Artian's Physical Terminal Reference Framework: A Carrier-Independent T-star/Tau Constructor Theorem for Activation-Gated Tests of QTT Axiom A1

Abstract

When do two clock labels become two physical experiments? An A1 reference-switch test is meaningful only if the two terminal labels are implemented by different physical write histories. This paper gives a carrier-independent answer. It represents the apparatus as a complete quantum instrument, reconstructs the laboratory write graph, and asks which physical event last wrote the durable record that survives to closure. Ontological reading. The primitive relevant to this theorem is the completed event: one finite source process closes and leaves a physical ledger record before a laboratory clock assigns its readout label. The candidate (T^\star) terminal carries a durable memory of that completion; the \(\tau\) terminal is defined or overwritten by a laboratory reference. The experiment therefore does not compare two names for time. It compares two physical histories of what last wrote the terminal record. The candidate source terminal is defined without using the desired result: \[ \boxed{ \mathfrak T_{T^\star}: C_E=1,\quad \Xi_L\le\epsilon_L,\quad \Xi_S\ge\eta_S,\quad M_S\ \text{continuous},\quad N_{\rm rec}=0,\quad N_{\rm proj}=1 } \] Here (C_E) certifies a completed source event, (Xi_L) bounds laboratory write susceptibility, (Xi_S) proves that the surviving record still depends on the source memory, (N_{\rm rec}=0) forbids a later reference overwrite, and (N_{\rm proj}=1) permits one final basis-selecting readout. Ordinary free evolution does not pass this constructor. Fifteen predeclared gates compute one activation bit: \[ \boxed{ G_{\rm PT}=\prod_{j=1}^{15}P_j } \] \[ \boxed{ G_{\rm PT}=1 \Longrightarrow \begin{cases} R_{\rm clk}^{\rm ordinary}=1,\\[1mm] R_{\rm clk}^{\rm QTT-A1} =\cos^q\!\left(\frac{\pi}{8}\right), \end{cases} \qquad G_{\rm PT}=0 \Longrightarrow \texttt{INELIGIBLE\_NO\_THEORY\_VERDICT} } \] The detector degree (q) is derived and frozen before target data. A four-history experiment then tests the crossing character ((0,1,1,0)), with the geometric-mean estimator \[ \boxed{ R_{\rm clk} = \sqrt{ \frac{|D_{\tau T^\star}D_{T^\star\tau}|} {|D_{\tau\tau}D_{T^\star T^\star}|} } \frac{1}{C_K N_\times^{\rm ordinary}} } \] The framework proves that software relabelling, passive data reduction, a dark interval, and zero laboratory-write rank by themselves cannot create a second clock terminal. It also makes any apparatus containing a programmed (22.5^\circ), (45^\circ), CHSH-standard, or target-equivalent overlap ineligible before unblinding. The theorem is the shared activation layer for matter-wave Sagnac, Faraday, Berry/holonomy, delocalized quantum-clock, monitored-recurrence, photon-storage, and related reference-switch tests. Platform qualification and empirical A1 judgment remain separate downstream tasks. Concept DOI: 10.5281/zenodo.21739215 Main book: Quantum Traction Theory: Main Book v10.01 Website: quantumtraction.org · Lexicon · Derivation Atlas · Observatory