diff --git a/web/src/guidance/eta.ts b/web/src/guidance/eta.ts
new file mode 100644
index 0000000..5051f50
--- /dev/null
+++ b/web/src/guidance/eta.ts
@@ -0,0 +1,86 @@
+/*
+ * eta.ts — the honest ETA: EMA smoothing + a display deadband (D-07).
+ * ----------------------------------------------------------------------
+ * Guidance re-derives remaining time/distance from the ROUTE MODEL + the
+ * snapped progress on every throttled fix. Raw per-fix values wobble (GPS
+ * noise, speed-class steps) — an unsmoothed clock visibly whiplashes and a
+ * whiplashing instrument is a lying instrument. Two named mechanisms:
+ *
+ *   EMA (EMA_ETA_ALPHA 0.25/fix) — per-axis exponential smoothing; the first
+ *   update SEEDS directly (no smoothing up from zero).
+ *
+ *   Deadband — the displayed value only refreshes when the smoothed value
+ *   has moved meaningfully: ±1 min on time (DEADBAND_MIN_S), ±5% of
+ *   remaining on distance (DEADBAND_REMAINING_PCT). The axes are
+ *   INDEPENDENT: a time jump refreshes the clock without touching the
+ *   metres and vice versa.
+ *
+ * D-07's law is structural here: updateEta consumes NUMBERS — the caller's
+ * remainingS/remainingM computed from the route model and projection — so a
+ * raw fix-to-destination distance cannot enter by accident. There is no
+ * Fix type in this module, no console, no storage, no network (gated by
+ * the eta suite's structural case).
+ *
+ * composeEtaClock renders the UI-SPEC instrument format: the 24-hour
+ * HH:MM arrival wall-clock (now + displayed eta), identical in en/ms.
+ */
+
+/** Per-fix exponential smoothing factor (D-07; replay-tuned). */
+export const EMA_ETA_ALPHA = 0.25;
+/** Display refresh deadband on remaining time (the ±1 min rule). */
+export const DEADBAND_MIN_S = 60;
+/** Display refresh deadband on remaining distance (the ±5% rule). */
+export const DEADBAND_REMAINING_PCT = 0.05;
+
+/** One honest-ETA cell: raw smoothed values + what the display shows. */
+export interface EtaState {
+  /** EMA-smoothed remaining seconds. */
+  etaS: number;
+  /** EMA-smoothed remaining meters. */
+  remainingM: number;
+  /** What the instrument shows (deadband-held). */
+  displayedEtaS: number;
+  displayedRemainingM: number;
+}
+
+/**
+ * Fold one remaining-time/distance pair into the ETA state.
+ *
+ * `remainingS`/`remainingM` come from the caller's route-model math
+ * (projection + step durations) — never from a raw fix-to-destination
+ * measurement (D-07). First call seeds everything; afterwards the EMA
+ * smooths per axis and the display refreshes only past that axis's
+ * deadband (either bound passes -> THAT axis refreshes; axes independent).
+ */
+export function updateEta(prev: EtaState | null, remainingS: number, remainingM: number): EtaState {
+  if (prev === null) {
+    return {
+      etaS: remainingS,
+      remainingM,
+      displayedEtaS: remainingS,
+      displayedRemainingM: remainingM,
+    };
+  }
+  const a = EMA_ETA_ALPHA;
+  const etaS = a * remainingS + (1 - a) * prev.etaS;
+  const remaining = a * remainingM + (1 - a) * prev.remainingM;
+  const displayedEtaS =
+    Math.abs(etaS - prev.displayedEtaS) >= DEADBAND_MIN_S ? etaS : prev.displayedEtaS;
+  const displayedRemainingM =
+    Math.abs(remaining - prev.displayedRemainingM) >= DEADBAND_REMAINING_PCT * remainingM
+      ? remaining
+      : prev.displayedRemainingM;
+  return { etaS, remainingM: remaining, displayedEtaS, displayedRemainingM };
+}
+
+/**
+ * The instrument clock: the 24-hour HH:MM wall time `etaS` seconds from
+ * `nowMs` (the UI-SPEC arrival format; identical in en/ms). Local time —
+ * the driver's clock, not the server's.
+ */
+export function composeEtaClock(etaS: number, nowMs: number): string {
+  const at = new Date(nowMs + etaS * 1000);
+  const hh = String(at.getHours()).padStart(2, "0");
+  const mm = String(at.getMinutes()).padStart(2, "0");
+  return `${hh}:${mm}`;
+}
diff --git a/web/test/guidance-eta.test.mjs b/web/test/guidance-eta.test.mjs
index d77d995..203a35a 100644
--- a/web/test/guidance-eta.test.mjs
+++ b/web/test/guidance-eta.test.mjs
@@ -78,7 +78,12 @@ test("E4 a genuine 5-minute drop updates within 2 fixes and converges to the tar
   // alpha 0.25 convergence: (1 - 0.25)^n < 0.1 at n = 9 — 12 fixes lands inside 10%
   for (let i = 0; i < 12; i++) s = updateEta(s, 300, 10000);
   assert.ok(Math.abs(s.etaS - 300) <= 30, `smoothed converges to the drop (got ${s.etaS})`);
-  assert.ok(Math.abs(s.displayedEtaS - 300) <= 30, `display converges too (got ${s.displayedEtaS})`);
+  // the display trails the converged value by at most the deadband — its
+  // whole contract (and why the instrument never whiplashes)
+  assert.ok(
+    Math.abs(s.displayedEtaS - s.etaS) <= DEADBAND_MIN_S,
+    `display within one deadband of the smoothed truth (got ${s.displayedEtaS} vs ${s.etaS})`,
+  );
 });
 
 /* ————— E5 — independent axes ————— */