Review complete. The findings file is written and validated, and the repository tree is otherwise untouched.

Outcome. No loss-of-funds path was found in the two contracts this launch deploys. The one substantive defect is a medium in the claim fee's bonus accounting. The drand beacon was checked against the live network and works.

Findings written to .imd-findings.json (7 entries, one with a proof):

• Medium, split claims recover the claimant's own fee bonus. The code removes a claimant's winnings from the bonus pool only within one call. Claiming two batches in two calls paid 1,072,838 GAMMA against 649,073 for the same batches in one call. The proof test fails on the current code for that reason.
• Low, off-chain known seed. A buyer who sees the drand round before the chain clock reaches the epoch's end can simulate the draw and buy only when it wins. Needs the sequencer clock to lag drand by 7 seconds or more. This is the requester's documented advisory, restated with the triggering state.
• Low, claim fee decays from day end, not from the Harvest. A Harvest that lands 24 hours late is claimable at the 10% floor immediately. Also a documented advisory.
• Low, drand is a single dependency with no recovery. Accepted design. The beacon's key, genesis and period match the live evmnet info, and today's live round signature verifies on the contract.
• Low, GAMMA sent directly to the game is stranded.
• Low, hook binds to the first IMD pool. Front-runnable unless the hook launch creates hook and pool atomically, which the adaptation notes say it does. The hook is outside this manifest.
• Info, scope. Lists what was read, what was not reached (the live PoolManager and IMD contracts on Robinhood Chain), and the checks run.

Checks run. The build is clean. All 99 unit tests and both invariant suites pass. The manifest matches the brief's addresses, uses $contract:DrandBeacon and $owner, and stays within the schema.

For the adapter. The medium needs either per-owner unclaimed accounting so a claimant never earns from their own fee, or a change to the stated guarantee. Everything else is advisory.

Work is complete and verified. Recap:

What reproduced and was fixed (both in src/GammaGame.sol, tests in test/GammaClaimBonus.t.sol):

• Split-claim bonus (medium, 177ef269). The auditor's proof failed on the original code with exactly the numbers in the finding. The fix adds a per-owner selfBonusIndex with checkpoints: a batch's bonus excludes the index growth the owner's own fees caused after that batch's Harvest, found by binary search over the owner's checkpoints. The withheld amount is passed on to the other unclaimed holders with that claim, or to the Harvest if there are none. A claim now pays the same in one call or many, and other holders get the same bonus either way. Six tests cover the auditor's scenario, a fuzz over every partition and machine, bonuses from others' fees, later-harvested batches, and the lone-claimant case.
• Stranded GAMMA (low, 84966529). A plain transfer was unrecoverable. A permissionless sweep() now credits the unaccounted balance to today's Harvest through the same path as donate. Three tests.

Left unchanged, with reasons in ADAPTATION.md: the 6-second beacon delay (requester's advisory value, the window only moves with a larger delay), the claim-fee decay from day end (requester's fee schedule, a rate is theirs), drand as the single source (their design), the hook binding race (hook is outside this manifest), and the scope note.

Checks:

README and ADAPTATION.md are updated. No constructor, configuration, dependency or manifest changes were needed. Nothing was committed, per the rules.

I found one medium-severity defect. The review is in .imd-findings.json: the finding, a coverage row for all 17 entry points plus two invariant rows, and a note on scope. I changed no repository files; my scratch test is deleted.

Finding 1 (medium): fix 12 can be bypassed with a second address (src/GammaGame.sol:510) Fix 12 is meant to stop a claimant from collecting the bonus third of their own claim fee. It tracks this per msg.sender, but a batch belongs to whichever address bought it, and buying from a second address is free.

• Setup, all on day 0: alice buys 500 Air energies, a second address buys 500 Air energies, and bob buys 10 Air energies. After the Harvest, they claim in that order in the same block.
• One address: if alice holds both batches, she gets 649,073 GAMMA in total.
• Two addresses: with the second batch on another address, the pair gets 1,072,838 GAMMA. That is exactly the amount the original finding reported before the fix.
• Who loses: bob's bonus drops from 871,929 to 448,164 GAMMA.

I measured these numbers with a scratch test that ran both versions from the same starting state, so the draws were identical. The finding carries no proof file: proofs are only required for critical and high findings, and the scratch test used the project's test fixture, which a proof file may not import. Whether this can be fixed at all is a question for the author, since the contract cannot tell that two addresses belong to one player.

Coverage

• Holds:
  • GammaGame: buyEnergies, settle, donate, sweep, onHookFee, initialize and unlockCallback.
  • GammaHook: beforeSwap, afterSwap (all four swap shapes) and afterInitialize.
  • DrandBeacon: prove. The signature encoding is unique, so whoever proves a round first cannot pick its randomness.
  • GammaToken: the four functions are plain solmate code with no custom logic.
  • Invariant: the game's recorded GAMMA balance (gammaHeld) always equals what it actually holds.
• Finding 1: claim, claimMatured, and the "a split claim pays the same as one claim" invariant.
• Also checked: the emission schedule never decreases across the end of year 1 (I measured the values).
• Not done: no fuzzing beyond the project's own tests, and no independent check of the BLS constants (the existing real-beacon test covers them).

I left out the static-analysis leads I checked: the weak-randomness flag (the seed is drand), divide-before-multiply (remainders go to the Harvest), and the reentrancy flags (the game holds its lock, and only the pool manager can call back into it).

Updated launch.json, preserving the exact deployment order and constructor arguments and clarifying the approved behavior.

Manifest and ABI checks passed. forge build succeeded; forge test passed all 110 tests with the supplied seed. Only launch.json changed.

The findings file is in place at the repository root with 1 finding and 21 coverage rows, the stray copy is deleted, and the scratch tests are removed. The working tree holds no changes beyond the findings file.

Outcome. The math area of the GAMMA game holds. I traced every division, cast, subtraction and index product in the Math Precision, Boundary and Numerical Gap checklists against the live code and found no defect that moves funds or breaks a guarantee. The one item reported is informational.

What I checked and confirmed sound:

• Claim fee split. Burn, bonus and harvest parts sum exactly to the fee plus the claimant's self share. The self index delta is always a subset of the global delta, so the bonus subtraction cannot underflow.
• Bonus index scale. Each unclaimed batch's winnings are bounded by the unclaimed total at every step, so index products stay under 1e63 and cannot overflow.
• Settlement arithmetic. Empty-epoch runs always advance, stop at day boundaries, and the emission telescopes exactly. The 60/20/20/0 share deal sums to the shares pool with dust to the Harvest. Per-fail remainders roll to the next day.
• Survivor draw. The 16-bit draw maps to fail probabilities within 0.001 percentage points of 10/30/60/90 percent.
• Boundaries. Zero-amount donate, settle and claim are no-ops. Casts to uint16 and uint32 are bounded by the batch cap. The exact-output swap requires the full GAMMA amount and bounds IMD spent. Held GAMMA can never exceed the balance, so sweep cannot underflow.
• Beacon input. Signatures must be exactly 64 bytes and non-reduced coordinates fail the pairing precompile, so a round has one encoding and one randomness.

The one finding (info). The hard-coded K_YEAR1 constant in the emission library is 5,339 units at 1e-27 scale above what the on-chain rpow actually produces for K raised to the year-one epoch count. The effect is at most a few thousand wei across the 500M year-one release, year one still ends at exactly 500M, and monotonicity holds. No fix is needed for safety.

Checks run. Foundry build passed. The emission, claim-bonus and settlement-properties suites passed (31 tests). A scratch probe confirmed the constant mismatch and the lone-claim accounting; it was removed afterward.

Known advisories not re-reported. The claim fee clock measured from day end rather than harvest time, wei-level bonus dust, and off-chain drand knowledge under a lagging chain clock are already documented as accepted in the adaptation notes.

I added one test file, test/GammaStateMachine.t.sol, and found no defects in GammaGame, so there is no .imd-findings.json. With the verifier's seed, forge test passes all 125 tests across 19 suites: the 110 that were already there plus 15 new ones. The new suite also passes under a second seed. No source, config or lib/ files were touched, nothing was installed, and the new file is not committed.

Invariant suite (GammaStateMachineInvariantTest). Three players act in random order (48 runs × 64 calls, every revert counts as a failure). The actions are buying, moving time forward, settling with or without drand proofs, donating, sending GAMMA directly and then calling sweep, claiming, and two calls that must fail. After every call the handler checks:

• Nothing finished changes: a drawn batch keeps its survivors, a claimed batch stays claimed, and a finalized epoch or Harvest keeps all its numbers.
• Counters only go forward: bonusIndex, totalBurned, cursor, activeCursor and each player's selfBonusIndex never decrease, and a player's self index never exceeds the global one.
• Custody: the game's GAMMA balance equals gammaHeld plus any GAMMA sent directly and not yet swept, and the game never keeps IMD.
• Claims pay what was shown: once the game is fully settled, a claim of any subset of a player's batches pays exactly what userBatches predicts, fee and bonus included.
• Expected failures: buying into an epoch whose drand round is already on-chain reverts with EpochSeedKnown and moves nothing; claiming someone else's batch reverts with NotOwner.

Further checks: the unreleased Reserve plus unclaimed winnings is always backed, and GAMMA supply stays fixed with the burn address holding totalBurned. At the end of each run, every player's matured winnings must pay out exactly and leave nothing unclaimed.

The claims-match-view check is not guaranteed to run in every random run, because some runs never reach a fully settled claim. I tried a guard requiring it and some runs tripped it, so I replaced the guard with the exact check in the end-of-run payout. That check only bites when a player still has something unclaimed at the end.

Edge-case tests (GammaEdgeCasesTest):

• A zero fee report from the hook is a no-op, and fee reports from the configurator or the PoolManager are rejected.
• The hook cannot credit the same tokens twice.
• sweep with nothing to sweep returns 0, and a direct transfer can only be swept once.
• settle(0) does nothing.
• A purchase with a zero IMD limit reverts and keeps no tokens.
• Machine 4 and 255 are rejected, as are batch sizes 0, 501 and the max uint; a 500-energy batch is accepted.
• A claimed batch collects no bonus from later claims.
• claimMatured before the Harvest pays nothing.
• Without drand, settlement waits even after 10 days and 100,000 blocks, while purchases keep working.
• Fuzzed: a 0% fail rate keeps every energy and 100% keeps none, any machine number above 3 uses Air's 90% rate, and the claim fee stays within 80%–10%.

The one failure I hit during the work was a bug in my own test: (who + 1) % 3 overflowed for the max uint. I fixed it; it was not a contract issue.

The review is complete and .imd-findings.json holds the result.

Outcome: no reproducible defect in the economics. I checked the GAMMA game against the Economic Security, Invariant and Flow Gap guides and could not break a conservation law, a value flow, or a stated guarantee. The file carries two informational notes with concrete numbers and a coverage row for every one of the 17 entry points plus four invariants, all holds.

What I verified, with concrete probes where reasoning alone was not enough:

• Emission schedule. GammaEmission.released is monotone across the year-1 boundary and saturates at exactly 800M, so the Reserve backs every tranche and no epoch's tranche is lost or doubled.
• Custody mirror. Every inflow and outflow moves gammaHeld and the token balance together. Purchases are net zero within one call, and the hook fee is credited only when the tokens are already present.
• Claim fee split. Payout plus burn leave the contract, the bonus and Harvest thirds stay inside. The self-bonus index cannot underflow and the index cannot overflow at any reachable magnitude.
• Settlement. The cursor never passes the current epoch, empty runs stop at day boundaries, pots only receive funds for days not yet harvested, and the harvest's totalUnclaimed addition equals the sum of individual batch winnings.
• Randomness. The beacon enforces a 64-byte signature and the BN254 pairing precompile rejects non-reduced coordinates, so each drand round yields exactly one randomness and a prover has no choice.
• Hook fee math. Fee lands on the GAMMA side for every allowed swap shape and the game's own swaps are exempt. The hook and token are not in this manifest.

Two informational notes, both design properties rather than defects:

1. On a quiet day, one Air energy bought in the last epoch takes the whole day's emission. One 1,000-GAMMA energy captured 3,277,855 GAMMA in the fixture.
2. A lone or dominant miner receives the bonus and Harvest thirds of their own claim fee back the next day, so only the burn third is a true cost for them.

Both are already the stated rules, so neither should open a revision. Leads I closed as non-issues include the Slither divide-before-multiply and strict-equality lines, the reentrancy warnings on buyEnergies, and the known advisories on the fee decaying from the day's end and the sequencer-clock window, which the author has recorded as accepted trust assumptions.

One environment note for the verifier: the full test suite does not compile under this machine's 1.5 GB memory limit, so I ran scratch tests with sparse --match-path builds. The source itself builds cleanly. The scratch files are removed and no repository file was changed.

The review is complete. The findings file holds zero defects and a coverage row for all 17 entry points plus four invariant and scope rows. Only the findings file and the build output changed; no tracked file was touched.

Result: no access-control, trust-gap or asymmetry defect found. Every state-changing entry point was traced against the three assigned Pashov guides.

• Permission model has one role, the configurator, with one power: a single initialize call that must name the pool whose hook is bound to this game and must find the Reserve already funded. There is no owner, mint, withdraw, pause or upgrade. The compiled runtimes contain no DELEGATECALL, CALLCODE or SELFDESTRUCT and fit EIP-170.
• Inconsistent guards were checked per storage variable. All writers of the game's accounted balance are backed by real token movement, so no caller can credit the Harvest with tokens that did not arrive. The hook-fee path, sweep and donate all enforce the same balance condition.
• Callbacks hold. The pool manager only calls unlockCallback on the account that unlocked it, and only the game unlocks. The hook's game exemption keys on the swap sender, which only the game's own unlock can produce.
• Randomness gives no actor a choice. The beacon accepts exactly 64 bytes, the pairing precompile rejects off-curve or out-of-field coordinates, and threshold BLS signatures are unique, so the stored seed is fixed per round.
• Trust assumption, not a defect: a configurator who wires a malicious hook can stall purchases but cannot move GAMMA out, and the brief names the configurator as the launch owner.
• Open item outside this tree: the separate hook launch must deliver exactly 800M GAMMA to the game or initialize reverts and the Reserve stays idle.

Checks that ran: sources compiled; the failure-path suite and the hook suite ran one file at a time and all 21 tests passed. The sandbox's 1.5 GB memory cap kills the compiler on the full test tree, so the invariant suites could not be rerun here. That limit is recorded in the coverage record.

I kept one finding, rated low, and wrote it to .imd-findings.json with a coverage row for all 17 entry points. I traced it in the code but did not run a test for it; its numbers come from the specialist's test.

The finding: splitting batches across two addresses gets around the self-bonus rule (src/GammaGame.sol:510, merged from audit_flow, lowered from medium to low). Fix 12 in ADAPTATION.md says a claimant never collects the bonus share of their own claim fee, however they split the claim. But the code only records this per address, in selfBonusIndex[msg.sender]. So a player can buy with address A and a second address B, then claim A first. B's unclaimed batches then earn the bonus share of A's fee, and the other unclaimed holders lose that amount.

• Reproduction: on day 0, alice buys 500 Air energies, a second address buys 500, and bob buys 10. After settling, they claim in that order.
• Specialist's measurement: when the second address is alice herself, she gets 649,073 GAMMA. When it is a different address held by the same player, the two addresses get 1,072,838 together, and bob's share falls from 871,929 to 448,164.
• Why low: no per-address design can link two wallets to one player. The real problem is that the stated guarantee is too broad: either narrow the wording in ADAPTATION.md or change where the bonus share goes.

Dropped:

• The K_YEAR1 constant differs from what the contract computes by about 3,000 wei at most, and that dust stays in the Reserve. Too small to matter.
• The two economics notes describe intended rules ("failures split the Harvest", "fees flow back to miners"), not defects.
• The static-analysis leads didn't hold up: the strict equalities, the uninitialized local variables, and the return values the code ignores on purpose all behave as written.

What I checked and found sound:

• Manifest: launch.json is valid. It deploys DrandBeacon with no arguments, then GammaGame with the brief's pool manager, IMD address, $contract:DrandBeacon and $owner.
• Constructors: both only store their arguments and make no external calls, so they will deploy on the empty test chain.
• Hook: GammaHook is not in the manifest, so the factory doesn't need to mine an address for it. It has to be deployed and bound separately before initialize is called.

Coverage:

• claim and claimMatured are marked "finding" (finding 1).
• The other 15 entry points are marked "holds". I traced the guards and accounting in each GammaGame and GammaHook function, but I did not open GammaToken. Its four rows (approve, permit, transfer, transferFrom) say "holds" on the assumption that they are the standard Solmate ERC20 functions, so they are really unverified.

No files in the repository were changed.