There is no claim form because there is no claim. When a peril's trigger holds for its window, the contract pays every active cover on that asset in one transaction. You do not file, you do not wait, and you do not argue.
Prices. Token price from on-chain TWAP; reference price from the primary oracle and at least two independent secondaries.
Attestations. Custodian reserve attestations posted on-chain on their published cadence.
Halt flags. Exchange halt status carried by the reference feed; issuer redemption status from the issuer contract.
Default notices. A registry where issuers, custodians or a governance quorum can post a default flag. Posting a false flag is slashable.
Every input is a public on-chain value. If you can read the block, you can predict the payout.
There is one thing to dispute: whether an input was wrong. If an oracle posted a bad value, the P4 peril exists for that. If a halt flag was wrong, the feed operator is slashed and the payout stands; the pool recovers from the operator's bond, not from you.
The pool never claws back a payout. A payout that turns out to have been triggered by a faulty input is the pool's loss and the input provider's liability.