Give every payout a bump reserve output and refuse configs that cannot pay a round (B-79, RND-21, RND-23, RND-24, RND-27, RND-38, RND-40, DAT-73, API-31, API-36, TX-11, ADR-17, ADR-29)

The pool normally holds exactly the round's bet outputs and the payout spent them all for
exactly the pool amount, so it had no change output: bump_fee could never accelerate it,
and a payout stuck in a mempool (never abandoned while a server knows it) kept the round in
`paying_out` and the whole lottery stopped.

- build_payout_transaction always has three outputs: winner, fee address, and a bump reserve
  of max(DUST_LIMIT_SATS, estimate_vsize(inputs, 3) * 10 sat/vB) paid to the reserve address
  m/84'/746'/0'/1/0. The reserve comes out of the platform's 30%, the network fee still out
  of the winner's 70%. Input value beyond winner share + commission (only rounds opened
  before the per-round pool address) is folded into the reserve output if >= dust, left to
  the network fee otherwise. `change_address` is replaced by `reserve_address`.
- `rounds.bump_reserve_sats` (Alembic e5a91c3d7b26, plain add_column) is written with the
  payout intent before the broadcast; /admin/rounds returns it.
- bump_fee takes the increase from the reserve output for a payout
  (_find_reducible_output; a payout already in flight with a change to the pool still falls
  back to that), never from the winner or fee-address outputs.
- payout_config_problem / rounds_can_open (RND-40): a bet amount and fee rate under which a
  round of 1 or of MAX_PARTICIPANTS_PER_ROUND participants could not cover the network fee,
  the reserve and dust outputs opens no round (lottery_configured=false); PUT /admin/config
  refuses such a bet amount or fee rate with 422 config_not_payable, judged on the resulting
  values, since the payout reads the fee rate live.

Ambiguity resolved: the reserve output and any excess input are one output (RND-23 says one
output to the reserve address), and bump_reserve_sats records that output's initial value.
DAT-22's "abandon clears all amounts" stays with B-96.

Tests changed because the spec changed: the four test_payout_builder tests asserted the old
two/three-output shape with change to the pool and the fee address receiving the whole 30%;
the whitespace fee_address test now spells out the amounts rounds_can_open reads. New: reserve
sizing, payout with 1 and with 400 participants (inputs = outputs + fee to the satoshi),
exact commission/reserve/dust boundary, excess folded or left to the fee, a real payout bumped
out of its reserve with the other outputs byte-identical and bumped five times, the old
reserve-less shape still raising RbfError, the scheduler output addresses and recorded
amounts, payability boundaries found independently by bisection, no round / unconfigured flag
for an unpayable config, a round in progress surviving it, PUT /admin/config refusals and the
migration column. Mutation-checked: dropping the reserve lookup in bump_fee and the payability
check in rounds_can_open each fail tests.

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

app/rounds/scheduler.py

@@ -25,7 +25,7 @@ from app.rounds.events import broadcaster
 from app.rounds.service import open_new_round_if_needed, round_deadline, winner_share
 from app.tx.outcome import BroadcastOutcome, broadcast_with_verdict
 from app.tx.versions import record_version
-from app.wallet.hd import derive_round_pool_key
+from app.wallet.hd import derive_pool_address, derive_round_pool_key
 from app.wallet.keystore import decrypt_round_seed, encrypt_round_seed
 from app.wallet.plm_network import PLM_MAINNET
 from app.wallet.psbt_builder import InsufficientFundsError, Utxo, build_payout_transaction
@@ -543,7 +543,7 @@ class RoundScheduler:
                 winner_share_sats=winner_sats,
                 fee_address=fee_address,
                 commission_sats=commission_share,
-                change_address=pool_address,
+                reserve_address=derive_pool_address(),  # B-79 (RND-38): the bump reserve's destination
                 fee_rate_sat_vb=fee_rate,
             )
         except InsufficientFundsError as exc:
@@ -579,6 +579,7 @@ class RoundScheduler:
             round_ = await session.get(Round, round_id)
             round_.winner_amount_sats = built.winner_sats
             round_.fee_amount_sats = built.commission_sats
+            round_.bump_reserve_sats = built.reserve_sats  # B-79 (DAT-73, DAT-22)
             round_.payout_txid = built.txid
             pending = PendingTransaction(
                 kind="payout",

app/rounds/service.py

@@ -11,6 +11,13 @@ from app.rounds.events import broadcaster
 from app.rounds.draw import new_server_seed, server_seed_commitment
 from app.wallet.hd import derive_pool_address
 from app.wallet.keystore import encrypt_round_seed
+from app.wallet.psbt_builder import (
+    DUST_LIMIT_SATS,
+    MAX_PARTICIPANTS_PER_ROUND,
+    MAX_TX_INPUTS,
+    estimate_vsize,
+    payout_bump_reserve,
+)
 
 logger = logging.getLogger(__name__)
 
@@ -81,19 +88,44 @@ def round_accepts_bets(round_: Round) -> bool:
     return datetime.now(timezone.utc) < round_deadline(round_)
 
 
-def rounds_can_open(config: RoundConfig) -> bool:
-    """Whether the instance is configured well enough to run a round at all (B-66).
+def payout_config_problem(bet_amount_sats: int, fee_rate_sat_vb: int) -> str | None:
+    """Why a round could not be paid out under this bet amount and fee rate, or None (B-79,
+    RND-40). Checked for the two extremes — 1 participant (the smallest platform share) and
+    MAX_PARTICIPANTS_PER_ROUND (the largest bump reserve, which grows with the inputs):
+    the winner's 70% must cover the network fee of the payout and still be at least dust, and
+    the platform's 30% must cover the bump reserve and still leave the fee address at least
+    dust. The smallest bet that can reach the pool is the amount minus the fee of the biggest
+    transaction a user may build (MAX_TX_INPUTS inputs, 2 outputs), so that is what every
+    participant is assumed to have contributed."""
+    net_bet = bet_amount_sats - estimate_vsize(MAX_TX_INPUTS, 2) * fee_rate_sat_vb
+    for participants in (1, MAX_PARTICIPANTS_PER_ROUND):
+        pool = participants * net_bet
+        share = winner_share(pool)
+        if share - estimate_vsize(participants, 3) * fee_rate_sat_vb < DUST_LIMIT_SATS:
+            return "winner_share_below_network_fee"
+        if pool - share - payout_bump_reserve(participants) < DUST_LIMIT_SATS:
+            return "commission_below_dust_limit"
+    return None
 
-    Only fee_address today, and only because a round without one is unpayable: the
-    payout pays the 30% commission to it, so build_payout_transaction cannot even be
-    built. It has no column default for exactly this reason (rounds/config.py) — an
-    operator must set their own, and until they do there is nothing to guess.
+
+def rounds_can_open(config: RoundConfig) -> bool:
+    """Whether the instance is configured well enough to run a round at all (B-66, B-79).
+
+    Two prerequisites, both because a round without them is unpayable: a fee_address — the
+    payout pays the platform's share to it, so build_payout_transaction cannot even be built,
+    and it has no column default (rounds/config.py) because an operator must set their own —
+    and a bet amount and fee rate under which a round of 1 or of
+    MAX_PARTICIPANTS_PER_ROUND participants can cover the payout's fee, the bump reserve and
+    dust outputs (payout_config_problem, RND-40). PUT /admin/config refuses the same
+    combinations, so this only trips on a configuration that predates the check.
 
     Anything else that would make a round unpayable belongs here too, next to it,
     rather than being discovered at payout time. Deliberately not about *pausing*,
     which is a decision an operator took (RoundConfig.paused) rather than a
     prerequisite they haven't met yet."""
-    return bool(config.fee_address.strip())
+    if not config.fee_address.strip():
+        return False
+    return payout_config_problem(config.bet_amount_sats, config.fee_rate_sat_vb) is None
 
 
 async def open_new_round_if_needed(session: AsyncSession) -> Round | None: