Stage 13: alphabet on the wire (UI alphabet-agnostic, TODO-4)

Live play now exchanges per-variant alphabet indices instead of concrete
letters (rack out; submit-play, evaluate, exchange, word-check in). The client
caches each variant's (index, letter, value) table behind
StateRequest.include_alphabet and renders the rack and blank chooser from it,
dropping the hardcoded value/alphabet tables. History, the durable journal and
GCG stay decoded concrete characters (ARCHITECTURE §9.1, unchanged).

- pkg/fbs: new AlphabetEntry + PlayTile; StateView.rack -> [ubyte] + alphabet;
  StateRequest.include_alphabet; SubmitPlay/Eval tiles -> [PlayTile];
  Exchange tiles + CheckWord word -> [ubyte] (committed Go + TS regenerated).
- engine: AlphabetTable + a cached per-variant codec (LetterForIndex/EncodeRack/
  DecodeTiles/DecodeWord) + BlankIndex sentinel; Go parity test.
- backend server edge maps index<->letter (new thin game.Service.GameVariant);
  game.Service domain methods, engine.Game and the robot keep one letter-based
  play path. The gateway forwards indices verbatim (no alphabet table).
- ui: lib/alphabet.ts in-memory cache; codec encodes/decodes indices; premiums.ts
  is geometry-only; the mock seeds a fixture table; the UI normalises display to
  upper case (codec + cache), leaving placement/board/checkword unchanged.

Parity moved to the Go engine.AlphabetTable test; premiums.ts loses its value
tables. Discharges TODO-4.

backend/internal/engine/alphabet_test.go

@@ -0,0 +1,110 @@
+package engine
+
+import (
+	"errors"
+	"slices"
+	"testing"
+)
+
+// TestAlphabetTableEnglish pins the English table against the solver ruleset: 26 letters,
+// contiguous indices, the concrete lower-case characters the solver emits and the standard
+// tile values. This is the real parity check the UI no longer carries (Stage 13).
+func TestAlphabetTableEnglish(t *testing.T) {
+	tab, err := AlphabetTable(VariantEnglish)
+	if err != nil {
+		t.Fatalf("AlphabetTable(english): %v", err)
+	}
+	if len(tab) != 26 {
+		t.Fatalf("size = %d, want 26", len(tab))
+	}
+	for i, e := range tab {
+		if int(e.Index) != i {
+			t.Errorf("entry %d has Index %d, want %d (index must equal position)", i, e.Index, i)
+		}
+	}
+	// a=index0/value1, q=index16/value10, z=index25/value10.
+	if tab[0].Letter != "a" || tab[0].Value != 1 {
+		t.Errorf("entry 0 = %q/%d, want a/1", tab[0].Letter, tab[0].Value)
+	}
+	if tab[16].Letter != "q" || tab[16].Value != 10 {
+		t.Errorf("entry 16 = %q/%d, want q/10", tab[16].Letter, tab[16].Value)
+	}
+	if tab[25].Letter != "z" || tab[25].Value != 10 {
+		t.Errorf("entry 25 = %q/%d, want z/10", tab[25].Letter, tab[25].Value)
+	}
+}
+
+// TestAlphabetTableRussianVariants pins both Russian variants: they share the 33-letter
+// alphabet but differ in tile values — most visibly ё (index 6), worth 3 in Russian
+// Scrabble and 0 in Эрудит.
+func TestAlphabetTableRussianVariants(t *testing.T) {
+	ru, err := AlphabetTable(VariantRussianScrabble)
+	if err != nil {
+		t.Fatalf("AlphabetTable(russian_scrabble): %v", err)
+	}
+	er, err := AlphabetTable(VariantErudit)
+	if err != nil {
+		t.Fatalf("AlphabetTable(erudit): %v", err)
+	}
+	if len(ru) != 33 || len(er) != 33 {
+		t.Fatalf("sizes = %d/%d, want 33/33", len(ru), len(er))
+	}
+	if ru[0].Letter != "а" || ru[0].Value != 1 {
+		t.Errorf("russian entry 0 = %q/%d, want а/1", ru[0].Letter, ru[0].Value)
+	}
+	if ru[6].Letter != "ё" || ru[6].Value != 3 {
+		t.Errorf("russian ё (entry 6) = %q/%d, want ё/3", ru[6].Letter, ru[6].Value)
+	}
+	if er[6].Letter != "ё" || er[6].Value != 0 {
+		t.Errorf("erudit ё (entry 6) = %q/%d, want ё/0", er[6].Letter, er[6].Value)
+	}
+	if ru[32].Letter != "я" || er[32].Letter != "я" {
+		t.Errorf("last letter = %q/%q, want я/я", ru[32].Letter, er[32].Letter)
+	}
+}
+
+// TestAlphabetTableUnknownVariant rejects a variant outside the catalogue.
+func TestAlphabetTableUnknownVariant(t *testing.T) {
+	if _, err := AlphabetTable(Variant(99)); !errors.Is(err, ErrUnknownVariant) {
+		t.Fatalf("got %v, want ErrUnknownVariant", err)
+	}
+}
+
+// TestRackCodecRoundTrip pins the rack/exchange index codec the edge uses: EncodeRack maps
+// concrete letters (with "?" for a blank) to indices (BlankIndex for the blank) and
+// DecodeTiles inverts it. EncodeRack is case-insensitive so it accepts the lower-case
+// Hand form and an upper-case letter alike.
+func TestRackCodecRoundTrip(t *testing.T) {
+	letters := []string{"c", "a", "t", "?"}
+	idx, err := EncodeRack(VariantEnglish, letters)
+	if err != nil {
+		t.Fatalf("EncodeRack: %v", err)
+	}
+	if want := []int{2, 0, 19, BlankIndex}; !slices.Equal(idx, want) {
+		t.Fatalf("EncodeRack = %v, want %v", idx, want)
+	}
+	back, err := DecodeTiles(VariantEnglish, idx)
+	if err != nil {
+		t.Fatalf("DecodeTiles: %v", err)
+	}
+	if !slices.Equal(back, letters) {
+		t.Fatalf("DecodeTiles = %v, want %v", back, letters)
+	}
+	if up, err := EncodeRack(VariantEnglish, []string{"C"}); err != nil || !slices.Equal(up, []int{2}) {
+		t.Errorf("EncodeRack upper-case = %v,%v; want [2],nil", up, err)
+	}
+}
+
+// TestDecodeWordAndBounds covers the word-check decode and the out-of-range guard.
+func TestDecodeWordAndBounds(t *testing.T) {
+	w, err := DecodeWord(VariantEnglish, []int{2, 0, 19})
+	if err != nil || w != "cat" {
+		t.Fatalf("DecodeWord = %q,%v; want cat,nil", w, err)
+	}
+	if _, err := LetterForIndex(VariantEnglish, 26); !errors.Is(err, ErrIllegalPlay) {
+		t.Errorf("out-of-range index: got %v, want ErrIllegalPlay", err)
+	}
+	if _, err := DecodeWord(VariantEnglish, []int{BlankIndex}); !errors.Is(err, ErrIllegalPlay) {
+		t.Errorf("blank in word: got %v, want ErrIllegalPlay", err)
+	}
+}