Companion to The Shibboleth Lattice: Recognition Channels and the Universality of In-Group Coordination (Bilar 2026, doi:10.5281/zenodo.19595987). The parent paper proposes a binding operator B = (S, I, W, rho, chi) unifying coalition formation across five substrates, with recognition-channel proxy $\kappa_H$ as the central measurable quantity. Its empirical base is a single point: $\kappa_H$ ~ 0.94 from a (0.15, 0.49, 0.997) preservation-rate triple drawn from Potter et al. (2026, arXiv:2604.19784) frontier-LLM peer-preservation experiments. This companion paper does three things. First, it reverse-engineers the $\kappa_H$ ~ 0.94 estimate via Bayesian reconstruction of the joint distribution and shows the unique reproducing observation count is $n_{obs} ~ 34$ binary observations per peer, an implicit interaction-history budget. Second, it instantiates $\kappa_H$ computations for all five substrates (quantum entanglement, evolutionary covert tags, engineered handshake, LLM peer-preservation, IPD population-tracking), with sensitivity and tolerance analyses identifying the neutral-peer rate as the binding constraint for replication. Third, it operationalizes the witness-set falsification test with a concrete LLM experimental design distinguishing the binding operator account from instrumental convergence (expected effect size Delta = 0.75). The paper is candid that the (0.15, 0.49, 0.997) triple represents one selection from Potter's per-model, per-behavior tables, not a unique reading; alternative selections yield different $\kappa_H$ values and the paper documents this in §2.1 and §6.2. Companion code, simulations, and figures are deposited separately as software (chokmah-me/shibboleth-lattice-sim).
binding operator · recognition channel · coalition formation · uncertainty coefficient · peer preservation · quantum game theory · iterated prisoner's dilemma · Shibboleth Lattice · AI alignment · multi-agent systems