complete covariance spectra, yet the same momentum-exit test has: \[ \boxed{S_F^{A}=S_F^{B},\qquad \mathbb E[T_A]=9\ \mathrm{ticks},\qquad \mathbb E[T_B]=16\ \mathrm{ticks}.} \] The higher statistics and exit overshoot differ. Heating alone therefore cannot select a full escape law. Retained-memory matrices and a quantum surviving channel provide separately reproducible examples; these finite-process certificates are not experimental trap lifetimes. One process, several independent checks The paper derives survival probabilities, restricted means, a tail-qualified full mean, stopped-work accounting and finite-window error bounds. An exact quartic comparison calculation also links barrier lowering to displacement and local-frequency change. A proposed near-critical tilt must produce those mechanical signatures under the specified preparation. The semiconductor-trap experiment of Stick et al. motivates the laboratory audit. Its published heating row and survival knee do not specify the independent environmental process, directional heating and complete detector packet required to identify its historical loss mechanism. The result here is the conditional source-to-observable theorem and its executable certificates; the historical joint-data verdict remains open. The main PDF contains the onboarding guide, nine theorem statements with proofs, axiom and constructor cards, three calculated figures, book anchors and a laboratory handover. The reconstruction ZIP includes the full Markdown and standalone LaTeX, declared packets, numerical executor, certificates, figure tables and checksums. Version 1.0. Stable concept DOI. Source dependencies: QTT Main Book, pp. 48–51, 71–74, 177–178 and 383–384; Completed-Event Transport and Quantum Coherence, Part XIX; and Physical Contact Selection and Predictive Transfer. Independent experimental context: Stick et al. (2006); comparison theory: Ryan, Jonas and Monroe (2026). Terminology · Corpus.