GPT-5.6 system card,
explained.

Not every request deserves the biggest brain. The card describes a router that sorts queries by estimated difficulty across tiers — reported as Sol / Terra / Luna — sending easy work to a cheap, fast tier and escalating only the hard cases to a heavier one. Since most real traffic is easy, the average cost tracks the small tier while peak capability stays available for the rare hard query.

That economic logic — cheap by default, expensive on demand — is the model-routing cascade, and its cost math is worked out in full in the model-routing handbook (expected cost, break-even escalation rate). What the system card adds on top is what happens at the hardest tier, where one pass isn't enough.

For the hardest tasks, the card describes an ultra mode that spends test-time compute in parallel: run several independent agents (reported as four) on the same problem, then let a verifier pick the best result. On verifiable work — code that must pass tests, math with a checkable answer — this is a clean win, because a wrong try is cheap to discard and a right try is easy to confirm.

If one agent solves it with probability p, then "at least one of N solves it" is 1 − (1 − p)^N — and a verifier turns that possibility into the answer you keep.

The solve-rate formula rises with N, so why not run forty agents? Because what matters is the marginal gain of each added agent — and it shrinks fast. Subtract consecutive terms and the value of the N-th agent is a clean geometric decay:

At p = 0.6: the 1st agent buys +0.60, the 2nd +0.24, the 3rd +0.10, the 4th +0.04 — while each agent costs the same. Cost is linear in N; benefit decays geometrically.

So there's a knee. The first few agents convert a coin-flip task into a near-certainty; past that, you're paying full price for crumbs. "Four" isn't a round number someone liked — it's roughly where marginal solved-rate drops below what the extra compute is worth. The runnable below lets you move p and watch the knee move with it.

A system card is also a safety document. Alongside capability numbers, a frontier lab reports a Preparedness-style assessment — dangerous-capability evaluations gating release. Tiered routing and ultra mode complicate that case: the same machinery that spends more compute to crack a hard benchmark can spend it to amplify misuse, and the strongest configuration (top tier, full ultra mode) is what the safety argument must actually cover — not the cheap default most users see.

That's the honest tension in these cards. The knee that makes ultra mode economical also makes the most capable setting a deliberate, bounded choice — which is exactly the setting the risk evaluations have to be measured against.

This card marks a shift in how frontier models ship: not as a single artifact but as a compute-allocation policy — route by difficulty, escalate by need, parallelize the hardest cases. The scaling law behind the "more compute → more accuracy" premise is the o1 system card's log-linear test-time-compute curve; the cost discipline is the model-routing and cost-engineering playbook. What this breakdown adds is the piece that sets the dial: the marginal value of the N-th parallel agent.

The takeaway generalizes well past any one lab. Any time you're tempted to throw more parallel samples at a verifiable task — best-of-N decoding, multi-agent voting, retry loops — compute Δ(N) = (1−p)^N−1·p and stop where it dips below your cost per try. Usually that's a small number.