Can output amounts be mapped to a tap branch? For the goal of secure partial spends of a single UTXO? Looking for feedback on this idea. I got it from Taro.

Merkel_tree_root_tweak = tagged_hash(“root” || left_hash || right_hash)

Tree_branch = tagged_hash(“branch” || left_hash || right_hash ) || right_output_sum + left_relative_output_amount

Tree_leaf = tagged_hash("leaf" || script ) || relative_output_amount

Transaction Validation:

There would be one output with an amount that is negative.

The negative amount would flag this transaction as relative amount spends.

The miner fee would be the absolute of the output amount.

The witness would include the txout amount.

Txout is less than other inputs that referencing this output.

Questions:

Would this require a hard fork?

Would the sum be required in the asset tree?. The sum at the root would be implicitly 1.0. How big can a taproot tree get before it is too cumbersome?

Could multiple taproot trees be put inside a tweak?

Am I missing anything vital?

Possible Benefits

Perhaps slightly increase privacy of output amounts?

Reduced growth rate of UTXO’s. This scheme would be consuming N inputs and producing 1 output.

Drawbacks

I think this would disable the ability for output change addresses to be the same as inputs as the spending amounts are absolute.

Transaction Example

Inputs : [1.5,.3,.1]

TapTree:

Branch sum :1

Change Address : .5

Branch sum: .5

AlicePubKey: .2

Branch sum: .3

BobPub and BobHash: .1

Branch sum: .2

CaroPub and DavePub and CarolDaveHash : .1

ErinPub and CarolDaveHash and after 10days : .1

Outputs: [-.0.001]

Alice spending example

Alice sends to new address : .1 * (sum of Inputs + outputs) = 0.18999

Alice New Change Address = .1 * (sum of Inputs + outputs) = 0.18999

Application

I think something like this would provide away to onboard a lot of lightning channels with a single UTXO output. An exchange could schedule open lightning channels at certain time intervals, perhaps every 10 minutes. Ideally, people would provide pubkeys and payment, to be placed in a tap leaf. Similar to selling seats for an aircraft flight.

Thanks for reading

Andrew