What trust is.
Trust is not a feeling. It is a measurable quantity between a model and an observer, built from two ingredients: how much the observer's relevant region is covered by the model's claims (coverage), and how well the model's centre of mass aligns with the observer's (fidelity). Trust is their integral.
Two objects, not one
[DRAFT — your claim] Trust requires two parties, not one. There is the model M and there is the observer M̂ — the thing that is reading the model, asking it questions, deciding whether to act on its outputs. Both are typed operators (Lecture 01). Trust is a quantity defined over the pair (M, M̂), not over M alone.
Coverage as overlap
[DRAFT] Coverage c is the proportion of the observer's relevant region that the model actually addresses. Drag M̂ into a region where M has nothing to say and c collapses. Drag it into M's body and c saturates. Coverage is geometric: it lives in the overlap of two regions.
Fidelity as centroid alignment
[DRAFT] Fidelity f is the alignment of the centres of mass — the agreement, within the covered region, between what the model says and what the observer expects. Coverage without fidelity is a model that talks loudly about the right topic but says the wrong things. Fidelity without coverage is a model that is precisely right about a region nobody asked about.
Why the product, not the sum
[DRAFT] T = c · f, not c + f, because each ingredient is necessary. A model with zero coverage is not partly trustworthy; it is untrustworthy. A model with zero fidelity inside its coverage is worse than no model. The product enforces the conjunction. The integral aggregates this conjunction across the observer's full domain of concern.
Trust is not confidence
[DRAFT] The model's reported confidence is an artifact of the model. Trust is an artifact of the relationship. Calibration is a property of M; trust is a property of (M, M̂). Conflating them is one of the most common, and most expensive, mistakes in model risk practice.
What this lets us do
[DRAFT] Once trust is a measurable quantity, governance becomes a real engineering discipline rather than a vibes exercise. You can compute it. You can monitor it. You can write down what should happen when it drops. Lecture 04 picks up there.