Mass-Qualified Coherence Witnesses for a Milligram Torsional Rotor: A Conditional Test of the QTT A6 Hard Wall

Which physical mass must share the measured coherence? A heavy mechanical host can contain a small quantum subsystem while most of its mass remains unchanged between branches. This paper derives a source-load-qualified coherence witness that distinguishes those cases. For orthogonally tagged product branches, the central bound is \[\boxed{F_\Psi(\rho)\le\frac12\left[1+\max_{T:\ b_a+\sum_{j\in T}b_j\le1}\prod_{j\notin T}r_j\right]\quad(\rho\in\mathfrak A_{\mathbf b}).}\] Here \(b_j=M_j/m_A\) is an independently certified Artian mass count, \(b_a\) is the tagging-system load, and \(r_j=|\langle u_j|v_j\rangle|\) is a branch overlap. The QTT source restriction limits each jointly coherent block to one source mass unit. Maximizing over all allowed blocks gives a conservative threshold without choosing a favorable physical partition from the judged outcomes. The bound gives full weight to the QTT mass-capacity hypothesis while preventing passive spectator mass from being credited as coherent mass. It extends the existing A6 orthogonal GHZ witness to nonorthogonal branches, finite mass and overlap intervals, mixed reference operators, and independently qualified source-to-detector maps. A new exact-rational relaxation provides certified conservative bounds when direct subset enumeration is too large. The physical detector relation is \[\mathbb E[Y]\le\alpha_{\rm A6}^{+}+\delta_{\rm source}+\varepsilon_{\rm measurement}.\] The paper proves this relation, supplies the exact randomized GHZ score, retains every attempted trial including losses, and derives a fixed-sample concentration test valid for history-dependent preparations under fresh-setting independence. The reconstruction package contains executable algebra and mutation checks, rational-bound routines, seeded synthetic controls and an inactive apparatus template. The application is Mishra and colleagues' November 2026 continuously monitored milligram free rotor. Its reported state estimates are checked against the primary preprint. Gaussian spectral and resolved-Kraus theorems quantify the additional preparation needed by a high-fidelity pure-target strategy, without denying mixed-state coherence or other entanglement routes. The methods theorem is closed under its printed premises; the rotor source-factorization and instrument certificate remain a separate experimental task. No new laboratory witness data or empirical QTT verdict is reported. A certified excess would exclude the frozen mass-budget realization. A below-bound result alone does not establish a mass wall. This Version 1.0 is a standalone methods and protocol publication; apparatus-specific prospective activation requires a separate frozen capsule before witness acquisition. Stable paper DOI | A6 hard-wall dependency | QTT Main Book | A6 reader anchor