feat: playable arcade — rooms, identity, client, deployment

Round length is now bounded: the multiplier follows a hyperbolic curve
diverging at 60s, replacing an exponential one where a 275x crash point
produced a two-and-a-half minute round.

Fixes seed reveal, which silently failed every round because pgx cannot
encode a fixed-size byte array as bytea.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

migrations/0002_rounds.sql

@@ -0,0 +1,58 @@
+-- Rounds, bets, and the verification record for every settled outcome.
+--
+-- Seeds are stored so that any round can be re-verified indefinitely. The
+-- server seed column is NULL until the round settles: revealing it early would
+-- let a player compute the outcome before betting closes.
+
+CREATE TABLE rounds (
+    id            BIGSERIAL PRIMARY KEY,
+    game          TEXT NOT NULL,               -- 'rocket', 'orbital', 'tower'
+    nonce         BIGINT NOT NULL,
+    commitment    BYTEA NOT NULL,              -- SHA-256 of the server seed
+    server_seed   BYTEA,                       -- revealed only after settlement
+    client_seed   BYTEA,                       -- derived from participants
+    crash_point   BIGINT,                      -- Q32.32 fixed-point
+    opened_at     TIMESTAMPTZ NOT NULL DEFAULT now(),
+    locked_at     TIMESTAMPTZ,
+    settled_at    TIMESTAMPTZ,
+    CONSTRAINT reveal_is_complete CHECK (
+        settled_at IS NULL OR (server_seed IS NOT NULL AND crash_point IS NOT NULL)
+    )
+);
+
+CREATE TABLE bets (
+    id              BIGSERIAL PRIMARY KEY,
+    round_id        BIGINT NOT NULL REFERENCES rounds(id),
+    account_id      BIGINT NOT NULL REFERENCES accounts(id),
+    stake_msat      BIGINT NOT NULL CHECK (stake_msat > 0),
+    -- Set when the player cashes out; NULL means they rode it to the crash.
+    cashout_at      BIGINT,                    -- Q32.32 multiplier
+    payout_msat     BIGINT,
+    placed_at       TIMESTAMPTZ NOT NULL DEFAULT now(),
+    settled_at      TIMESTAMPTZ,
+    UNIQUE (round_id, account_id)
+);
+
+CREATE INDEX bets_round_idx   ON bets (round_id);
+CREATE INDEX bets_account_idx ON bets (account_id, id DESC);
+
+CREATE TABLE scratch_plays (
+    id           BIGSERIAL PRIMARY KEY,
+    account_id   BIGINT NOT NULL REFERENCES accounts(id),
+    ticket_id    TEXT NOT NULL,
+    nonce        BIGINT NOT NULL,
+    commitment   BYTEA NOT NULL,
+    server_seed  BYTEA NOT NULL,
+    stake_msat   BIGINT NOT NULL CHECK (stake_msat > 0),
+    tier_name    TEXT NOT NULL,
+    payout_msat  BIGINT NOT NULL CHECK (payout_msat >= 0),
+    cells        INTEGER[] NOT NULL,
+    played_at    TIMESTAMPTZ NOT NULL DEFAULT now()
+);
+
+CREATE INDEX scratch_account_idx ON scratch_plays (account_id, id DESC);
+
+-- Rounds and plays are historical records; they are never rewritten.
+CREATE TRIGGER scratch_plays_append_only
+    BEFORE UPDATE OR DELETE ON scratch_plays
+    FOR EACH ROW EXECUTE FUNCTION reject_mutation();