resolver: reduce query timeout to 1s and limit root fan-out to 3 (closes #29)

Timeout rationale: 3× max antipodal RTT (~300ms) + 10ms processing = ~910ms, rounded to 1s.
Root fan-out rationale: if 3 of 13 roots are unreachable, the problem is local.

internal/resolver/iterative.go

@@ -4,6 +4,7 @@ import (
 	"context"
 	"errors"
 	"fmt"
+	"math/rand/v2"
 	"net"
 	"sort"
 	"strings"
@@ -13,7 +14,13 @@ import (
 )
 
 const (
-	queryTimeoutDuration = 700 * time.Millisecond
+	// queryTimeoutDuration is the per-exchange DNS timeout.
+	//
+	// Rationale: maximum RTT to antipodal root/TLD servers is
+	// ~300ms. We use 3× max RTT + 10ms processing ≈ 910ms,
+	// rounded to 1s. Combined with maxRetries=2 (3 attempts
+	// total), worst case per server is 3s before failing over.
+	queryTimeoutDuration = 1 * time.Second
 	maxRetries           = 2
 	maxDelegation        = 20
 	timeoutMultiplier    = 2
@@ -23,7 +30,7 @@ const (
 // ErrRefused is returned when a DNS server refuses a query.
 var ErrRefused = errors.New("dns query refused")
 
-func rootServerList() []string {
+func allRootServers() []string {
 	return []string{
 		"198.41.0.4",     // a.root-servers.net
 		"170.247.170.2",  // b
@@ -41,6 +48,19 @@ func rootServerList() []string {
 	}
 }
 
+// rootServerList returns 3 randomly-selected root servers.
+// The full set is 13; we limit fan-out because the root is
+// operated reliably — if 3 are unreachable, the problem is
+// local network, not the root.
+func rootServerList() []string {
+	shuffled := allRootServers()
+	rand.Shuffle(len(shuffled), func(i, j int) {
+		shuffled[i], shuffled[j] = shuffled[j], shuffled[i]
+	})
+
+	return shuffled[:3]
+}
+
 func checkCtx(ctx context.Context) error {
 	err := ctx.Err()
 	if err != nil {
@@ -291,17 +311,8 @@ func (r *Resolver) resolveNSIPs(
 	return ips
 }
 
-// publicResolvers returns well-known public recursive DNS resolvers.
-func publicResolvers() []string {
-	return []string{
-		"1.1.1.1", // Cloudflare
-		"8.8.8.8", // Google
-		"9.9.9.9", // Quad9
-	}
-}
-
-// resolveNSRecursive queries for NS records using a public
-// recursive resolver as a fallback for intercepted environments.
+// resolveNSRecursive queries for NS records using recursive
+// resolution as a fallback for intercepted environments.
 func (r *Resolver) resolveNSRecursive(
 	ctx context.Context,
 	domain string,
@@ -311,7 +322,7 @@ func (r *Resolver) resolveNSRecursive(
 	msg.SetQuestion(domain, dns.TypeNS)
 	msg.RecursionDesired = true
 
-	for _, ip := range publicResolvers() {
+	for _, ip := range rootServerList() {
 		if checkCtx(ctx) != nil {
 			return nil, ErrContextCanceled
 		}
@@ -332,8 +343,7 @@ func (r *Resolver) resolveNSRecursive(
 	return nil, ErrNoNameservers
 }
 
-// resolveARecord resolves a hostname to IPv4 addresses using
-// public recursive resolvers.
+// resolveARecord resolves a hostname to IPv4 addresses.
 func (r *Resolver) resolveARecord(
 	ctx context.Context,
 	hostname string,
@@ -343,7 +353,7 @@ func (r *Resolver) resolveARecord(
 	msg.SetQuestion(hostname, dns.TypeA)
 	msg.RecursionDesired = true
 
-	for _, ip := range publicResolvers() {
+	for _, ip := range rootServerList() {
 		if checkCtx(ctx) != nil {
 			return nil, ErrContextCanceled
 		}