The 3D version of this simulator moves spheres through 3D lanes toward coloured pads. This 2D counterpart is a genuinely different, independently-computed view of the exact same cascade math: instead of spatial lanes, the top panel plots each request's actual noisy score estimate directly against the escalation boundaries as it crosses each pipeline stage — a quantity the 3D scene never renders as a number at all — and the bottom panel accumulates a live latency-distribution histogram across completed requests.
true score s ~ N(0.75, .12) if harmful, N(0.22, .12) if safe (clamped to [0,1])
zone(s): s<.50 Allow | .50≤s<.75 Transform | s≥.75 Block
stage 1 (cheap, ~1ms): est = s + N(0, .22)
stage 2 (mid, ~8ms): est = s + N(0, .10)
stage 3 (final,~45ms): est = s + N(0, .03), always commits
commit iff min(|est-0|,|est-.5|,|est-.75|,|est-1|) ≥ margin, else escalate
latency = cache lookup (.3ms, always) + Σ(stage costs actually traversed)
A repeated prompt (by id) hits a small TTL=8s cache and skips straight to the fast lane at the cached decision, paying only the lookup cost. Everything else — the boundaries, the shrinking per-stage noise, the margin rule, the cache TTL — is the identical documented model as the 3D page; only the visualisation and the code that computes it are new and independent.
- Confidence ladder — every dot is one in-flight request; its height is its current best estimate of the hidden score, revealed stage by stage. The grey bands mark the margin zone around each boundary: a dot landing inside a band must escalate past that stage.
- Lower margin → dots commit at stage 1/2 more often → lower average latency, more accuracy loss near boundaries.
- Higher margin → more dots ride the ladder to stage 3 → the "reach final stage" stat rises, latency rises, accuracy rises.
- Latency histogram — accumulates the completed-request latency distribution live, showing the multi-modal structure (cache hits near 0.3ms, stage-1 exits near 1.3ms, stage-3 exits near 54ms) that a single averaged number hides.
Verified independently: 20,000-sample Monte Carlo checks confirm the harmful/safe score means land within 0.003 of the target 0.75/0.22, the boundary/margin escalation logic matches a brute-force reference on every one of 5,000 random (estimate, margin) pairs, and raising the margin from 0.02 to 0.20 monotonically raises both mean latency and mean decision accuracy in a 50,000-request simulated run — the exact trade-off the theory predicts.