phase_LL
plain-language theorem explainer
Names the Newtonian weak-field gravitational phase on the LL interferometer branch at the package's fixed BMV geometry (SI anchors G, ħ plus the named masses, time, and LL separation). Anyone citing the certified BMV witness band or the clean-null falsifier uses this as one of the four branch phases. The body is a direct application of the weak-field phase model to those parameters.
Claim. Let $\phi_{LL}$ be the Newtonian weak-field branch phase at the named geometry: $\phi_{LL} := \Phi_{\mathrm{wf}}(G_{\mathrm{SI}},\hbar_{\mathrm{SI}},m_1,m_2,T,r_{LL})$, where $\Phi_{\mathrm{wf}}$ is the weak-field phase functional and $r_{LL}$ is the LL path separation in SI units.
background
This module is the BMV falsifier floor, not a pillar-3 discriminator. BMV entanglement is expected from any quantum mediator, so the package cannot separate Recognition Science from GR+QFT. What it does certify is: under the Newtonian weak-field phase model plus a fixed named geometry, the two-mass joint state is non-product, with entangling invariant in a rational band bounded away from $0 \bmod 2\pi$.
The four branch phases $\phi_{LL},\phi_{LR},\phi_{RL},\phi_{RR}$ are the model inputs to that algebra. Each is the weak-field phase evaluated at one of the four path-pair separations. External SI anchors supply $G$ (CODATA) and $\hbar$ (exact since SI 2019); sibling defs fix the masses, interaction time, and the four distances.
Upstream, BMVPositive.weakFieldPhase is the MODEL phase formula. The Track 2 channel-uniqueness results force amplitude-linearity of the gravitational channel under structural premises; they do not fix the numerical magnitude of these phases. That magnitude premise remains MODEL/OPEN.
proof idea
Pure definitional wrapper: instantiate the weak-field phase functional at the package constants $G_{\mathrm{SI}}$, $\hbar_{\mathrm{SI}}$, $m_1$, $m_2$, $T$, and the LL separation $r_{LL}$. No proof obligations.
why it matters
One of the four named phases that feed the entire certified band. 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 what rs_bmv_witness_band places in $[1/2,7/10]\subset(0,2\pi)$, yielding nonzero determinant of the branch amplitude matrix (rs_bmv_geometry_entangled).
The model-point falsifier clean_null_refutes_rs takes exact equality hypotheses $\varphi_{LL}=\phi_{LL}$ (and cyclic) and concludes that a measured product state contradicts the package. Honest scope from the module doc: a clean null refutes the package {weak-field phases + named geometry}; extending that to framework-level falsification of RS requires the unformalized premise that RS produces these Newtonian magnitudes, which is MODEL/OPEN.
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