phase_RR
plain-language theorem explainer
Defines the Newtonian weak-field gravitational phase on the right-right spatial branch of a two-mass BMV geometry, evaluated at fixed SI anchors. Anyone citing the certified BMV witness band or the clean-null falsifier needs this as one of the four named branch phases. It is a direct application of the weak-field phase formula to the RR separation.
Claim. Let $\phi_{RR}$ be the weak-field branch phase at the named RR geometry: $\phi_{RR} = \mathrm{weakFieldPhase}(G_{\mathrm{SI}},\hbar_{\mathrm{SI}},m_1,m_2,T,r_{RR})$, i.e. the Newtonian phase $(G m_1 m_2 T/\hbar)\cdot(1/r_{RR})$ at the SI-anchored masses, interaction time, and right-right separation.
background
The module builds a falsifier floor for Bose-Marletto-Vedral (BMV) gravitational entanglement. Four spatial branches (LL, LR, RL, RR) label the pairwise separations of two masses in a Stern-Gerlach-style superposition. Each branch accumulates a Newtonian weak-field phase of the form $(G m_1 m_2 T/\hbar)(1/r)$.
The SI anchors $G_{\mathrm{SI}}$ and $\hbar_{\mathrm{SI}}$ are external CODATA values (not RS-native $G=\phi^5/\pi$ or $\hbar=\phi^{-5}$). Sibling defs fix the masses, interaction time $T$, and the four separations $r_{LL},r_{RR},r_{LR},r_{RL}$. The entangling invariant is then $\Delta\Phi=(G m_1 m_2 T/\hbar)(1/r_{LL}+1/r_{RR}-1/r_{LR}-1/r_{RL})$.
Panel framing is explicit: BMV entanglement is predicted by any quantum mediator, so this package is excluded from the pillar-3 discriminator. It only certifies that a clean product-state null at this geometry contradicts the Newtonian weak-field phase package.
proof idea
One-line definitional wrapper. Unfolds to BMVPositive.weakFieldPhase applied to the six SI model inputs $G_{\mathrm{SI}}$, $\hbar_{\mathrm{SI}}$, $m_1$, $m_2$, $T$, and $r_{RR}$. No tactics, no lemmas beyond that call.
why it matters
Supplies the RR corner of the four-tuple $(\phi_{LL},\phi_{LR},\phi_{RL},\phi_{RR})$ that feeds every certified statement in the file. Downstream, branchPhaseInvariant_eq_deltaPhi shows the BMV branch-phase invariant of these four phases is definitionally $\Delta\Phi$; rs_bmv_witness_band places $\Delta\Phi$ in the rational band $[1/2,7/10]\subset(0,2\pi)$ and concludes nonzero amplitude-matrix determinant; rs_bmv_geometry_entangled extracts the entanglement claim; clean_null_refutes_rs turns exact equality to these phases into a model-point falsifier against a measured product state.
Framework role is deliberately narrow: the algebra is THEOREM-grade, but the premise that the RS gravitational channel actually produces Newtonian weak-field magnitudes at this geometry remains MODEL/OPEN (Track 2.C/2.D force channel form, not phase magnitude). A clean null therefore refutes the package, not automatically the whole framework.
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