Parent: necessity
Formal backing for necessity. Each note is written to the standard of an independent paper that would earn an A: precise (often measure-theoretic) setup, explicit hypotheses, complete proofs of every non-trivial step, a clean separation of what is proved here vs what is cited (with attribution), and an honest scope declaration of what is not covered.
- adaptive-commitment-value — The value of a gate. Option value, value of information, and the value of adaptivity are one quantity E[max] − max[E]; nonnegative (Jensen), monotone in information and in risk. Self-contained but for Strassen.
- reliability-and-checkpointing — Why long runs fail, and the optimal checkpoint. pⁿ reliability decay; expected rework n/pⁿ → n/pᵏ; exact per-interval cost in a Poisson model, then the rigorous √(2δM) limit.
- simon-ando — Near-decomposability ⇒ two timescales. Degenerate first-order perturbation proves the spectral gap and the K×K aggregated generator; the symmetric 4×4 is demoted to a numerical check.
- holmstrom-informativeness — Where to gate an untrusted executor. Convexified principal–agent program, infinite-dim duality, λ>0 proved, the informativeness principle with a strict-improvement direction (reusing the convexity of adaptive-commitment-value).
A note on honesty: these were produced under repeated pressure to stop overselling "self-contained." They bottom out, where they must, on genuinely deep cited theorems (Strassen, Lidskii/Kato, Rockafellar, Luenberger) — and say so explicitly rather than papering over the gap.