AIM Framework glossary
Source Opacity Theorem
Canonical definition
Source Opacity Theorem is the information-theoretic proof that source-decomposition information is irreversibly destroyed by the Decision Hub's integration of A, I, and M signals into a single utility scalar. Let U = (UA, UI, UM) be the source-specific utility vector and let S be the source-identity variable. The Decision Hub computes V = f(U) = wA UA + wI UI + wM U_M. Since f is a deterministic, non-injective many-to-one map (its kernel is two-dimensional), no measurable function of V can recover U exactly; by the Data Processing Inequality, I(S; V) ≤ I(S; U) and I(S; g(V)) ≤ I(S; V) for any introspective function g. Source-decomposition information is irreversibly destroyed in integration, and no downstream processing can recover it. Formalised in Chapter 9 and Appendix A, Section A.2 (M5a).
Explanation
The Source Opacity Theorem elevates Source Opacity from a psychological observation ("people can't tell where their desires come from") to a mathematical necessity conditional on one architectural premise. The mathematics is general: for any many-to-one integration, the Data Processing Inequality guarantees that no function of the integrated output can recover information the integration discarded, so any neural system that integrates multiple motivational signals into a single decision variable destroys the source decomposition in the integrated signal, not as a design flaw but as a consequence of the map being many-to-one. The architectural premise is Scalar-Only Delivery (restatement B1, Appendix A, Section A.5.6): conscious access operates on the integrated Scalar and receives no parallel pre-integration channel. Given that premise, introspection is a function of the integrated output and inherits the information loss, and no amount of careful self-examination, meditation, or therapeutic technique can recover what the integration step destroyed. The premise is evidenced rather than assumed: source-specific circuits are active within the Transmission Window while conscious awareness of the integrated wanting arrives only afterwards (see Source-Tagging; Chapter 9, Section 9.9.9 separates this timing barrier from Source Opacity proper), and the Choice Blindness record shows subjects sincerely explaining choices they did not make, which is what downstream-only access predicts. This is why the Knowledge Patch and the Two-Question Diagnostic route around introspection rather than trying to improve it: they use external behavioural evidence (satiation tests, audience-removal tests) to infer the source-attribution that the architecture necessarily discards. See Source Opacity, Camouflage Architecture, Knowledge Patch, Two-Question Diagnostic, Conscious Cognition, Evidence.
Epistemic status
Theorem (Appendix A, Section A.2, M5a).