What's a good stopping point? Making the case for the capabilities enabled by CTV+CSFS

In the discourse on improving Bitcoin's efficiency, particularly in handling transactions and commitments to sibling prevouts, a significant focus has been placed on optimizing the hashing process to avoid quadratic hashing issues. The conversation revolves around the proposal of using MuHash as a method for simplifying this process. Traditionally, validating a sibling commitment in a transaction requires hashing all other prevouts, leading to an O(n^2) complexity. However, with the adoption of MuHash, this complexity is reduced to O(n), as it allows for the validation of sibling commitments by precomputing a hash over all prevouts and then selectively removing one, which can be achieved in constant time (O(1)). This approach significantly streamlines the process, aligning with the goal of reducing computational overhead.

Despite the potential benefits of MuHash, concerns have been raised regarding its applicability, especially due to its lack of a compact membership proof. This limitation makes it less suitable for scenarios where such proofs are critical. In practice, MuHash has been utilized within Bitcoin Core for comparing UTXO sets in snapshots, but to validate membership, iterating through the entire population is necessary. This aspect underlines the need for careful consideration of the use cases of MuHash within the broader context of Bitcoin development.

Further discussions suggest exploring the utility of MuHash beyond its current application, proposing its integration into more targeted approaches like generalizing CTV / TEMPLATEHASH to commit to sibling prevouts efficiently. By precomputing a MuHash accumulator containing SHA256 hashes of each input in the transaction, and then manipulating this accumulator to compute sibling commitments, the process remains constant in time regardless of the number of inputs. This method holds promise for enhancing predictability and efficiency in committing to the next transaction, presenting a potentially low-cost solution that leverages existing codebase components.

Moreover, the conversation touches upon BitVM/CTV ideas, emphasizing the potential benefits of inspecting other inputs for applications that leverage connector outputs. However, the lack of detailed demonstration or description for the BitVM use case poses challenges in fully assessing its viability and impact on Bitcoin users. The dialogue reflects a cautious stance towards adopting new expressive capabilities without a clear understanding of their practical benefits and implications.

In summary, the exchange among developers underscores a collective effort to refine Bitcoin's transaction handling mechanisms through technical innovations like MuHash, while also recognizing the importance of pragmatism and thorough evaluation in integrating new features. The ongoing dialogue exemplifies the dynamic and collaborative nature of Bitcoin development, as contributors work towards solutions that balance efficiency, security, and usability.