I think the biggest problem of sum tree is the lack of flexibility to redefine 
the values with softforks. For example, in the future we may want to define a 
new CHECKSIG with witness script version 1. That would be counted as a SigOp. 
Without a sum tree design, that’d be easy as we could just define new SigOp 
through a softfork (e.g. the introduction of P2SH SigOp, and the witness v0 
SigOp). In a sum tree, however, since the nSigOp is implied, any redefinition 
requires either a hardfork or a new sum tree (and the original sum tree becomes 
a placebo for old nodes. So every softfork of this type creates a new tree)

Similarly, we may have secondary witness in the future, and the tx weight would 
be redefined with a softfork. We will face the same problem with a sum tree

The only way to fix this is to explicitly commit to the weight and nSigOp, and 
the committed value must be equal to or larger than the real value. Only in 
this way we could redefine it with softfork. However, that means each tx will 
have an overhead of 16 bytes (if two int64 are used)

You could find related discussion here: 
https://github.com/jl2012/bitcoin/commit/69e613bfb0f777c8dcd2576fe1c2541ee7a17208
 
<https://github.com/jl2012/bitcoin/commit/69e613bfb0f777c8dcd2576fe1c2541ee7a17208>

Maybe we could make this optional: for nodes running exactly the same rules, 
they could omit the weight and nSigOp value in transmission. To talk to legacy 
nodes, they need to transmit the newly defined weight and nSigOp. But this 
makes script upgrade much complex.


> On 12 Dec 2016, at 00:40, Tier Nolan via bitcoin-dev 
> <bitcoin-dev@lists.linuxfoundation.org 
> <mailto:bitcoin-dev@lists.linuxfoundation.org>> wrote:
> 
> On Sat, Dec 10, 2016 at 9:41 PM, Luke Dashjr <l...@dashjr.org 
> <mailto:l...@dashjr.org>> wrote:
> On Saturday, December 10, 2016 9:29:09 PM Tier Nolan via bitcoin-dev wrote:
> > Any new merkle algorithm should use a sum tree for partial validation and
> > fraud proofs.
> 
> PR welcome.
> 
> Fair enough.  It is pretty basic.
> 
> https://github.com/luke-jr/bips/pull/2 
> <https://github.com/luke-jr/bips/pull/2>
> 
> It sums up sigops, block size, block cost (that is "weight" right?) and fees.
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