AIM Framework glossary
Bayesian Fixed Point (False Equilibrium)
Canonical definition
A Bayesian fixed point (or false equilibrium) is a stable Belief state where P(H\\|all evidence) approaches 1 for a false Hypothesis H\ because the Hypothesis generates evidence patterns that confirm itself, creating self-reinforcing feedback such that Bayesian updating (though individually rational at each step) converges toward shared falsehood rather than Truth under conditions of Source Opacity and endogenous evidence generation.
Explanation
In standard Bayesian epistemology, evidence is assumed to be generated independently of the Individual's Beliefs about Hypotheses. But under Source Opacity + confabulation, this assumption fails: the Hypothesis shapes the evidence (confabulated narratives justify the behaviour), which updates the Hypothesis (strengthening Belief in the false narrative), which generates more confirming evidence (further behaviour consistent with the narrative). If a false Hypothesis H\ is self-reinforcing in this way, the system converges to a stable fixed point where everyone believes H\ with near-certainty, despite H\ being false. Example: "I am fundamentally achievement-oriented" (false Hypothesis) generates evidence (I pursue high-status opportunities) that confirms the Hypothesis (because status-seeking looks like achievement-seeking under Source Opacity), which strengthens the Belief (I must really value achievement), which generates more evidence (I continue pursuing status). The fixed point is stable because no internal observation contradicts it, all evidence is reinterpreted through the lens of H\. This is why individual reasoning cannot escape mimetic escalation: the mathematics of rational updating itself produces the lock-in.
Epistemic status
Framework-Specific Named Result.
Derivation
Chapter 13, Section 13.3.3; Appendix A, Section A.5.8.1; Chapter 13, Section 13.4.3; Appendix A, Section A.5.8.3.
Also in the entry
Distinction from Bayesian Lock-In. The Bayesian Fixed Point names the mathematical property of the equilibrium itself, the stable Belief state where P(H*\|all evidence) → 1 for a false Hypothesis under endogenous-evidence dynamics. Bayesian Lock-In names the dynamic process by which an Individual's Hypothesis Space narrows until that equilibrium is reached, with the Lock-In's signature feature being that the M-Hypothesis becomes structurally unavailable for consideration. Fixed Point is the destination; Lock-In is the trajectory and the mechanism by which the Individual arrives at it. Lock-In additionally specifies the source-channel asymmetry (A-priors and I-priors are partially corrigible via exogenous evidence; M-priors are architecturally non-corrigible without the Knowledge Patch).