namespaced merkle tree. an authenticated data structure that indexes particles by namespace, doubling as a data availability layer
structure
an NMT extends the standard merkle tree by ordering leaves under namespace identifiers:
$$\text{NMT} = \text{Merkle}\bigl(\{(ns_i, d_i)\}_{i=1}^{n}\bigr) \quad \text{sorted by } ns_i$$
each leaf carries a namespace tag $ns_i$ and data $d_i$. internal nodes store the minimum and maximum namespace of their subtrees, enabling efficient range proofs over a single namespace without downloading the rest
properties
- completeness: a namespace proof covers all leaves in the requested namespace — the verifier knows nothing was withheld
- ordering: leaves are sorted by namespace, so all entries for a given namespace form a contiguous range
- each namespace corresponds to a content type or domain partition in the cybergraph
role in cyber
the NMT provides the data availability guarantee for bbg. when a neuron syncs a namespace, the tree proves that every particle and cyberlink in that namespace was included. light clients verify availability by sampling random shares and checking namespace proofs against the root
relation to consensus
during block production, the NMT root commits to the full ordered data of the block. validators reconstruct and verify the tree; any omission breaks the namespace range property and is detectable. this makes censorship of specific namespaces provably observable
see bbg, particles, cyberlinks, cybergraph, hemera