feat!: Add new path for pda seed input

[schouhy]

🎯 Purpose

Private PDAs previously could only be used through a program that used Claim::Pda or pda_seeds to establish the binding between the PDA account_id and the npk. This meant you couldn't call auth_transfer directly to fund a private PDA, you always needed a wrapper. This PR removes that limitation.

⚙️ Approach

• Add an optional seed: Option<(PdaSeed, ProgramId)> field to the PrivatePdaInit and PrivatePdaUpdate variants of InputAccountIdentity. When the seed is provided, the circuit verifies AccountId::for_private_pda(pda_program_id, seed, npk, identifier) == pre_state.account_id directly, establishing the binding without needing a Claim::Pda or caller pda_seeds. It also verifies is_authoried is set to false.
• Add binding logic in execution_state.rs for when an external seed is supplied
• Remove the authorization check on private pda claiming in the ppt circuit. Authorization checks only remains on public account claiming.
• Rename pda_fund_spend_proxy to pda_spend_proxy. The fund path is now handled directly via auth_transfer.
• Rewrite fund_private_pda in integration tests to use auth_transfer directly with the external seed

🧪 How to Test

RISC0_DEV_MODE=1 cargo test

🔗 Dependencies

None

🔜 Future Work

Update wallet commands to use the external seed path when appropiate.

📋 PR Completion Checklist

Mark only completed items. A complete PR should have all boxes ticked.

• Complete PR description
• Implement the core functionality
• Add/update tests
• Add/update documentation and inline comments

[Pravdyvy]

lgtm

[moudyellaz]

lgtm thanks, left some minor comments casue i struggled a bit.

[moudyellaz]

One more thing on commit hygiene: the PR title carries feat!: but none of the individual commits (b37e3ca8...e4a71961) use the Conventional Commits ! marker or a BREAKING CHANGE: footer. If the merge is a squash-merge that lifts the PR title, we'll be fine on the changelog side, but if any of these land as-is (e.g., on a rebase merge), the breaking nature gets lost.

Could you add a BREAKING CHANGE: footer to b37e3ca8 (the type-shape change) and mark it with !, and the same on eb5f54d7 for the rename? That way the convention is honored regardless of merge strategy.

[Arjentix]

I don't get why we need this change...

[Arjentix]

I mean, now you can claim other users pda-derived accounts, no?

[schouhy]

we need to remove the authorization constraint on claiming private pdas because otherwise there will be no way for bob to send some funds to alice in a (newly initialized) private pda for which bob doesn't know the nsk. It's the same reason we don't impose authorization on claiming a regular private account. The surface area for griefing attacks is reduced compared to public pdas because private ones depend on the npk and an identifier
.
But yes, you could claim other users pdas for a specific npk and identifier.