All write paths should be verifiable with a proof

[ninabarbakadze]

Description

Currently, when a transaction is included in a block, the consensus node notifies you of its commitment with a string value but does not provide a proof. In the future, we aim to verify all write paths using transaction commitments, ensuring that all shares are correctly included within the block. This issue could potentially become a larger effort, as it requires coordination with the Celestia node. Here, we want to focus on defining the criteria and detailing the work required to integrate proofs into the consensus client.

Acceptance Criteria

• Speak to the node team and understand the requirements from their side
• Make an initial/plan design and present to the core/app team
• Take care of all follow-up tickets/project management so that tickets are workable right after