feat(mmr): prototype Mountain Merkle Belt benchmarks

[krushimir]

Note

Draft/WIP, opening for visibility. This is stacked on #984 and extends the MMR/frontier benchmark work with an experimental Merkle Mountain Belt prototype.

Adds an experimental MmrBelt prototype with:

• paper-aligned belt shape and rightmost merge behavior
• indexed hash-array storage
• structured range/belt bagging for the commitment root
• authenticated belt membership proofs
• verified summary deltas
• PartialMmrBelt client-side sync state
• benchmarks against current MMR and Merkle frontier paths

Current scope covered:

• recency-biased proof verification
• append/build/commitment/open/verify benchmarks
• summary transition verification
• partial client resync for tracked leaves

[krushimir]

I reran the MMB benchmarks against the current prototype. The useful signal is split into two parts.

Recency Verification

At 65,536 leaves:

recency k	legacy MMR committed peaks	Frontier (len, root)	MMB (len, root)
1	~19.43us	~13.35us	~1.58us
4	~18.84us	~13.28us	~2.37us
16	~18.85us	~13.30us	~5.48us
64	~18.85us	~13.71us	~8.63us
128	~18.83us	~13.26us	~10.54us
512	~18.82us	~13.26us	~13.30us
1,024	~18.85us	~13.25us	~14.85us
4,096	~18.77us	~13.23us	~17.99us
16,384	~18.80us	~13.20us	~21.06us

This is the strongest positive signal from the prototype: MMB is much faster for newest/recent proofs, roughly competitive around k ~= 512, and worse for older leaves.

Append + Commitment/Root

leaves	MMR + commitment	Frontier + root	MMB live root	MMB deferred + root	MMB deferred append-only
1,000	~7.54us	~7.97us	~5.39us	~13.04us	~2.01us
1,023	~15.51us	~16.58us	~4.03us	~11.63us	~2.14us
1,024	~7.81us	~8.89us	~5.72us	~12.51us	~2.18us
50,000	~22.38us	~12.93us	~14.95us	~30.43us	~21.53us
65,535	~37.67us	~26.50us	~14.67us	~27.53us	~19.42us
65,536	~19.81us	~13.71us	~22.30us	~32.42us	~26.47us

The append/root numbers are mixed. Live MMB root maintenance helps at merge-heavy MMR boundaries, while deferred root readout is only useful if roots are read less frequently than appends. If a commitment is required after every append, live maintenance is the relevant MMB comparison.

These numbers are useful prototype signals, not a validation of the full MMB paper construction.

[huitseeker]

THis looks great!