Artian's Entropy and Second-Law Reference Theorem: Completed Records, Access Loss, and the A2-A3 Source-Volume Ledger

Abstract

A Two-Coordinate Second Law with a Separate Source-Volume Ledger This paper separates two statements often compressed into one word. Completed physical records do not disappear from the source history, while a laboratory channel can lose access to distinctions that remain present in the full state. Their joint entropy-production coordinate is \[ \boxed{ \Delta\mathbf S_{\rm QTT} = \begin{pmatrix} k_B\,\Delta N_{\rm rec}\\[2pt] k_B\displaystyle\sum_e \left[ D(\rho_e\Vert\omega_e) -D(\Phi_e\rho_e\Vert\Phi_e\omega_e) \right] \end{pmatrix} \in\mathbb R_{\ge0}^{2} } \] The first coordinate is a QTT completed-history theorem. The second is the standard quantum data-processing loss, kept with its conventional provenance. Microstate recurrence does not reverse the first coordinate because \(N_{\rm rec}\) is a history variable, not a function of the instantaneous microstate. The paper also gives an exact, separately typed A2/A3 source ledger. For the explicit branch in which the full Artian mass inventory \(B=M/m_A\) is present from the first counted source tick, \[ \boxed{ N_{\rm SQ}^{A2}=BN_T, \qquad N_{\rm SQ}^{A3}=12BN_T(N_T+1), \qquad V_{\rm src}^{A3}=48\pi B\ell_A^3N_T(N_T+1) } \] A2 supplies one finite 24-pixellate support packet per Artian mass-count unit per tick. A3 seeds twenty-four White-Void fronts per unit and tick, with each active front minting one space quantum per tick. This is a finite source-volume theorem, not an entropy coefficient. The former universal \(24-1=23\) entropy law is therefore retired: \(23B\) appears only as the first-tick value of an optional difference between two distinct source ledgers. The paper preserves and strengthens the modular-access, Clausius, fluctuation, surface-entropy, Page-capacity, recurrence-separation, decoherence, and blind-test sections. It also defines the exact wrong-falsification boundary for the completed-record timing tests. Verification: 45/45 operational and typed-ledger checks passed. 10/10 independent access-completeness checks passed. Zero fitted source parameters in the finite-ledger audit. QTT remains a new and speculative framework pending discriminating tests. Status ledger: SIGMA-COMPLETED-RECORD-SECOND-LAW-CLOSED SIGMA-ACCESS-LOSS-DATA-PROCESSING-CLOSED SIGMA-A2-A3-VOLUME-LEDGER-CLOSED-GIVEN-FIXED-ORIGIN-B SIGMA-UNIVERSAL-23-ENTROPY-COEFFICIENT-RETIRED SIGMA-RECORD-TO-TIMING-OBSERVATION-PENDING Version: 4.0 Concept DOI: 10.5281/zenodo.20045306 Author: Ali Attar Website: quantumtraction.org Reader anchors: QTT Main Book, concept DOI Completed-Record Fan-Out and Timing-Access Framework Record-Fan-Out Timing Blind Test Dynamic-Circuit Record-Timing Extension The Equation on the Tombstone Testing Counting Entropy