clean_null_refutes_rs
plain-language theorem explainer
At the exact Newtonian weak-field model point for the named BMV geometry, a vanishing amplitude-matrix determinant is impossible. Citation target for the BMV falsifier floor: if the four branch phases equal the rational model values and the joint state is product (det = 0), one obtains a contradiction. Proof is pure substitution into the already-certified geometry-entangled lemma for those phases. Experimentally meaningful content lives in the band-robust sibling, not here.
Claim. Let $\varphi_{LL},\varphi_{LR},\varphi_{RL},\varphi_{RR}$ be real branch phases equal respectively to the Newtonian weak-field model phases at the named BMV geometry. If the determinant of the two-qubit branch amplitude matrix built from those four phases is zero, then a contradiction follows.
background
This module is the BMV falsifier-band package for Recognition Science gravity. Panel framing is binding: BMV entanglement is predicted by any quantum mediator, so the package is permanently excluded from the pillar-3 discriminator slot and serves only as the falsifier floor.
The local objects are the four Newtonian weak-field branch phases (exact rational model values at a fixed named geometry and coherence time) and the pure two-qubit branch amplitude matrix assembled from them. The entanglement witness used throughout is purely algebraic: nonzero determinant of that matrix, i.e. the non-product criterion for a pure two-qubit state. No entanglement entropy is claimed.
Upstream, the geometry-level lemma already proves that at those exact model phases the determinant is nonzero (the entangling invariant sits in $[1/2, 7/10]$, bounded away from $0 \bmod 2\pi$). The present declaration is the model-point reading of that fact as a falsifier: product-state data under exact phase match refutes the package.
proof idea
One-line wrapper. Substitute the four equality hypotheses so the free phase variables become the named model phases, then apply the upstream geometry-entangled lemma, which already shows that the determinant of the branch amplitude matrix at those phases cannot vanish. The null hypothesis is therefore False. No new arithmetic is performed here.
why it matters
Records the model-point form of the BMV falsifier floor named in the module header: under the package {Newtonian weak-field phase model + named geometry}, a clean null (product joint state) is a formal contradiction. Downstream it is cited by the status record BMVFalsifierStatus (documentation flags for the certified package) and sits beside the congruence same_branch_phases_same_BMV_witness, which explains why the same witness cannot discriminate RS from GR+QFT or any other quantum mediator sharing the phases.
Honest scope from the doc-comment and module header: extending "refutes the package" to "refutes the framework" needs the unformalized MODEL/OPEN premise that the RS gravitational channel produces Newtonian weak-field phase magnitudes at this geometry. Track 2.C/2.D forcing cited elsewhere forces amplitude-linearity of the channel under named structural premises; it does not fix phase magnitudes. Within the stated package there is no free parameter that softens a clean null at the model point.
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