QTT Completed-Event Transport and Quantum Coherence

Abstract

Real-dial dynamics, conditional interactions, and optical interference \[G-F^{T}GF=L^{T}ML,\qquad L=0,\quad FJ=JF\quad\Longrightarrow\quad U_F^\dagger U_F=I.\] When does completed-record transport become unitary quantum evolution? A positive counting metric, a fixed coherent encoding and an oriented real dial supply an exact answer within the declared source class. The positive operator on the right measures information lost outside the retained sector. Zero leakage and dial compatibility yield complex-linear unitary propagation without supplying a target amplitude matrix. Physical preparation and coherent coordinates. An independently identified preparation map now connects the established source-work law to laboratory preparations. Total coherent capacity and its normalized ray are retained separately. Capacity attenuation with a fixed dial reference gives \[\Xi\circ R_m=s_m\circ\Xi,\qquad s_mx=x/\sqrt m,\qquad X_\alpha=\sqrt{C_\alpha}R_J(\theta_\alpha)e_\alpha.\] For desired reduced capacities \(a_\alpha=C_\alpha/m\), actual capacities \(b_\alpha\), and independently calibrated phase errors \(\delta_\alpha\), the exact preparation distance is \[\varepsilon^2=\sum_\alpha\left[(\sqrt{b_\alpha}-\sqrt{a_\alpha})^2+4\sqrt{a_\alpha b_\alpha}\sin^2(\delta_\alpha/2)\right].\] It supplies an explicit work-error tolerance, \(|\Delta W|/E_*\le2\sqrt m\,kR\varepsilon+mk\varepsilon^2+b_0+mb_1\), under the stated operator, amplitude and work-readout bounds. Closed-loop action and curvature pullbacks identify which complete coordinate changes preserve the source test. The preparations and tolerances must be determined independently of the target residual. Populated effective interaction certificates. Direct and image Coulomb work populate an effective valuation table with the inherited photon coefficient. Exact work defects distinguish full positional anharmonicity from coherent-amplitude refinement. A constrained finite-field calculation proves quadratic excess work for affine loading, while canonical loops provide a potential-independent kinetic-action certificate. These are effective field/work exposures, not newly claimed integer-event counts. The four-corner work \(W_\times=V(d+q_b-q_a)-V(d-q_a)-V(d+q_b)+V(d)\) cancels separate trap contributions. With \(\kappa_C=V''(d)\) and a specified third-derivative bound, \[|W_\times+\kappa_Cq_aq_b|\le\tfrac12 M_3|q_aq_b|(|q_a|+|q_b|).\] This gives a finite-amplitude route from independently calibrated static work to predicted exchange. The full preparation, heating and detector model is kept separate from the reserved motion data. The source-coefficient and static-work transfer tracks test different parts of the construction. From finite source qualification to observable error. A finite dual certificate propagates independently established transaction identities to every history with a supplied complete decomposition. Finite-depth work-gradient and action-curvature telescopes retain the unresolved deepest-scale remainders. In a fixed capacity-normalized chart with reference quadratic work \(x^TKx\), source time \(\tau=T/t_A\), bounded force defect \(\epsilon_E\), and curvature defect \(\kappa<2\), the resulting trajectory bound is \[\|x(\tau)-x_0(\tau)\|\le d_0+\tau\frac{\epsilon_E+\kappa\|K\|R}{2-\kappa}.\] The bound requires the stated domain, work/action calibration and time window. Its error quantities must be independently derived or calibrated, not adjusted to a target trace. An exact-rational checker verifies supplied history decompositions without promoting formal success into physical source qualification. The fourth-face UEL normalization remains an inherited source relation; this extension does not claim a direct measurement of its four-volume. Microscopic selection and real interactions. The new development makes the source-selection question a transaction-level calculation. For independently identified funded histories, the difference between one preparation and reduced copies determines the work-refinement defect. If the legal source valuations obey \(Bc=b\), with \(c=c_0+Nu\), the exact certificate is \[\frac{E(x)-mE(x/\sqrt m)}{E_*}=c^Td_m(x),\qquad c^Td_m=0\ \text{for every legal }c\ \Longleftrightarrow\ N^Td_m=0,\ c_0^Td_m=0.\] This is a proved necessary-and-sufficient condition under its stated affine-domain hypotheses. A complete microscopic funding table has not yet been supplied that establishes this condition from A1-A7 alone. Explicit integer coincidence counts show why fixed transaction prices and removal of duplicate receipts are insufficient by themselves. A complementary source-work theorem derives refinement from fixed, identified UEL contact allocations. A multi-port action classification isolates load curvature invisible to individual dial charges. The closed-loop converse theorem gives \[\oint_\gamma\beta=m\oint_{s_m\gamma}\beta\quad\Longrightarrow\quad d\beta(x)=d\beta(0),\qquad s_mx=x/\sqrt m.\] The implication requires the declared loop domain, successive refinements and continuity at zero. With independently established action normalization, quadratic work and common-dial symmetry, it yields \(\hbar J\dot x=Hx\). Exact endpoint terms change no closed-loop dynamics. Finite-error certificates separate functional theorems from finite experimental qualification. A calculated ion-exchange interaction. The inherited photon-edge coupling and Coulomb recovery determine a trapped-ion coupling from independently specified nominal geometry, confinement and mass. With source mass counts \(B_i=M_i/m_A\), \[g t_A=\frac{\alpha_0\eta_{\rm im}}{\widetilde d^3\sqrt{B_aB_b\widetilde\omega_a\widetilde\omega_b}},\qquad t_{\rm swap}=\frac\pi{2g},\qquad\Delta f=\frac g\pi.\] The same coefficient determines transfer timing, splitting, phase and detuning response. A grounded-plane correction is derived from the potential; sensitivity and covariance formulas show how geometry uncertainty propagates to the joint predictions. The resonant rotating-wave relation \(\Delta f\,t_{\rm swap}=1/2\) and the coupled-mode interaction are shared electromagnetic results, not newly claimed QTT-exclusive equations. Using the published nominal apparatus inputs of Brown et al. gives 162.61 microseconds against 155(1) for one exchange time, 3.075 kHz against 3.0(5) for the mode splitting, and 447.58 microseconds against 437(4) for a second exchange period. No observed exchange rate is fitted in the constructor. The timing residuals are 4.91% and 2.42%; rounded geometry and missing calibration covariance prevent a complete sigma verdict. The original experiment already supplied the same independently calculated Coulomb and image correction, separately from its four-parameter trajectory fit. This retrospective calculation is not presented as a blind predictive victory. Retained source and optical results. The full development includes finite interacting contacts and an autonomous 64-record source; lossless-routing and finite-real-time theorems; balanced-rail pi/8 selection; a complete reference-detector model and eleven memory histories; conditional counted-frequency and composition theorems; two transverse photon modes with helicities \(+\hbar\) and \(-\hbar\); source-current force and work coupling; and the stationary relation \(\Delta E_{\rm lab}=\hbar\omega_{\rm lab}\). Their original premises and observational scopes remain intact. The inherited photon-edge constructor reaches both atomic color and leading decay without a transition-strength fit: \[\alpha_0^{-1}=4\pi[8+\pi\cos(\pi/8)+\lambda_\gamma],\qquad\frac{\omega_{21}}{\Omega_*}=\frac38\chi_\mu\alpha_0^2,\qquad\frac{\Gamma_{2p\to1s}}{\Omega_*}=\left(\frac23\right)^8\chi_\mu\alpha_0^5.\] The fixed inverse coupling is 137.0359991659975..., retaining GREEN numerical compatibility with CODATA 2022 at -0.523927 quoted standard uncertainties. Explicit wavefunction integration gives \(\Gamma_{2p\to1s}/\omega_{21}=2^{11}\alpha_0^3/3^9=4.04328772872712\ldots\times10^{-8}\). The leading lifetime is 1.596193893 ns against the cited 1.60 +/- 0.01 ns measurement. The atomic coefficients are known relations; the QTT contribution is the inherited source coupling and its readout construction. The twenty-term matched hydrogen calculation, with explicitly attributed QED, recoil and nuclear inputs, retains a centroid of 2466061412376252.435 Hz and conditional known-input uncertainty 634286637.8 Hz. Its pulls against the 2011 and 2013 measurements remain -0.001278259 and -0.001278232. These are correlated compatibility checks, not independent discovery significances. The Lamb specific difference is 187225891.249 Hz with conditional known-input uncertainty 126.919 Hz; common inverse-cube contact terms cancel exactly. The source-electron candidate, soft matching, constructor chronology and unquantified model contributions retain their stated status. Version 4.0 preserves Parts I-XXII and adds preparation transport, coherent capacity/phase coordinates, effective Coulomb and action certificates, and finite cross-work calibration bounds. Earlier source-work, microscopic, ion, optical and atomic results remain complete. The open PDF and reconstruction replay inherited and new mathematical checks, original calculation scripts and separate observation audits. Software passes do not establish microscopic physical selection. QTT remains a speculative physical framework; no new experimental data or qualified external review is claimed. Existing experimental seals and the main book are unchanged. Ali Attar, Independent Researcher, Colombes, France. ORCID: 0009-0008-9931-2691. Source dependencies: Main Book, Photon-Edge Gate, Maxwell Dynamics, Hamiltonian, Lagrangian, Completed-Event Hamiltonian. These identify proof dependencies, not independent evidence. External observations and context: Brown et al. ion exchange, CODATA 2022, hydrogen lifetime, Parthey et al., Matveev et al., geometric quantum mechanics, informational rec