diff --git a/systems/README.md b/systems/README.md
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@@ -38,3 +38,6 @@ misbehaving, it belongs in `operations/`.
 
 - [interactive-data-interfaces](./interactive-data-interfaces.md) — spatial budgets,
   selection semantics, causal motion, stable updates and verification boundaries
+- [simulated-pressure-ink](./simulated-pressure-ink.md) — streaming
+  perfect-freehand: speed relative to brush size, speed-scaled easing,
+  time-normalized; stamp circles so the renderer cannot gap
diff --git a/systems/simulated-pressure-ink.md b/systems/simulated-pressure-ink.md
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+# simulated pressure ink
+
+A finger or mouse reports no pressure, but a line whose width never changes
+reads as a tool, not a hand. Perfect-freehand's answer is to simulate pressure
+from speed, and the version that holds up is the streaming one: each sample
+updates a small state, nothing looks at the whole stroke, and the stored points
+already carry their width so replay and peers need no model at all.
+
+## the model
+
+Three passes per sample, all easing (exponential moving averages):
+
+- **streamline** the position toward the raw sample. Jittery input becomes a
+  fluid line. The final sample skips the easing so the stroke ends under the
+  finger instead of a fraction short of it.
+- **speed** is distance per nominal sample interval *divided by the brush
+  size*. A fat brush needs a faster hand to thin. Measuring speed in absolute
+  px/ms was the mistake that made the earlier attempt feel wrong: one constant
+  cannot serve a 6 px pen and a 200 px marker.
+- **pressure** eases toward `1 - speed` at a rate that itself scales with
+  speed. A flick thins at once; slowing down thickens gradually. Start at
+  quarter pressure so a stroke swells in.
+
+Radius is `size * (0.5 - thinning * (0.5 - pressure))`: nominal pressure paints
+exactly `size`, and thinning 0.55 spans 0.45× to 1.55× of it. Thinning 1 lets a
+flick reach zero width, so a user-facing knob should stop short of it.
+
+Normalize both easings to wall-clock time (`1 - (1 - α)^(dt / nominal)`), or a
+60 Hz mouse and 120 Hz coalesced touch draw different lines for the same hand
+motion.
+
+## rendering is a separate problem
+
+Perfect-freehand's whole-stroke outline self-intersects at sharp corners on
+sparse input and leaves V-shaped gaps. Do not fix that in the model. Stamp a
+circle at every point and a trapezoid between neighbours: every joint is a
+full disc, so the stroke cannot gap, and the model only has to produce a
+position and a radius. Densify long segments at render time so sparse samples
+do not read as beads.
+
+## sources
+
+- tinydraw `core/src/ink_stream.cpp`, `core/include/tinydraw/ink_config.h`
+  (github.com/aliceisjustplaying/tinydraw), read 2026-09-19. A C++ streaming
+  port of perfect-freehand for an ESP32 finger-drawing device.
+- doodl `src/ui/ink.ts`, `src/ui/draw.ts`, commit `55973eb`, 2026-09-19. The
+  earlier whole-stroke attempt and its corner-gap fix are commits `68db9e8`
+  and `1474776`, reverted in `3e73da0`; the absolute-speed attempt is `1ab4d35`.
+- perfect-freehand `packages/perfect-freehand/src/getStrokePoints.ts`,
+  `getStrokeOutlinePoints.ts` (github.com/steveruizok/perfect-freehand).