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

Abstract

What must be supplied before the Schrödinger equation can be recovered from a finite address model? Let the source state be a square-summable family of real-(J) amplitudes, \[ \mathcal H_{\rm src} = \ell^2(\mathcal W)\widehat\otimes\mathcal H_{{\rm lab},\mathbb R}, \] and let one fixed normalized address functional read that family: \[ P_c\rho = \sum_{w\in\mathcal W}\overline{c_w}\,\rho_w, \qquad c\in\ell^2(\mathcal W), \qquad \lVert c\rVert_2=1. \] The map is bounded and coisometric on its readout subspace. If the source generator is address-blind, projection commutes exactly with the evolution. For the constant positive scalar clock relation (d\tau=N\,dT), the resulting generator map is \[ \boxed{ J\hbar\,\partial_\tau\Psi = H_{\rm lab}\Psi, \qquad H_{\rm lab}=\frac{H_T}{N}, \qquad \Psi=P_c\rho }. \] Packaging the real complex structure (J) as multiplication by (i) gives the familiar laboratory equation (i\hbar\partial_\tau\psi=H_{\rm lab}\psi). The theorem is exact within its printed premises. Stone's theorem supplies a self-adjoint generator after strong continuity, the group law, and unitarity are declared. It does not select the physical Hamiltonian. Galilean dispersion, (p^2/(2m)), scalar potentials, and gauge minimal coupling retain their standard low-energy provenance. The A6 ultraviolet gate If A6 imposes a finite spectral-width wall on the exact source generator, the unbounded textbook Hamiltonian cannot itself be the ultraviolet source operator. It can only be the infrared shadow of a bounded completion. The presently printed kernel conditions do not select that completion uniquely: the family \[ K_a(x)=e^{-ax}, \qquad a\ge1, \] contains infinitely many positive, entire, normalized kernels with \[ \left\lVert H_{\rm NR}K_a(H_{\rm NR}/E_A) \right\rVert \le \frac{E_A}{ae} Two finite-capacity no-go results A bounded spectrum alone does not imply a finite Gibbs trace: (H=0) on an infinite-dimensional Hilbert space gives (\operatorname{Tr}e^{-\beta H}=\infty). Finite source thermodynamics additionally needs finite operational local dimension and a finite active address count. Likewise, local address capacity and local (2\pi) closure do not imply a global coherent-mass ceiling. For (K) legal saturated addresses, \[ B_{w_j}=1, \qquad Q_{w_j}^{\rm bundle}=2\pi, \qquad B_{\rm total}=\sum_{j=1}^{K}B_{w_j}=K. \] A global (B\le1) theorem therefore requires a separate cross-address no-stacking law. Version 3.0 records the earlier cat-scale ceiling as an open theorem target rather than a derived result. Scientific status QTT-SCHRODINGER-REAL-J-COMPLEX-PACKAGING: CLOSED / STANDARD IDENTITY QTT-SCHRODINGER-STONE-GENERATOR: CLOSED GIVEN P3 QTT-SCHRODINGER-ADDRESS-PROJECTION-INTERTWINING: CLOSED GIVEN P2-P4 QTT-SCHRODINGER-A1-CONSTANT-LAPSE-MAP: CLOSED QTT-SCHRODINGER-A6-BOUNDED-SOURCE-GENERATOR: CLOSED GIVEN A6 QTT-SCHRODINGER-UV-KERNEL-UNIQUENESS: OPEN / NO-GO CERTIFIED QTT-SCHRODINGER-GLOBAL-COHERENT-MASS-CEILING: NOT DERIVED / NO-GO CERTIFIED Version: 3.0 Concept DOI: 10.5281/zenodo.20119662 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory: Main Book v10.01 Related QTT anchors The Born Rule from Finite Address-Capacity Counting Observation as Access Artian Action-Rotor Reference Framework A6 Quantum-Capacity Necessity and Independence Theorem The Artian's Capacity Wall Corpus Tree entry Derivation Atlas node QTT Lexicon entry Included public files PDF paper, Version 3.0 Full reconstruction, claim-certificate, and verification package