Zone matrix: what the rules do between zones

internal/matrix walks each pair's rules in order, as nftables would, for
new connections: zone → zone (forward), zone → the firewall (input) and
back (output), with the built-ins that act on new connections. A rule
for the whole pair decides it; one for part of its traffic (addresses,
services, times, rates, a quota) is an exception; the rest falls to the
policy. Rules whose addresses all lie in networks connected to other
zones are left out of a pair. GET /matrix (with ?changeset, pending
changes), hc matrix [FROM TO], and a Matrix page whose cells open their
rules.

e2e: 166 checks, among them the matrix of the maintainer's imported
ruleset.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

internal/api/types.go

@@ -422,3 +422,38 @@ type TraceStatus struct {
 	Packets []TracePacket `json:"packets"`
 	Error   string        `json:"error,omitempty"`
 }
+
+// Matrix is what the rules do to new connections between zones:
+// zone → zone (the forward chain), zone → the firewall (input) and the
+// firewall → zone (output). "firewall" stands for the machine itself.
+type Matrix struct {
+	Zones []string     `json:"zones"`
+	Cells []MatrixCell `json:"cells"`
+}
+
+// MatrixCell is one pair: what happens to new connections from From to
+// To that no exception covers (Verdict, decided by DecidedBy), and the
+// exceptions: rules and built-ins that decide for some of them (some
+// addresses, services, times…), in the order they are checked.
+type MatrixCell struct {
+	From       string            `json:"from"`
+	To         string            `json:"to"`
+	Chain      string            `json:"chain"`
+	Verdict    string            `json:"verdict"` // allowed or blocked
+	DecidedBy  string            `json:"decided_by"`
+	RuleID     int64             `json:"rule_id,omitempty"` // the deciding rule
+	Exceptions []MatrixException `json:"exceptions"`
+}
+
+// MatrixException is a rule (or built-in) that decides for part of a
+// pair's traffic.
+type MatrixException struct {
+	RuleID int64  `json:"rule_id,omitempty"` // 0: a built-in, or port forwards
+	Chain  string `json:"chain"`
+	Label  string `json:"label"`
+	// Verdict is allowed, blocked, logged (and goes on), or unknown (a raw
+	// rule Housecarl can't read).
+	Verdict string `json:"verdict"`
+	// What it covers: "from trusted · ssh", "Monday 08:00–17:00".
+	What string `json:"what"`
+}