Chapter 10 — Information, Discovery, and the Value of Awareness
Part III · The Awareness Bench · Week 9
K→𝒢→Q→Ξ
The information position \(Q\): the missing layer. Discovery is not exercise, and unawareness is not risk. The Actuary’s Theorem prices what enumeration cannot — through diversification.
Learning objectives
- LOS 10.2 — State the two-layer information architecture and distinguish revelation from discovery.
- LOS 10.4 — State and apply the Actuary’s Theorem for pricing the unenumerable.
- LOS 10.6 — Price awareness rents and the economics of secrecy.
The laboratory module
Module 10 — The Awareness Bench. A layer viewer, a perceived-criterion classifier, an actuary bench (Monte-Carlo), and a rent table.
The Actuary’s Theorem. Discoveries arrive as a Poisson process with intensity \(\lambda\); each carries a value mark drawn i.i.d. from \(\nu\) (mean \(m\)). The per-system unawareness premium has mean
\[\pi^* = m\int_0^\infty \lambda(t)\,e^{-rt}\,dt.\]
For a single system this is an interval, not a price. But a diversified portfolio of \(n\) systems converges: \(\overline{\Pi_U} \to \pi^*\) almost surely and in \(L^2\), with risk vanishing at rate \(1/\sqrt{n}\). Diversification prices what enumeration cannot. The bench’s batched Monte-Carlo reproduces this — the portfolio estimate lands on \(\pi^*\) with standard error below \(\pi^*/10\).
Guided experiments
- Produce one pure revelation and one pure discovery and observe which layer moves.
- Find the \(n\) at which the portfolio premium’s standard error falls below \(\pi^*/10\), then break stationarity with the regime toggle and report the bias.
- Run the rent table through all four disclosure/capacity combinations.
ch10 · 8/8 PASS