QTT Completed-Event Transport and Quantum Coherence

Real-dial dynamics, conditional interactions, and optical interference \[G-FTGF=LTML, L=0, FJ=JF U_F^ U_F=I.\] 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. A2 endurance, physical phase closure, and finite occupation. Persistence requires a sufficient continuing record, not merely a log of visible changes. A finite operational quotient identifies which markers future contacts can distinguish. For a specified orthogonal connection on the resulting preparation graph, the complete zero-defect sector is classified by \[ L_Uγ(U_γ-I), D_U(x)=∑e:u→ vw_e\|x_v-U_ex_u\|^2.\] On a single real oriented dial, a nonzero parallel section exists exactly when each fundamental cycle has an integer full turn. Higher-dimensional fibers require a common fixed vector, not identity of every holonomy. Equal-weight cycles have an exact unit-total-capacity mismatch floor, \[min\|x\|=1 D_U(x) =4wsin^2\!(dist(Φ,2π Z)/2m).\] The graph, reference and source selection must be identified independently. Reversible capacity renewal can retain a nontrivial twist; the paper proves that counterexample and checks the sign of a proposed energy-selection mechanism. A separately qualified work/action law yields \(Emode=Ω I\), without confusing a spectral mismatch floor with a photon energy spacing. Two exact finite mode constructions. Equal-address insertion into a symmetric inventory of \(K\) binary capacity slots gives \[d_K^|n=√(n+1)(1-n/K)\,|n+1, [d_K,d_K^]=I-2N/K.\] A compressed bosonic insertion instead satisfies \[b_K^ b_K=N, [b_K,b_K^]=I-(K+1)|K K|.\] These are different finite constructors. Their insertion strengths, boundary terms and physical qualifications are printed explicitly; neither is silently declared to be the uniquely selected microscopic photon source. In particular, the usual quadratic finite-oscillator energy requires a top-level work correction to reproduce an exactly equally spaced ladder. Work and phase, compared independently. For a self-adjoint work operator on a single connected occupation ladder with nonzero adjacent insertion links, the exact classification is \[[H,B]=- Aω B H=E_0I+ Aω N.\] Stationarity of the occupations is a consequence, not an extra premise. The inherited convention is \( A=\). The earlier canonical photon result remains valid. This theorem identifies the stronger microscopic bridge: the source must qualify physical work and its action normalization independently of a desired phase evolution. Replacing \( A\) by an arbitrary positive action scale leaves the counting theorems unchanged, separating integer structure from an independent SI value of Planck's constant. The finite examples introduce no target-fitted coefficients and no new observational claim. The paper retains its full optical, atomic, ion-exchange, source-work and preparation results, and adds explicit closure certificates, finite-mode proofs, countermodels and conditional experimental discriminants. Mathematical closure, physical source selection and empirical status remain separate. 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 \[Ξ∘ R_m=s_m∘Ξ, s_mx=x/√ m, X_α=√C__J(θ_α)e_α.\] For desired reduced capacities \(a_α=C_α/m\), actual capacities \(b_α\), and independently calibrated phase errors \(δ_α\), the exact preparation distance is \[ε^2=∑_α[(√b_α-√a_α)^2+4√a_α b_αsin^2(δ_α/2)].\] It supplies an explicit work-error tolerance, \(|Δ W|/E_*≤2√ m\,kRε+mkε^2+b_0+mb_1\), 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 \(W_×=V(d+q_b-q_a)-V(d-q_a)-V(d+q_b)+V(d)\) cancels separate trap contributions. With \(κ_C=V''(d)\) and a specified third-derivative bound, \[|W_×+κ_Cq_aq_b|≤12 M_3|q_aq_b|(|q_a|+|q_b|).\] 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 \(τ=T/t_A\), bounded force defect \(ε_E\), and curvature defect \(κ<2\), the resulting trajectory bound is \[\|x(τ)-x_0(τ)\|≤ d_0+τε_E+κ\|K\|R/2-κ.\] 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 \[E(x)-mE(x/√ m)/E_*=c^Td_m(x), c^Td_m=0\ for every legal c\ \ N^Td_m=0,\ c_0^Td_m=0.\] 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 \[∮_γβ=m∮s_mγβ dβ(x)=dβ(0), s_mx=x/√ m.\] 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 \( J x=Hx\). 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 \(B_i=M_i/m_A\), \[g t_A={α_0ηᵢₘ}{ d^3√B_aB_bω_aω_b}, tswap=π{2g},Δ f= gπ.\] 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 \(Δ f\,tswap=1/2\) 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 predicti