Artian Rotor-to-Wavefunction Projection Theorem: A Conditional QTT Recovery of the Schrödinger Equation, the A6 Bounded-Generator Gate, and the Macroscopic-Ceiling No-Go

What must be supplied before the Schrödinger equation can be recovered from a finite address model? A finite address ledger can reproduce Schrödinger evolution through an exact source-to-wavefunction projection. The result identifies the readout, the generator domain, and the clock conversion that make the recovery valid. \[\boxed{\begin{gathered}P_c\rho=\sum_w\overline{c_w}\rho_w,\quad\|c\|_2=1,\\J\hbar\partial_T\rho=(I\otimes H_T)\rho,\quad d\tau=N\,dT,\\\Psi=P_c\rho,\quad J\hbar\partial_\tau\Psi=\frac{H_T}{N}\Psi.\end{gathered}}\] The normalized address map is a coisometry. For an address-blind self-adjoint generator it intertwines source evolution with laboratory evolution; packaging the real rotor \(J\) as \(i\) gives the familiar equation. A constant positive lapse divides the laboratory generator by \(N\). Finite capacity and a sharp coherence wall can coexist with that projection. Version 3.1 constructs compatible local dynamics and a controlled evolution for physically recorded legal partitions. For certified positive source loads \(b_i\), the admissible mixed states are \[\mathfrak A_{\mathbf b}=\operatorname{conv}\!\bigcup_{\pi:\,\sum_{i\in C}b_i\le1}\left\{\bigotimes_{C\in\pi}\sigma_C\right\}.\] Primitive-local operations preserve this class. With an actual classical partition record, unitary evolution inside each legal block followed by forgetting the record also preserves it. An arbitrary entangling gate need not: two primitives of load \(3/5\) each provide an explicit Bell-state counterexample. The global physical postulate excludes a jointly coherent domain above \(B_\Gamma=M_\Gamma/m_A=1\), even transiently. It is a state-admissibility wall, not a localization lifetime. The paper also proves the precise alternative implication from complete branchwise funding: \[\boxed{\rho_{\Gamma,w}\ne0\Rightarrow B_w\ge B_\Gamma,\quad B_w\le1\quad\Longrightarrow\quad B_\Gamma>1\Rightarrow\rho_\Gamma=P_c\rho_\Gamma=0.}\] This implication is proved; the physical source functional establishing complete funding remains a separate derivation target. Independent domains can carry a total mass above one. The inherited local-budget counterexample excludes an inference from local capacity alone, not the global postulate itself. The bounded-generator theorem, exact projection defect, ultraviolet-kernel nonuniqueness, and finite-trace counterexample remain intact. A corrected bounded completion keeps the source cap valid for every positive lapse. The release adds explicit preparation and witness tests, ontology and book anchors, and a reproducible 47-check mathematical certificate. Empirical selection of the physical wall remains open. A6 hard-wall companion · Main Book v10.01 · A6 lexicon · Artian's Universe