fix(run): fidelity readout never rounds a near-unity F to a bare 1

packages/ui/src/amicode/problem.test.ts

@@ -118,6 +118,20 @@ describe("runChipText", () => {
   test("solving f outside [0,1] renders no F readout (objective ≠ fidelity)", () => {
     expect(runChipText([{ runId: "r", status: "solving", fidelity: 79.3, iteration: 0 }])).toBe("solving…")
   })
+  test("near-unity fidelity never rounds to a bare 1 — precision extends until the gap shows", () => {
+    expect(runChipText([{ runId: "r", status: "finished", fidelity: 0.99997, iteration: 60 }])).toBe(
+      "F=0.99997 · 60 iter",
+    )
+    expect(runChipText([{ runId: "r", status: "finished", fidelity: 0.99999997, iteration: 60 }])).toBe(
+      "F=0.99999997 · 60 iter",
+    )
+    // solving mirror: a tiny live objective is a near-unity F
+    expect(runChipText([{ runId: "r", status: "solving", fidelity: 0.00003, iteration: 12 }])).toBe(
+      "solving… F=0.99997",
+    )
+    // a true 1 (and only a true 1) still renders bare
+    expect(runChipText([{ runId: "r", status: "finished", fidelity: 1, iteration: 60 }])).toBe("F=1 · 60 iter")
+  })
 })
 
 describe("railState", () => {

packages/ui/src/amicode/problem.ts

@@ -244,8 +244,17 @@ export function mergeChips(entities: Record<string, Record<string, unknown>>, sc
 // --- run chip ----------------------------------------------------------------
 
 function formatFidelity(value: number): string {
-  // up to 4 significant decimals, trailing zeros trimmed
-  return String(Number(value.toFixed(4)))
+  // 4 decimals for ordinary values (trailing zeros trimmed) — but NEVER let
+  // rounding collapse a near-unity or near-zero fidelity into exactly "1"/"0":
+  // the gap from perfect IS the result (Kate 2026-07-28, a 0.99997 run showed
+  // "F = 1"). Precision extends one digit at a time until the gap survives,
+  // capped at 10; only a true 1 or 0 renders bare.
+  if (value === 1 || value === 0) return String(value)
+  for (let digits = 4; digits <= 10; digits++) {
+    const rounded = Number(value.toFixed(digits))
+    if (rounded !== 1 && rounded !== 0) return String(rounded)
+  }
+  return String(value)
 }
 
 export function runChipText(statuses: RunStatusView[]): string | undefined {