Keel v2 contracts, part 2a: the heart, pulse fees, launch permit and launch fee. Continue the existing Keel v2 project (part 1: KeelV2Factory, KeelV2Hook, KeelV2Token, FixedRateModule). Nothing is deployed yet, so change part 1 code directly where needed. Keep everything immutable: no proxies, no upgrade paths, no sweep or rescue functions, no admin power over funds already credited. Keep Solidity 0.8.26, Cancun, via IR, bytecode_hash none, vendored deps, offline tests.

1. Router and heart wiring (factory). Add set-once owner functions setRouter(address) and setHeart(address), same pattern as setTakeoverContract (nonzero, has code, cannot be changed or cleared). Add views router() and heart().

2. Launch permit and launch fee (factory). launch becomes payable and takes a permit: launch(name, symbol, metadata, quote, startTick, baseFeeBps, deadline, signature). Owner sets signer via setSigner(address) (replaceable, nonzero) and launchFee via setLaunchFee(uint256), default 0.0001 ether, max 0.01 ether. Public views: signer(), launchFee(), nonces(address creator). Require msg.value == launchFee, forward it to teamRecipient in the same call (revert if the transfer fails). Require block.timestamp <= deadline and a valid EIP-712 signature by signer over Launch(address creator, address quote, int24 startTick, uint256 deadline, uint256 nonce) with domain name "Keel", version "2", chainId, verifyingContract = factory; creator = msg.sender; per-creator nonce increments on use. Keep the existing per-quote tick bounds check. The off-chain signer picks the tick so every token starts at a $5,000 market cap.

3. Buyer identity (hook). In afterSwap, a buy counts for the heart only when sender == factory.router() and hookData is exactly 32 bytes; buyer = abi.decode(hookData, (address)). Any other caller still trades normally, with no heart credit. hookData keeps being forwarded to the module unchanged.

4. Pulse (hook). Each pool keeps a decaying buy counter: pulse (uint128, 1e18 = one buy) and pulseUpdatedAt. On every buy whose gross quote input is at least heart.minBuy(quote) (or every buy while heart is unset), set pulse = pulse * 2^(-elapsed / 1 hour) + 1e18. Add view pulseOf(bytes32 poolId) returning the decayed value now. Use a fixed-point exp2 that cannot overflow or revert for any elapsed time (cap elapsed at 64 half-lives, then zero).

5. Heart call (hook). After a counted buy, call heart.onBuy(token, quote, buyer, grossQuoteIn, tokensOut) with a fixed gas stipend (200k) inside try/catch. A failing or out-of-gas heart must never revert or change the swap. Emit HeartCallFailed(poolId) on failure. tokensOut is the token amount the swap delivered.

6. PulseRateModule (new IRulesModule). Same creator controls as FixedRateModule (lowerRate, scheduleRaise 24h +1% max, applyRaise, cancelRaise, creatorAction). feeBps(poolId) = 100 + (rate - 100) * min(pulse, HOT) / HOT, with HOT = 6e18 and rate = the creator's current rate (100..500). Result always in 100..500. View only: reads hook.pulseOf. The anti-snipe decay in the hook stays as it is.

7. KeelHeart (new contract). One heartbeat for all v2 pools.

• Constructor(hook, owner). Owner (two-step ownership) may only setMinBuy(quote, rawAmount) and add quotes to a list of at most 16. No other powers, no withdrawal.
• onBuy only from hook. Ignore if grossQuoteIn < minBuy[quote] or minBuy[quote] == 0. If the current round is over (deadline != 0 and now >= deadline), end it first. If no round is running, start one: deadline = now + 300. Otherwise deadline = min(deadline + 30, now + 600). Record lastBuyer, lastToken, lastTokens = tokensOut, round number. Emit Beat(round, buyer, token, quote, grossQuoteIn, deadline).
• fund(quote, amount): anyone adds to the current pot. ETH via msg.value (quote = address(0)), ERC20 via transferFrom with exact balance-change check. Only listed quotes. Emit Funded(round, quote, from, amount).
• end(): anyone, once now >= deadline and the round has a buyer. Winner = lastBuyer. Eligible only if lastToken.balanceAt(winner, block.number - 1) >= lastTokens (KeelV2Token from part 1 already keeps per-block checkpoints; keep balanceAt reverting for the current block, so nothing done inside the end() block can count). If eligible: for each listed quote, prize[round][quote] = pot[quote] * 7000 / 10000 and pot keeps the rest for the next round. If not eligible: nothing is awarded, the whole pot carries over. Store the round result (winner, token, endBlock, eligible). Emit Flatline(round, winner, eligible). Next round starts on the next counted buy.
• claim(round, to): only that round's winner, once, pays every quote's prize. Exact transfer checks, nonReentrant, solvency check: balance of each quote >= pot + unpaid prizes. Emit Claimed(round, winner, to).
• Exact public views (the site reads these): state() returns (uint256 round, uint256 deadline, address lastBuyer, address lastToken); quoteList() returns (address[]); potOf(address quote); minBuy(address quote); prizeOf(uint256 round, address quote); result(uint256 round) returns (address winner, address token, uint256 endBlock, bool eligible, bool claimed).

8. Tests. Extend the suite: permit and nonce replay, wrong fee, fee forwarding; router-only heart credit and spoofed hookData from a non-router caller; pulse decay math and caps; PulseRateModule bounds at pulse 0, HOT and above; heart timer start, +30 s, 600 s cap, end after deadline, sells never touching the timer, heart revert or gas burn never breaking a swap, winner holding check pass and fail (sold part before end, sold and bought back before end, received tokens by transfer, tokens moved in and out inside the end() block, end() called many blocks after the deadline), 70/30 split per quote, claim once, funding in ETH and ERC20, multiple rounds. Invariants: heart solvent, hook solvent, a swap result is identical with or without a heart.

9. Gas. Measure with forge snapshot and document in the README: a plain swap, a router buy that counts (heart running, round start, round end inside onBuy), a non-router buy, and a sell, each with and without a heart set. Report the extra gas a counted buy costs over part 1. Keep heart.onBuy at most 120k gas on every path, assert it in a test, and keep the 200k stipend as the hard ceiling.

Deliver: updated source, tests, README section for part 2a, REVIEW.md update. Do not deploy.