Where Could Inter-Branch Signaling Still Hide? A Conditional No-Go Result, a Distinguishability–Susceptibility Bound, an Experimental Map, and a Proposed Torsion-Balance Test

We ask whether any mechanism could allow signaling between Everett branches, and we try to answer by exclusion. First, we restate a no-signaling lemma in its minimal form (any linear trace-preserving operation on the receiver’s system leaves the sender’s reduced state unchanged) and we state plainly that the associated theorem is conditional and close to tautological: all of its content sits in an assumption (C1) that the sender’s operation does not act on the receiver’s algebra. We then give that assumption quantitative content for coherence-mediated channels: a distinguishability–susceptibility bound χ·S ≤ S₀/2, exact under a stated hypothesis, under which well-separated branches and a strong inter-branch channel are mutually exclusive. This bound is a reframing of the known distinguishability–visibility complementarity, applied to the inter-branch signaling question; we state the hypothesis’s limits and do not claim a general no-go. We correct a statement in an earlier version of our work about collapse models. Second, we review six definitions of “branch” and show that, in the decoherence-based ones, the no-coupling condition fails only at the order of the decoherence residual, so the open question is controllability, not existence of coupling. Third, we compile a map of experimental tests of the premises of quantum mechanics, with numbers read from primary sources: the electromagnetic sector of linearity, the Born rule and logarithmic nonlinearity are closed at high precision, while the gravitational sector has no numerical experimental bound. Fourth, we analyze that sector: a mean-field gravitational coupling is excluded at order one by the Page-Geilker experiment, and the causal nonlinear model of Kaplan and Rajendran dilutes local effects by 1/N. Fifth, we propose a quantitative redo of the Page-Geilker experiment with a modern torsion balance, a paired-replay control, and a sensitivity projection that is an optimistic white-noise ceiling. Six rounds of AI-generated candidate mechanisms, each adversarially verified, produced zero survivors. We claim no positive result. What is new here is the bookkeeping, the correction, the reframed bound, the map, and the proposal; the no-signaling lemma itself is standard.