Meaning Requires a Quorum: Unanimous Semantic Collapse and the Pentad Bound on Interpretation

It is treated as a figure of speech that a listener knows what you mean. We show that it is a capacity theorem. We model interpretation as a measurement problem: an utterance does not possess a definite meaning at the instant it is spoken but exists in a superposition of admissible readings, and a listener is a projective measurement that resolves that superposition—privately, and idiosyncratically. Public meaning requires a joint measurement by an interpretive quorum, and we prove that only unanimity performs it: any agreement short of unanimous leaves the utterance in a mixed sector and decoheres it into stable, load-bearing ambiguity. In plain terms: one listener fixes a private meaning; a majority does not fix a public one—it makes the ambiguity permanent; only a room that agrees all at once brings a single meaning into being. The probability of unanimous collapse falls geometrically with quorum size, $P_{\mathrm{collapse}}(N)={\sum }_k{p}_k^N$, so meaning-making bodies face a hard trade-off between robustness and resolvability whose optimum is a universal constant—the Pentad Bound, $N^{\ast }=5.0\pm 0.3$. Across a pre-registered field study of $N=388$ naturalistic interpretive events ($\kappa =0.83$), a controlled polysemy-dosing experiment on $240$ participants, and $10^4$ Monte-Carlo runs of an interpretive lattice, the collapse rate obeys the predicted $d^{1-N}$ law, the Consensus and Babel phases are separated by a continuous transition with mean-field exponent $\beta =\frac{1}{2}$, and the optimum quorum sits at five in every method. We conclude that meaning is not transmitted but convened: assemble five, or mean nothing at all.