phase_RL
plain-language theorem explainer
Names the Newtonian weak-field gravitational phase on the right-left spatial branch of a two-mass BMV geometry, evaluated at the module's fixed SI anchors and separations. Anyone citing the certified BMV witness band or the clean-null falsifier needs this as one of the four branch phases. The body is a direct specialization of the weak-field phase model to the RL radius.
Claim. Let $\phi_{RL}$ be the Newtonian weak-field branch phase for the right-left path pair at the named BMV geometry: $\phi_{RL} := \Phi_{\mathrm{wf}}(G,\hbar,m_1,m_2,T,r_{RL})$ in SI units, with $G$ and $\hbar$ the external anchors and $r_{RL}$ the RL center-of-mass separation.
background
The module builds a falsifier floor for Bose-Marletto-Vedral style gravitational entanglement. Four classical path combinations (LL, LR, RL, RR) each pick up a weak-field gravitational phase; the joint two-qubit branch state is entangled precisely when a certain phase invariant is bounded away from $0 \bmod 2\pi$.
The phase model is an explicit MODEL input: BMVPositive.weakFieldPhase evaluates the Newtonian weak-field phase from $G$, $\hbar$, the two masses, interaction time $T$, and a single branch separation. SI anchors $G_{\mathrm{SI}}$ and $\hbar_{\mathrm{SI}}$ are CODATA/SI-2019 external constants; the geometry radii $r_{LL}, r_{LR}, r_{RL}, r_{RR}$ are named model inputs of Section 1.
Panel framing is binding: BMV entanglement is predicted by any quantum mediator, so this package cannot discriminate RS from GR+QFT. It only certifies that a clean product-state null at this geometry contradicts the package {weak-field phases + named geometry}.
proof idea
Pure definitional specialization. The value is the weak-field phase functional applied to the module's SI constants, masses, time, and the RL separation $r_{RL}$. No proof obligations; no simplification beyond that application.
why it matters
One of the four named phases that feed the certified witness. Downstream, branchPhaseInvariant_eq_deltaPhi shows the BMV branch-phase invariant of $(\phi_{LL},\phi_{LR},\phi_{RL},\phi_{RR})$ is definitionally $\Delta\phi$. That invariant is then pinned in the rational band $[1/2, 7/10] \subset (0, 2\pi)$ by rs_bmv_witness_band, which yields nonzero determinant of the branch amplitude matrix (rs_bmv_geometry_entangled).
The model-point falsifier clean_null_refutes_rs takes exact equalities of observed phases to these four definitions (including $\phi_{RL}$) and concludes that a measured product state is contradictory. Framework-level reading remains MODEL/OPEN: Track 2 channel uniqueness does not force the magnitude of these Newtonian phases.
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