The Artian's Capacity Wall: Necessity and Countermodel Theorems for Quantum Speed, Source-Level Ultraviolet Finiteness, and Shared Information
Year: 2026
Type: preprint
Abstract: One local wall, three exact consequences Version: 1.0 Concept DOI: 10.5281/zenodo.21702144 Author: Ali Attar Website: quantumtraction.org Main book: Quantum Traction Theory: Main Book v10.01 Here capacity wall means a source-level per-address bound on generator width, reduced action, mutually distinguishable records, and their shared funding. It is distinct from the quantum-channel capacity \(Q(\mathcal N)\) of quantum Shannon theory. The dynamical face turns a local spectral-width ceiling into a tight quantum-speed theorem: \[ \boxed{ \Theta_{\rm FS}(\psi_0,\psi_T) \le \frac{1}{2\hbar}\int_0^T {\rm diam}\,{\rm spec}\,H_w(t)\,dt \le \frac{T}{2\widetilde t_A} } \] and therefore \[ \boxed{ T\ge 2\widetilde t_A\arccos\sqrt F, \qquad T_\perp\ge\pi\widetilde t_A. } \] The orthogonalization constant is saturated by a two-level system. The informational face begins with one faithful reference state. If every mutually orthogonal physical record obeys \(D(|\psi_j\rangle\langle\psi_j|\Vert\omega)\le C_\star\), then \[ \boxed{ M\le e^{C_\star}. } \] For a finite region this produces a finite-dimensional physical observable algebra, a finite Gibbs trace, bounded exact moments, and norm-convergent Dyson evolution: \[ \boxed{ 1\le Z_R(\beta)={\rm Tr}\,e^{-\beta H_R} \le D_R\le d_\star^{N_R}. } \] The shared-capacity face blocks multiplication of one local budget by species relabelling. For a finite region and for depth-\(L\) local boundary generation, \[ \boxed{ S_{\rm vN}(\rho_A)\le N_A\log d_\star, \qquad S_{\rm vN}(\rho_A)\le 2L\,b(A)\log d_\star. } \] The QTT surface ledger is kept in its exact saturation form: \[ \boxed{ N_H^{\rm QTT} = \eta_H\frac{A}{4\ell_A^2}, \qquad 0\le\eta_H\le1. } \] The familiar quarter-area equality is the stationary capacity-saturated row \(\eta_H=1\). The separate modular-to-von-Neumann normalization bridge remains explicitly open. The three converse countermodels combine into the paper's master necessity statement: \[ \boxed{ \begin{gathered} \text{nonzero local orthogonalization time}\\ +\ \text{finite exact source regions}\\ +\ \text{finite species-independent record capacity} \end{gathered} \Longrightarrow \text{an A6-equivalent local capacity wall}. } \] The result does not assert that QTT is the only possible syntax for that wall. It identifies the mathematical work that any equivalent local principle must perform. The upstream independence question is closed separately: A1, A4, primitive A7 closure, and textbook quantum mechanics do not derive A6 in the declared weak class. This paper is the downstream complement: it establishes why A6, or a mathematically equivalent local law, is necessary for the three universal consequence families. Reproducibility: the release includes the 25-page PDF and a reconstruction package containing the LaTeX source, proof-status ledger, four scientific audits, verification script, 10-check machine certificate, render audit, and SHA-256 manifest. All 10 computational checks pass. Related anchors: A6 independence and countermodel theorem QTT Main Book v10.01 QTT Lexicon: A6 Quantum Capacity Artian's Universe and source/readout ontology QTT Derivation Atlas QTT DOI Map / Corpus Tree
Author: Attar, Ali
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171853493