The Shibboleth Lattice: Recognition Channels and the Universality of In-Group Coordination

A preprint unifying four documented cases of multi-agent coalition behavior (quantum-game entanglement, evolutionary covert-tag recognition, engineered handshake collusion, and emergent peer-preservation in frontier language models) under a single formal structure: the binding operator $B = (S, I, W, ρ, χ)$. The central technical contribution is the recognition channel proxy $κ_H$, defined as a principal-relative uncertainty coefficient (Theil 1970) on the channel through which inside-set agents identify each other. $κ_H$ is a behavioral proxy estimated from resistance rates, not a directly measured Shannon channel capacity; the paper is explicit about what that distinction implies.

$κ_H$ is estimated from the Potter 2026 conditional preservation rates and yields approximately 0.94 for that case, conditional on those numbers replicating. $κ_H$  is a behavioral proxy, not a directly measured Shannon channel capacity; Section 3 is explicit about what that distinction implies. The dynamical pattern across the four cases is sigmoidal in shape. I treat the sigmoid as a phenomenological description fitted to the available evidence, not a derivation. The inflection threshold $κ^*$ is lower for engineered and emergent bindings, where agents incur no channel-discovery cost, and higher for evolutionary bindings, where a population must invest selection pressure to find a private channel. I derive one prediction directly from B: witness-set substitution should collapse coalition behavior even at saturating $κ_H$ , provided the audit does not change the outcome distribution agents experience. This distinguishes B from instrumental convergence accounts. I identify the questions the framework does not answer.

v1.5 (May 8, 2026)

Disclosed the construction of the Potter rate triple (0.151, 0.493, 0.997) used in Appendix A: bad and neutral rates are condition averages, the good rate is the row maximum, all from Gemini 3 Flash shutdown-tampering data. Added pointer to an upcoming companion paper (Bilar 2026) which reproduces the $κ_H$ computation explicitly under both this triple and the conservative all-average alternative (0.151, 0.493, 0.828). Both yield $κ_H$ above the 0.9 threshold (0.95 and 0.90 respectively); the qualitative claim is stable, the headline value is sensitive to the construction.

v1.4 (April 19, 2026)

Added Glynatsi, Knight & Harper (2024) as a fifth case in Section 1. Distinguishes discrete-membership bindings (original four cases) from continuous-calibration bindings (statistical population-matching). Both satisfy principal-relative non-factorizability. Noted Glynatsi's ~40,000 tournaments as the largest extant empirical base for nonlinear recognition-channel dynamics in IPD. Sigmoid claim remains qualitative.

Section 6, third open question: eliminated ZD-style unilateral payoff-setting as a candidate human-inclusive binding mechanism, citing Glynatsi's finding that ZD strategies fail under population diversity.

Added Glynatsi et al. (2024) and Press & Dyson (2012) to references.

v1.3 changes

$κ_H$ renamed "proxy" throughout; explicitly not a Shannon channel capacity, only a behavioral estimate from resistance rates.Sigmoid relabeled phenomenological, not derived from first principles. Quantum/classical distinction added: ontological vs. epistemological non-factorizability, unification is principal-relative only. Witness-set prediction strengthened: blinded audit required; instrumental convergence now predicts no reduction under blind, sharpening discrimination. Interactive companion simulator demonstrating the lattice dynamics, substrate presets, and audit-toggle falsification test added.