All three invariants hold in the code, provided the vault is deployed with a correct startTime. I found no critical or high issues: no path that mints, releases ahead of schedule, or pulls tokens from someone else's approval. The report is at artifacts/report.md, with a short README and the test file artifacts/Audit.t.sol. All 18 tests in that file pass on solc 0.8.30, with the fuzz tests at 2000 runs each.

Findings:

• Medium – vault start time isn't checked (EmissionVault.sol:21-25). The contract accepts any start time. Deployed with a start in the past (for example 0), about 684M UP can be released immediately. A start far in the future locks everything forever. The deploy script checks this, but only when the deployment is simulated, not on-chain.
• Medium – the distributor can take the whole unreleased backlog at once (EmissionVault.sol:52-57). This doesn't break invariant 2, because nothing vests early. But the schedule is front-loaded: after a year with no releases, one call can take 642.4M UP, 94% of everything that will ever be released. Fix: make the distributor a multisig or timelock, add a per-day cap, or fix the recipient to a set distribution contract.
• Low – BatchPay can end up holding tokens (BatchPay.sol:15-30). Anyone can send tokens directly to BatchPay, and they can never be recovered, so "holds no funds between calls" is only true of funds that go through pay. Nobody can steal those tokens.
• Low – some fee tokens short-pay recipients silently (BatchPay.sol:26-29). A token that takes a fee only on the outgoing leg passes both balance checks while recipients get less than they were sent. Normal fee-on-transfer tokens revert at line 25, as intended.
• Informational:
  • Locked remainder: the halving series only ever releases 683,999,999.99…9974 UP, so about 16M UP (2.29%) stay in the vault forever.
  • Halving shift: exact for the first 24 halvings, then rounds down. After 20 halvings it pays 3.62396… UP per day, at halving 81 it pays 1 wei, and from halving 82 (about 20.2 years) it pays 0. It never reverts and can never divide by zero, and the loop runs at most 82 times (22k gas).
  • Timestamps: at and before startTime the vault reports 0, and the first release is possible at startTime + 1 day.
  • Timing: only the chain's sequencer can nudge epoch boundaries, by up to about 1 hour on Arbitrum-based chains. The distributor on its own cannot.
  • Token-to-vault link: nothing on-chain ties the token to its vault. The 70/30 split is only as good as the constructor argument.
  • Gas: 400 new recipients cost 10,789,075 gas, and 1000 cost 26.86M. One recipient that reverts blocks the whole batch.
• Also checked:
  • Reentrancy: BatchPay blocks re-entry, and it only ever pulls from the caller, so a malicious token cannot reach anyone else's approval.
  • Overflow: the files have no unchecked blocks, and an overflowing batch total reverts.

What I could not verify:

• Deployed contracts: nothing has been deployed, so the real startTime and distributor are unknown.
• Chain limits: I didn't query Robinhood Chain for its gas limits, data fees or timestamp settings. The timestamp bounds come from Arbitrum's documentation, and the chain details from third-party sites.
• Vendored OpenZeppelin: I didn't diff the vendored copy against upstream.
• Proof strength: the evidence is fuzzing, not a formal proof.
• Compiler output: I assumed the compiler is correct and didn't inspect the bytecode.
• UpHook: not reviewed, as you asked.

To build, I rebuilt the repo from the bundle on top of this workspace's base commit, and forge downloaded solc 0.8.30 once. The three files in artifacts/ are untracked and nothing was committed; git status doesn't list them, which suggests the repo ignores that folder.