Observability Gap
“Observability Gap: The discrepancy between the causal information required for valid inference and the information actually available through observable signals. When the gap is large, no amount of sophisticated reasoning can compensate for missing information.”
— Coherent Without Grounding, Grounded Without Success (2026), §2.2
Why it matters
The Observability Gap supplies the structural variable along which the Bidirectional Coherence Paradox is observed: the gap's magnitude determines whether prior-dominated or signal-dominated reasoning prevails, and therefore which side of the paradox an LLM exhibits. It is the precondition that makes the inversion analytically tractable rather than merely anecdotal.
Notes
Formally characterised by the mutual information between observables and causal factors, normalised by the entropy of the causal factors:
Gap(C, O) = 1 − I(O; C) / H(C)When Gap ≈ 0 observables fully determine causal states; when Gap ≈ 1 observables
provide negligible information about true causes. The Observability Gap is presented as
an epistemic condition rather than a practical limitation: it bounds what an agent can
in principle come to know, regardless of the sophistication of its reasoning.