L1

Essential vs accidental complexity, and why adding people to a late project makes it later.

A stable matching always exists and is findable in O(n^2), but it's optimal for the proposing side. Mechanism design in twenty lines.

Functions belong at the endpoints; lower layers can only optimize, never guarantee. The single most useful design principle in networking.

Least privilege, fail-safe defaults, economy of mechanism; plus the confused deputy as the canonical violation.

How to reason about decisions made without the future, with a provable ratio. Rent-vs-buy shows up in caching, autoscaling, and connection pooling.

L = lambda W, with essentially no assumptions. Capacity planning from one line of algebra.

O(log n) proof that one item belongs to a huge set. Git, certificate transparency, and every blockchain are the same data structure.

Constant space, no false negatives, a tunable false-positive rate, and the exact formula for the tradeoff.

Adding a node should move 1/n of the keys, not all of them. One idea, and virtual nodes to fix its variance (Balls into bins and the power of two choices).

One inequality generating the entire read/write consistency tradeoff space.

There is no global "now"; causality is the only ordering you get. The foundational conceptual shift of the whole part.

Verifying vs finding. State it properly, including what a proof either way would actually change.

Four conditions, all necessary for deadlock; break any one. The cleanest example of a characterization theorem doing engineering work.

Four grammar classes, four machine classes, one ladder. Why you can't parse HTML with a regex, stated as a theorem.

One machine simulates all others. Interpreters, VMs, and the stored-program computer are all this one theorem.

Every reasonable model of computation computes the same functions. Why "it's Turing-complete" is a meaningful thing to say about CSS, SQL, and your YAML config.

Expectations add even when events are hopelessly dependent. Averaging as an existence proof: if the mean is 5, some input hits 5.

Collisions arrive at sqrt(N), not N. Sets every hash length, UUID size, and nonce width you will ever choose.

Agreement over a lossy channel is impossible. Why exactly-once delivery is a lie and idempotency is the real answer.

Systems mirror the communication structure of the organizations that build them. Empirical, not proven — and the inverse maneuver as its practical use.