Allow backfill progress whenever shared capacity is positive

chasm/lib/scheduler/backfill_capacity_progress_test.go

@@ -2,7 +2,6 @@ package scheduler_test
 
 import (
 	"fmt"
-	"os"
 	"testing"
 	"time"
 
@@ -19,10 +18,7 @@ func TestBackfillCapacityNativeControl(t *testing.T) {
 	testBackfillCapacityProgress(t, 450)
 }
 
-func TestBackfillCapacityCounterexample(t *testing.T) {
-	if os.Getenv("TEMPORAL_RUN_MIGRATION_COUNTEREXAMPLES") != "1" {
-		t.Skip("set TEMPORAL_RUN_MIGRATION_COUNTEREXAMPLES=1")
-	}
+func TestBackfillCapacityProgress(t *testing.T) {
 	for _, n := range []int{451, 1000} {
 		t.Run(fmt.Sprint(n), func(t *testing.T) { testBackfillCapacityProgress(t, n) })
 	}

chasm/lib/scheduler/backfiller_capacity_internal_test.go

@@ -28,7 +28,7 @@ import (
 //
 //	pending   = max(0, bufferedCount - retainedActionCount)
 //	available = max(0, maxBufferSize/2 - pending - generatorReserve)
-//	result    = available / max(1, backfillerCount)
+//	result    = min(available, max(1, available / max(1, backfillerCount)))
 func TestBackfillerBufferCapacity(t *testing.T) {
 	cases := []struct {
 		name             string
@@ -77,7 +77,7 @@ func TestBackfillerBufferCapacity(t *testing.T) {
 		{"single backfiller gets the whole remainder", 0, 0, 1000, 50, 1, 450},
 		{"ten backfillers each get an even share (regression)", 0, 0, 1000, 50, 10, 45},
 		{"backfillers exactly dividing remainder get one each", 0, 0, 1000, 50, 450, 1},
-		{"more backfillers than remainder truncate to zero", 0, 0, 1000, 50, 451, 0},
+		{"more backfillers than remainder still make progress", 0, 0, 1000, 50, 451, 1},
 		{"zero backfillers are clamped to one", 0, 0, 1000, 50, 0, 450},
 		{"negative backfillers are clamped to one", 0, 0, 1000, 50, -3, 450},
 	}

chasm/lib/scheduler/backfiller_tasks.go

@@ -293,5 +293,6 @@ func backfillerBufferCapacity(bufferedCount, retainedActionCount, maxBufferSize,
 	backfillerCount = max(1, backfillerCount)
 	pending := max(0, bufferedCount-retainedActionCount)
 	available := max(0, (maxBufferSize/2)-pending-generatorReserve)
-	return available / backfillerCount
+	// Pure tasks serialize on the tree and recompute the shared budget after each enqueue.
+	return min(available, max(1, available/backfillerCount))
 }